ChemWiki - User contributions [en]

Kh1015DFT

2018-08-15T14:37:46Z

Kh1015: /* Density Functional Theory */

=='''Density Functional Theory'''==
In a top-down modelling strategy, the behaviour of materials are predicted by extracting empirical parameters <ref name="Ox" />. Conversely, in a bottom-up strategy, the properties of materials are predicted using quantum mechanics, which is a fundamental theory of materials <ref name="Ox" />.

Density Functional Theory (DFT) is a very effective technique for studying molecules, nanostructures, solids and surfaces and interfaces. DFT is categorized under a bottom-up ab-initio approach.

Many material properties involve it being in a bulk of hundreds of thousands of atoms. Direct DFT is not feasible to model materials in bulk. QM/MM model is used instead where the bulk is sub-divided into quantum mechanics (QM) and molecular mechanics (MM) sub-systems, where a classical Newtonian description is sufficient <ref name="Ox" />.

For example, in the modelling of crack propagation in brittle solids, the bulk could be described using linear elasticity theory. Only the crack tip and an area surrounding it need to be modelled using ab-initio QM method <ref name="Ox" />.

Other than understanding the properties of existing materials, DFT has also been used to predict the properties of materials yet to be made. For example, the discovery of BiPt as a superior catalyst for hydrogen production than pure Pt was done computationally. Subsequently, Greeley et al. successfully synthesized the new material <ref name="Greeley" />.

There are several known instances where DFT breaks down: inaccuracy when describing van der Waals binding of biological molecules, red-shift in the optical absorption spectra and inaccurate prediction of some non-metallic transition metal oxides to be metallic <ref name="Ox" />.

=='''References.'''==
<references>
<ref name="Ox">F. Giustino, in ''Materials Modelling using Density Functional Theory'', Oxford University Press, 2014.
</ref>
<ref name="Greeley"> J. Greeley, T.F. Jaramillo, J. Bonde, I.B. Chorkendorff, J.K. Norskov, ''Nat Mater.'', 2006, '''5''', 909.</ref>
</references>

Kh1015DFT

2018-08-15T14:31:45Z

Kh1015: /* Density Functional Theory */

=='''Density Functional Theory'''==
In a top-down modelling strategy, the behaviour of materials are predicted by extracting empirical parameters <ref name="Ox" />. Conversely, in a bottom-up strategy, the properties of materials are predicted using quantum mechanics, which is a fundamental theory of materials <ref name="Ox" />.

Density Functional Theory (DFT) is a very effective technique for studying molecules, nanostructures, solids and surfaces and interfaces. DFT is categorized under a bottom-up ab-initio approach.

Many material properties involve it being in a bulk of hundreds of thousands of atoms. Direct DFT is not feasible to model materials in bulk. QM/MM model is used instead where the bulk is sub-divided into quantum mechanics (QM) and molecular mechanics (MM) sub-systems, where a classical Newtonian description is sufficient <ref name="Ox" />.

For example, in the modelling of crack propagation in brittle solids, the bulk could be described using linear elasticity theory. Only the crack tip and an area surrounding it need to be modelled using ab-initio QM method <ref name="Ox" />.

Other than understanding the properties of existing materials, DFT has also been used to predict the properties of materials yet to be made. For example, the discovery of BiPt as a superior catalyst for hydrogen production than pure Pt was done computationally. Subsequently, Greeley et al. successfully synthesized the new material <ref name="Greeley" />.

=='''References.'''==
<references>
<ref name="Ox">F. Giustino, in ''Materials Modelling using Density Functional Theory'', Oxford University Press, 2014.
</ref>
<ref name="Greeley"> J. Greeley, T.F. Jaramillo, J. Bonde, I.B. Chorkendorff, J.K. Norskov, ''Nat Mater.'', 2006, '''5''', 909.</ref>
</references>

Kh1015DFT

2018-08-15T14:31:21Z

Kh1015:

=='''Density Functional Theory'''==
In a top-down modelling strategy, the behaviour of materials are predicted by extracting empirical parameters <ref name="Ox" />. Conversely, in a bottom-up strategy, the properties of materials are predicted using quantum mechanics, which is a fundamental theory of materials <ref name="Ox" />.

Density Functional Theory (DFT) is a very effective technique for studying molecules, nanostructures, solids and surfaces and interfaces. DFT is categorized under a bottom-up ab-initio approach.

Many material properties involve it being in a bulk of hundreds of thousands of atoms. Direct DFT is not feasible to model materials in bulk. QM/MM model is used instead where the bulk is sub-divided into quantum mechanics (QM) and molecular mechanics (MM) sub-systems, where a classical Newtonian description is sufficient <ref name="Ox" />.

For example, in the modelling of crack propagation in brittle solids, the bulk could be described using linear elasticity theory. Only the crack tip and an area surrounding it need to be modelled using ab-initio QM method <ref name="Ox" />.

Other than understanding the properties of existing materials, DFT has also been used to predict the properties of materials yet to be made. For example, the discovery of BiPt as a superior catalyst for hydrogen production than pure Pt was done computationally. Subsequently, Greeley et al. successfully synthesized the new material.

=='''References.'''==
<references>
<ref name="Ox">F. Giustino, in ''Materials Modelling using Density Functional Theory'', Oxford University Press, 2014.
</ref>
<ref name="Greeley"> J. Greeley, T.F. Jaramillo, J. Bonde, I.B. Chorkendorff, J.K. Norskov, ''Nat Mater.'', 2006, '''5''', 909.</ref>
</references>

Kh1015DFT

2018-08-15T14:28:36Z

Kh1015: /* Density Functional Theory */

=='''Density Functional Theory'''==
In a top-down modelling strategy, the behaviour of materials are predicted by extracting empirical parameters <ref name="Ox" />. Conversely, in a bottom-up strategy, the properties of materials are predicted using quantum mechanics, which is a fundamental theory of materials <ref name="Ox" />.

Density Functional Theory (DFT) is a very effective technique for studying molecules, nanostructures, solids and surfaces and interfaces. DFT is categorized under a bottom-up ab-initio approach.

Many material properties involve it being in a bulk of hundreds of thousands of atoms. Direct DFT is not feasible to model materials in bulk. QM/MM model is used instead where the bulk is sub-divided into quantum mechanics (QM) and molecular mechanics (MM) sub-systems, where a classical Newtonian description is sufficient <ref name="Ox" />.

For example, in the modelling of crack propagation in brittle solids, the bulk could be described using linear elasticity theory. Only the crack tip and an area surrounding it need to be modelled using ab-initio QM method <ref name="Ox" />.

Other than understanding the properties of existing materials, DFT has also been used to predict the properties of materials yet to be made. For example, the discovery of BiPt as a superior catalyst for hydrogen production than pure Pt was done computationally. Subsequently, Greeley et al. successfully synthesized the new material.

=='''References.'''==
<references>
<ref name="Ox">F. Giustino, in ''Materials Modelling using Density Functional Theory'', Oxford University Press, 2014.
</ref>
</references>

Kh1015DFT

2018-08-15T14:24:26Z

Kh1015: /* Density Functional Theory */

Kh1015DFT

2018-08-15T14:23:30Z

Kh1015: /* Density Functional Theory */

Kh1015DFT

2018-08-15T14:21:22Z

Kh1015: /* Density Functional Theory */

Kh1015DFT

2018-08-15T14:19:28Z

Kh1015: /* Density Functional Theory */

Kh1015DFT

2018-08-15T14:16:39Z

Kh1015: /* Density Functional Theory */

Kh1015DFT

2018-08-15T14:09:10Z

Kh1015: /* Density Functional Theory */

Kh1015DFT

2018-08-15T14:02:32Z

Kh1015: /* Density Functional Theory */

Kh1015DFT

2018-08-15T14:02:12Z

Kh1015: /* Density Functional Theory */

Kh1015DFT

2018-08-15T14:00:13Z

Kh1015: /* Density Functional Theory */

=='''Density Functional Theory'''==
In a top-down strategy, the behaviour of materials are predicted by extracting empirical parameters <ref name="Ox" />.

=='''References.'''==
<references>
<ref name="Ox">F. Giustino, in ''Materials Modelling using Density Functional Theory'', Oxford University Press, 2014.
</ref>
</references>

Kh1015DFT

2018-08-15T13:57:35Z

Kh1015:

=='''Density Functional Theory'''==

=='''References.'''==
<references>
<ref name="Ox">F. Giustino, in ''Materials Modelling using Density Functional Theory'', Oxford University Press, 2014.
</ref>
</references>

Kh1015DFT

2018-08-15T13:54:49Z

Kh1015: Created page with "=='''Density Functional Theory'''=="

=='''Density Functional Theory'''==

KH1015TDSQM

2018-03-14T22:48:18Z

Kh1015: Blanked the page

KH1015TDSQM

2018-03-14T22:44:38Z

Kh1015: Created page with "A) Molecular Spectroscopy: 1) Introduction. In the spectroscopy experiments, we can consider using semi-classical approach, where light is treated classically and the mater q..."

A) Molecular Spectroscopy:
1) Introduction.
In the spectroscopy experiments, we can consider using semi-classical approach, where light is treated classically and the mater quantum mechanically. Light (or radiation) can be described semiclassically because of correspondence principle (which states that for large quantum numbers, the quantum mechanical results coincide with that of classical mechanics) and wavelengths of interest are larger than the size of the spectroscopically active atom or molecule by at least 137 times (which is the fine structure constant, which is based on ratio of size of H atom to smallest wavelength capable of causing spectral transitions between bound electronic states).
In classical picture, the intensity of light is related to the square of the amplitude of the wave, rather than concentration of photons. One exception when we cannot treat light classically is when we describe the delocalized wavefunctions of the electronic bands in the metal where the systems are comparable in size to optical wavelengths.
2) The Classical Description of Electromagnetic Radiation:
2.1) Maxwell Equation:
In this model, light can be described as oscillating electric (E ⃗ ⃗) and magnetic fields (B ⃗ ⃗) perpendicular to the propagation direction. Maxwell equation necessitates the electric and magnetic fields to be in phase and orthogonal to each other. Physically, electric field is a result of electric charges or time-dependent magnetic fields; and magnetic field is a result of electric current or time-dependent electric fields.

Rep:Kh1015TSEx3RD

2018-03-14T10:35:56Z

Kh1015: /* Part 1: Parameters from Reaction Profile. */

==Exercise 3 Results and Discussion.==

'''Note to Reader/Marker:'''
<br>The compartmentalization of the Results and Discussion into 5 parts was based on relevant discussion idea and for convenient navigation during the write-up. Also, the Jmol files in this page could display the relative energies of the MOs but they could not visualize the MOs. In response, the visualized HOMO of each TS was attached next to the Jmol files for viewing purposes.

===Part 1: Parameters from Reaction Profile.===
Figure 4.3 under Methodology section shows the reaction scheme for Exercise 3.

Referring to Table 5.3.2, calculations at PM6 level showed that only the Diels-Alder minor-regio-isomers were non-spontaneous. The Diels-Alder endo-major-regioisomer (referred to as endo product in Table 5.3.1) was calculated to be the kinetic product (based on lowest activation Gibbs-Free Energy equalled to 83.2 kJ mol<sup>-1</sup>) and an associated rate of reaction of 0.0165 s<sup>-1</sup> at 298.15K. The rate constant was calculated using the formula described under Introduction > Part D. The cheletropic product was calculated to be the thermodynamically favourable product (based on the most negative Δ Gibbs-Free Energy equalled to -155 kJ mol<sup>-1</sup>). This prediction could be verified experimentally by doing a kinetic study and analysis of ratio of Diels-Alder (including the regioisomers) and cheletropic products formed at rtp.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.3.1: Summary of Calculated Gibbs-Free Energy of Species in Diels-Alder and Cheletropic Reactions at 298.15 K and 1 atm (PM6 level).
|-
|rowspan="2"|''' '''
|colspan="12"|'''States'''
|-
|'''5,6-dimethylenecyclohexa-1,3-diene'''
|'''Sulfur Dioxide'''
|'''Endo TS'''
|'''Endo Product'''
|'''Exo TS'''
|'''Exo Product'''
|'''TS of Endo-Minor-Regioisomer'''
|'''Endo-Minor-Regioisomer'''
|'''TS of Exo-Minor-Regioisomer'''
|'''Exo-Minor-Regioisomer'''
|'''Cheletropic TS'''
|'''Cheletropic Product'''
|-
|'''Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
|468
| -313
|238
|57.0
|242
|56.3
|268
|172
|276
|177
|260
| -0.00263
|}

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.3.2: Summary of Calculated Reaction Profile Parameters for Diels-Alder and Cheletropic Reactions at 298.15 K and 1 atm (PM6 level).
|-
|''' '''
|'''Endo-Major-Regioisomer'''
|'''Exo-Major-Regioisomer'''
|'''Endo-Minor-Regioisomer'''
|'''Exo-Minor-Regioisomer'''
|'''Cheletropic'''
|-
|'''Activation Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
|83.2
|87.2
|113
|121
|106
|-
|'''Δ Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
| -97.6
| -98.2
|17.7
|22.2
| -155
|-
|'''Predicted Rate of Reaction (x10<sup>-6</sup> s<sup>-1</sup>)'''
|16,500
|3,280
|0.010
|0.004
|1.67
|}

===Part 2: Comparison of Reaction Profiles on a Standardized Reaction Coordinate.===

Figure 5.3.1 shows the comparison of the Diels-Alder and Cheletropic Reaction Profiles on a Standardized Reaction Coordinate at 298.15 K and 1 atm (PM6 level). In the Standardized Reaction Coordinate, the reactants' coordinates are set to -1, those of TS set to 0 and those of products set to 1. This was done to align the all the reaction states independent of the rate on a common scale such that the relative energetics could be compared between possible reaction paths.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Comparison.png|frame|Figure 5.3.1: Comparison of the Diels-Alder and Cheletropic Reaction Profiles on a Standardized Reaction Coordinate at 298.15 K and 1 atm (PM6 level).]]
|}

===Part 3: Rationalizing the Reaction Profile Parameters.===

Xylylene is an unstable compound because it is a system of 8 π electrons (4n anti-aromatic rule). From the IRC of all the reactions examined (excluding Diels-Alder minor-regio-isomers), it was observed that as xylelene reacted with sulfur dioxide, the 6 membered-ring would end up with a stable 6 π electrons system (4π+2 aromatic rule) in the product. This provided a strong thermodynamic driving force for the reaction with sulfur dioxide to proceed.

For all the reactions examined, there was no identifiable secondary orbital contribution from the Gaussview MO visualizations.

Referring to Figure 5.3.2-5.3.5, the calculated steric interactions were similar for Diels-Alder endo-exo products that react at the same regio-position. Because of similar steric interactions and electronic interactions within each set, the products that reacted at the same position would possess similar activation Gibbs-Free Energy (calculated) as shown in Table 5.3.2. However, when comparing '''between''' the two sets of Diels-Alder regio-isomers, it could be seen that the activation Gibbs-Free Energy for the minor-regio-isomer set was much higher than the other set ({113, 121} against {83.2, 87.2} where each element of the sets is in the form {endo, exo} and reported in kJ mol<sup>-1</sup>). For both sets, the TS formation involved severance of π interactions in the xylylene system. In the major-regio-isomer set, the activation Gibbs-Free Energy was reduced because there was a corresponding formation of favourable aromatic interaction in the 6-membered ring.

Referring to Figure 5.3.2-5.3.3 and 5.3.6, when comparing between the Diels-Alder major regio-isomer set and the cheletropic product, the steric clash (Red being not favourable and Blue being favourable) in the cheletropic TS was calculated to be higher than those in the Diels-Alder major regio-isomer set. This was due to the approach of two orthogonal lone pairs of S atom towards the 5,6-dimethylenecyclohexa-1,3-diene in the chelotropic TS (Orange colour) that was not present in the Diels-Alder reactions. This contributes to the observation that the calculated activation Gibbs-Free Energy of the cheletropic product, 106 kJ mol<sup>-1</sup>, was much higher than those of the endo and exo products, 83.2 and 87.2 <sup>-1</sup> respectively.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Endo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.2: Non Covalent Interactions in the Transition State During Diels-Alder Endo Product Formation.]]
|[[File:KH1015 Exo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.3: Non Covalent Interactions in the Transition State During Diels-Alder Exo Product Formation.]]
|[[File:KH1015 Var Endo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.4: Non Covalent Interactions in the Transition State During Diels-Alder Endo Minor-Regioisomer Formation.]]
| [[File:KH1015 Var Exo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.5: Non Covalent Interactions in the Transition State During Diels-Alder Exo Minor-Regioisomer Formation.]]
| [[File:KH1015 Isoindene-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.6: Non Covalent Interactions in the Transition State During Cheletropic Product Formation.]]
|-
|}

===Part 4: IRC.===
====1. Diels-Alder Products.====
=====1.A. Endo Major-Regio-Isomer.=====
Referring to Figure 5.3.7, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:Kh1015 Endo Diels Alder.gif|frame|left|Figure 5.3.7: IRC for Formation of Diels-Alder Endo Product at 298.15 K and 1 atm (PM6 Level).]]
|| [[File:KH1015 Endo Diels Alder IRC Graph.png|thumb|Figure 5.3.8: IRC Graph of Energy against Reaction Coordinate for the formation of Endo Product at 298.15 K and 1 atm (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_Diels_Alder_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.9: Jmol of TS of Endo Path.</title>
<color>white</color>
<size>400</size>
<script>frame 14; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 ENDO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Endo Diels Alder-TS HOMO Isovalue 0.02 Cube Grid Coarse.png|thumb|Figure 5.3.10: HOMO of the TS of Endo Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

=====1.B. Exo Major-Regio-Isomer.=====
Referring to Figure 5.3.11, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:Kh1015 Exo Diels Alder.gif|frame|left|Figure 5.3.11: IRC for Formation of Diels-Alder Exo Product (PM6 level).]]
|| [[File:KH1015 Exo Diels Alder IRC Graph.png|thumb|Figure 5.3.12: IRC Graph of Energy against Reaction Coordinate for the formation of Exo Product (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_Diels_Alder_IRC_Graph_Gradient.png here]for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.13: HOMO of TS of Exo Path.</title>
<color>white</color>
<size>400</size>
<script>frame 74; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 EXO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Exo Diels Alder-TS HOMO.png|thumb|Figure 5.3.14: HOMO of TS of Exo Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

=====2.A. Endo Minor-Regio-Isomer.=====
Referring to Figure 5.3.15, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Var Endo Diels Alder.gif|frame|left|Figure 5.3.15: IRC for Formation of Endo Minor-Regioisomer.]]
|| [[File:KH1015 Var Endo Diels Alder IRC Graph.png|thumb|Figure 5.3.16: IRC Graph of Energy against Reaction Coordinate for the formation of Endo Minor-Regioisomer (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Var_Endo_Diels_Alder_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.17: HOMO of Endo Minor-Regioisomer Path.</title>
<color>white</color>
<size>400</size>
<script>frame 24; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 VAR ENDO DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Var Endo Diels Alder-TS HOMO.png|thumb|Figure 5.3.18: HOMO of TS of Endo Minor-Regioisomer Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

=====2.B. Exo Minor-Regio-Isomer.=====
Referring to Figure 5.3.19, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Var Exo Diels Alder.gif|frame|left|Figure 5.3.19: IRC for Formation of Exo Minor-Regioisomer.]]
|| [[File:KH1015 Var Exo Diels Alder IRC Graph.png|thumb|Figure 5.3.20: IRC Graph of Energy against Reaction Coordinate for the formation of Exo Minor-Regioisomer (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Var_Exo_Diels_Alder_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.21: HOMO of TS of Exo Minor-Regioisomer Path.</title>
<color>white</color>
<size>400</size>
<script>frame 16; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 VAR DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Var Exo Diels Alder-TS HOMO.png|thumb|Figure 5.3.22: HOMO of TS of Exo Minor-Regioisomer Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

====2. Cheletropic Product.====
Referring to Figure 5.3.23, the IRC calculation at PM6 level showed that the two C-S sigma bonds were formed in a synchronous fashion in a concerted mechanism and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:Kh1015 Isoindene.gif|frame|left|Figure 5.3.23: IRC for Formation of Cheletropic Product.]]
|| [[File:KH1015 Isoindene IRC Graph.png|thumb|Figure 5.3.24: IRC Graph of Energy against Reaction Coordinate for the formation of Cheletropic Product (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Isoindene_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.25: HOMO of TS of Cheletropic Path.</title>
<color>white</color>
<size>400</size>
<script>frame 36; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 ISOINDENE ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Isoindene-TS HOMO.png|thumb|Figure 5.3.26: HOMO of TS of Cheletropic Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

===Part 5: Interactive Vibration Animations.===

Figures 5.3.27-5.3.31 show the interactive vibration animations.

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.27: Interactive Vibration Animation of the Endo TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 ENDO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Endo</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton>
<script>measure 14 18; measure 11 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>Endo</target>
</item>
<item>
<script>frame 15; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i334/cm</text>
<target>Endo</target>
</item>
<item>
<script>frame 16; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>63/cm</text>
<target>Endo</target>
</item>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.28: Interactive Vibration Animation of the Exo TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 EXO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Exo</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Exo</target>
</jmolbutton>
<jmolbutton>
<script>measure 14 18; measure 11 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>Exo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Exo</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Exo</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>Exo</target>
</item>
<item>
<script>frame 75; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i352/cm</text>
<target>Exo</target>
</item>
<item>
<script>frame 76; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>66/cm</text>
<target>Exo</target>
</item>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Exo</target>
</jmolbutton>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.29: Interactive Vibration Animation of the Endo Minor-Regioisomer TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 VAR ENDO DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>EndoVar</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>EndoVar</target>
</jmolbutton>
<jmolbutton>
<script>measure 5 17; measure 2 18</script>
<text>TS C-C Equilibrium Distance</text>
<target>EndoVar</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EndoVar</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>EndoVar</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>EndoVar</target>
</item>
<item>
<script>frame 25; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i453/cm</text>
<target>EndoVar</target>
</item>
<item>
<script>frame 26; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>57/cm</text>
<target>EndoVar</target>
</item>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.30: Interactive Vibration Animation of the Exo Minor-Regioisomer TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 VAR DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>ExoVar</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>ExoVar</target>
</jmolbutton>
<jmolbutton>
<script>measure 2 18; measure 5 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>ExoVar</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExoVar</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>ExoVar</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>ExoVar</target>
</item>
<item>
<script>frame 17; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i483/cm</text>
<target>ExoVar</target>
</item>
<item>
<script>frame 18; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>53/cm</text>
<target>ExoVar</target>
</item>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.31: Interactive Vibration Animation of the Cheletropic TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 ISOINDENE ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Cyclohexene</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton>
<script>measure 11 17; measure 14 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>Cyclohexene</target>
</item>
<item>
<script>frame 37; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i487/cm</text>
<target>Cyclohexene</target>
</item>
<item>
<script>frame 38; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>74/cm</text>
<target>Cyclohexene</target>
</item>
</jmolmenu>
</jmol>

Rep:Kh1015TSEx2RD

2018-03-14T10:35:40Z

Kh1015: /* Exercise 2 Results and Discussion. */

==Exercise 2 Results and Discussion.==

'''Note to Reader/Marker:'''
<br>The compartmentalization of the Results and Discussion into 4 parts was based on relevant discussion idea and for convenient navigation during the write-up.

===Part 1: Determining the Type of Diels-Alder Reaction.===
Figure 4.2 under Methodology section shows the reaction scheme for Exercise 2.

Referring to Figure 5.2.5 and 5.2.10, both of the endo and exo reactions were calculated to be inverse-electron-demand Diels Alder reactions at B3YLP-6-31 G(D) level, whereby the electron-poor dienophile (cyclohexadiene) interacted with the electron-rich diene (1,3-dioxole).

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.2.1: Summary of MO Interactions To Form the TS for Both Endo and Exo Reactions (Same Set of Orbitals for Both, Difference is only in the Relative Approach Orientation).
|-
|'''TS Symmetry Label (in Increasing Energy Level)'''
|'''Constituent Fragment Orbital Interactions (Cyclohexadiene - 1,3 Dioxole)'''
|-
|Anti-Symmetrical
|MO22-MO20 (Bonding)
|-
|Symmetrical
|MO23-MO19 (Bonding)
|-
|Symmetrical*
|MO23-MO19 (Anti-Bonding)
|-
|Anti-Symmetrical*
|MO22-MO20 (Anti-Bonding)
|}

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 HOMO of Cyclohexadiene (MO22).png|thumb|150px|Figure 5.2.1: HOMO of Cyclohexadiene (MO 22, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_CYCLOHEXADIENE_B3LYP-6-31G(D).LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Cyclohexadiene_B3LYP-6-31G(d).chk *.chk] output.]]
|[[File:KH1015 LUMO of Cyclohexadiene (MO23).png|thumb|150px|Figure 5.2.2: LUMO of Cyclohexadiene (MO 23, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_1-4-BUTADIENE_S-CIS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_1-4-Butadiene_S-cis.chk *.chk] output.]]
|[[File:KH1015 HOMO of 1,3 Dioxole (MO19).png|thumb|150px|Figure 5.2.3: HOMO of 1,3-Dioxole(MO 19, B3YLP-6-31 G(D) Calculation. Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_DIOXANE_B3LYP-6-31G(D).LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Dioxane_B3LYP-6-31G(d).chk *.chk] output.]]
|[[File:KH1015 LUMO of 1,3 Dioxole (MO20).png|thumb|150px|Figure 5.2.4: LUMO of 1,3-Dioxole(MO 20, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_DIOXANE_B3LYP-6-31G(D).LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Dioxane_B3LYP-6-31G(d).chk *.chk] output.]]
|}

=====Endo Product ((3aR,4S,7R,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====
{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
| colspan="4"|[[File:KH1015 Chemdraw TS Molecular Orbital Endo.png|thumb|center|400px|Figure 5.2.5: Frontier MO diagram for the formation of the Endo TS.]]
|-
|[[File:KH1015 HOMO-1 MO 40.png|thumb|150px|Figure 5.2.6: HOMO-1 of Endo TS (MO 40, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:ENDO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 HOMO MO 41.png|thumb|150px|Figure 5.2.7: HOMO of Endo TS (MO 41, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:ENDO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 LUMO MO 42.png|thumb|150px|Figure 5.2.8: LUMO of Endo TS (MO 42, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:ENDO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 LUMO+1 MO 43.png|thumb|150px|Figure 5.2.9: LUMO+1 of Endo TS (MO 43, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:ENDO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|}

=====Exo Product ((3aS,4R,7S,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
| colspan="4"|[[File:KH1015 Chemdraw TS Molecular Orbital Exo.png|thumb|center|400px|Figure 5.2.10: Frontier MO diagram for the formation of the Exo TS.]]
|-
|[[File:KH1015 HOMO-1 Exo MO40.png|thumb|150px|Figure 5.2.11: HOMO-1 of Exo TS (MO 40, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_EXO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 HOMO Exo MO41.png|thumb|150px|Figure 5.2.12: HOMO of Exo TS (MO 41, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_EXO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 LUMO Exo MO42.png|thumb|150px|Figure 5.2.13: LUMO of Exo TS (MO 42, B3YLP-6-31 G(D) Calculation).Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_EXO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 LUMO+1 Exo MO43.png|thumb|150px|Figure 5.2.14: LUMO+1 of Exo TS (MO 43, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_EXO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|}

===Part 2: Parameters from the Reaction Profile.===

Referring to Table 5.2.2, it can be seen that the Gibbs-Free Energies of the different species are much larger than the Δ Gibbs-Free Energy in Table 5.2.3. From the calculation of this reaction, it can be observed that the activation Gibbs-Free Energy and energy released/absorbed were only a small fraction relative to the total energy of the system (less than 0.01%).

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.2.2: Summary of Calculated Gibbs-Free Energy of Species in Both Endo and Exo Reactions at 298.15 K and 1 atm (B3YLP-6-31 G(D) level).
|-
|rowspan="2"|''' '''
|colspan="6"|'''States'''
|-
|'''Cyclohexadiene'''
|'''1,3-Dioxole'''
|'''Endo TS'''
|'''Endo Product'''
|'''Exo TS'''
|'''Exo Product'''
|-
|'''Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
| -612,593
| -701,189
| -1,313,622
| -1,313,849
| -1,313,614
| -1,313,846
|}

Referring to Table 5.2.3, calculations showed that both reactions were spontaneous and that the endo product was the kinetically (based on activation Gibbs-Free Energy) and thermodynamically favourable product (based on Δ Gibbs-Free Energy). The endo path had a lower activation Gibbs-Free Energy (160 against 168 kJ mol<sup>-1</sup>) with higher rate constant at 298.15 K (5.77 against 0.23 x 10<sup>-16</sup>), and had a more negative Δ Gibbs-Free Energy (-67.4 against -63.8 kJ mol<sup>-1</sup>), which meant that it was more stable than the exo form. The rate constant was calculated using the formula described under Introduction > Part D. This prediction could be verified experimentally by doing a kinetic study and analysis of ratio of endo to exo products formed at rtp.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.2.3: Summary of Calculated Reaction Profile Parameters for Both Endo and Exo Reactions at 298.15 K and 1 atm (B3YLP-6-31 G(D) level).
|-
|''' '''
|'''Activation Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
|'''Δ Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
|'''Predicted Rate of Reaction (x10<sup>-16</sup> s<sup>-1</sup>)'''
|-
|'''Endo-Path'''
|160
| -67.4
|5.77
|-
|'''Exo-Path'''
|168
| -63.8
|0.23
|}

===Part 3: Secondary Orbital Interactions and Sterics.===
Referring to MO 41 for both endo and exo TS in Figure 5.2.15 and 5.2.17, the calculation showed favourable secondary orbital interaction in the endo TS that was not present in the exo TS due to the relative orientation of the two reacting fragments, which would lower the activation energy. Referring to Figure 5.2.16 and 5.2.18, there are significant non-favourable steric interactions (Red being not favourable and Blue being favourable) in the exo TS between the methyl-group and the 6-membered-ring (Green) that was not present in the exo TS due to the relative orientation of the two reacting fragments, which would raise the activation energy. Conversely, both secondary orbital interaction and steric clash accounted for the lower calculated activation energy of the endo path relative to exo path, 160 kJ mol<sup>-1</sup> against 168 kJ mol<sup>-1</sup>.

=====Endo Product ((3aR,4S,7R,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====
{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol>
<jmolApplet>
<title>Figure 5.2.15: HOMO of Endo TS (Default view is MO 41, B3YLP-6-31 G(D) Calculation).</title>
<color>white</color>
<size>400</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>KH1015 ENDO B3YLP-6-31 G(D) FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:Kh1015 Endo B3LYP 631Gd Steric Clash surface.png|thumb|Figure 5.2.16: Non Covalent Interactions in the Endo TS (B3YLP-6-31 G(D) Calculation).]]
|-
|}

=====Exo Product ((3aS,4R,7S,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====
{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol>
<jmolApplet>
<title>Figure 5.2.17: HOMO of Exo TS (Default view is MO 41, B3YLP-6-31 G(D) Calculation).</title>
<color>white</color>
<size>400</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>KH1015 EXO B3YLP-6-31 G(D) FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Exo B3LYP 631Gd Steric Clash surface.png|thumb|Figure 5.2.18: Non Covalent Interactions in the Exo TS (B3YLP-6-31 G(D) Calculation).]]
|-
|}

===Part 4: Interactive Vibration Animation of TS for Both Endo and Exo Path.===
Both Figure 5.2.19 and 5.2.20 contained interactive vibration animation of the Endo and Exo TS (B3YLP-6-31 G(D) level).

=====Endo Product ((3aR,4S,7R,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.2.19: Interactive Vibration Animation of the Endo TS (B3YLP-6-31 G(D) level).</title> //Initialise the applet
<uploadedFileContents>KH1015 ENDO B3YLP-6-31 G(D) FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Endo</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton>
<script>measure 1 2; measure 5 6</script>
<text>TS C-C Equilibrium Distance</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>Endo</target>
</item>
<item>
<script>frame 17; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i521/cm</text>
<target>Endo</target>
</item>
<item>
<script>frame 18; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>66/cm</text>
<target>Endo</target>
</item>
</jmolmenu>
</jmol>

=====Exo Product ((3aS,4R,7S,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.2.20: Interactive Vibration Animation of the Exo TS (B3YLP-6-31 G(D) level).</title> //Initialise the applet
<uploadedFileContents>KH1015 EXO B3YLP-6-31 G(D) FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Cyclohexene</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton>
<script>measure 1 17; measure 4 15</script>
<text>TS C-C Equilibrium Distance</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>===Select Vibration===</text>
<target>Cyclohexene</target>
</item>
<item>
<script>frame 21; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i529/cm</text>
<target>Cyclohexene</target>
</item>
<item>
<script>frame 22; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>99/cm</text>
<target>Cyclohexene</target>
</item>
</jmolmenu>
</jmol>

===Part 5: Interactive Vibration Animations (PM6 Level).===
The IRC calculations at PM6 level showed that the two C-C sigma bonds were formed in a synchronous fashion in a concerted mechanism for both paths and that the TS for both reactions had been optimized.

====Endo Product ((3aR,4S,7R,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).====

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex2 Endo PM6 IRC.gif|frame|left|Figure 5.2.21: IRC for Formation of Diels-Alder Endo Product ((3aR,4S,7R,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole) (PM6 Calculation).]]
|| [[File:KH1015 Endo PM6 IRC Graph.png|thumb|Figure 5.2.22: IRC Graph of Energy against Reaction Coordinate for the formation of Endo Product (PM6 Calculation). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_PM6_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|}

====Exo Product ((3aS,4R,7S,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).====

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:Kh1015 Exo Crosscheck PM6 IRC.gif|frame|left|Figure 5.2.23: IRC for Formation of Diels-Alder Exo Product ((3aS,4R,7S,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole)) (PM6 Calculation).]]
|| [[File:KH1015 Exo PM6 IRC Graph.png|thumb|Figure 5.2.24: IRC Graph of Energy against Reaction Coordinate for the formation of Exo-Product (PM6 Calculation). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_PM6_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|}

Rep:Kh1015TSEx1RD

2018-03-14T10:35:18Z

Kh1015: /* Part 1: Symmetry Discussion. */

==Exercise 1 Results and Discussion.==
__FORCETOC__
'''Note to Reader/Marker:'''
<br>The compartmentalization of the Results and Discussion into 3 parts was based on relevant discussion idea and for convenient navigation during the write-up.
===Part 1: Symmetry Discussion.===
Figure 4.1 under Methodology section shows the reaction scheme for Exercise 1.

Figure 5.1.5 shows the graphical representation of MO interactions between s-cis butadiene and ethene during the formation of the TS. Figures 5.1.1-5.1.4 and 5.1.6-5.1.9 show the visualized MO output from GaussView (isovalue=0.02 and medium cube grid). Table 5.1.1 summarizes the MO interactions to form the TS in terms of the label of the constituent MOs in Gaussview outputs.

It can be concluded that the symmetry requirement of an allowed reaction is strictly when the constituent MOs have the same symmetry. Consequently, symmetrical-symmetrical or antisymmetrical-antisymmetrical interaction has a non-zero orbital overlap integral. Meanwhile, non-symmetrical interactions of the constituent MOs are symmetry-forbidden. Conversely, symmetrical-antisymmetrical or antisymmetrical-symmetrical interaction has a zero orbital overlap integral.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.1.1: Summary of MO Interactions To Form the TS.
|-
|'''TS Symmetry Label (in Increasing Energy Level)'''
|'''Constituent Fragment Orbital Interactions (S-Cis Butadiene - Ethene)'''
|-
|Anti-Symmetrical
|MO12-MO6 (Bonding)
|-
|Symmetrical
|MO11-MO7 (Bonding)
|-
|Symmetrical*
|MO12-MO6 (Anti-Bonding)
|-
|Anti-Symmetrical*
|MO11-MO7 (Anti-Bonding)
|}

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 HOMO of S-Cis Butadiene (MO11).png|thumb|150px| Figure 5.1.1: HOMO of S-Cis Butadiene (MO 11, PM6 Method). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_1-4-BUTADIENE_S-CIS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_1-4-Butadiene_S-cis.chk *.chk] output.]]
|[[File:KH1015 LUMO of S-Cis Butadiene (MO 12).png|thumb|150px|Figure 5.1.2: LUMO of S-Cis Butadiene (MO 12, PM6 Method). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_1-4-BUTADIENE_S-CIS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_1-4-Butadiene_S-cis.chk *.chk] output.]]
|[[File:KH1015 HOMO of Ethene (MO6).png|thumb|150px|Figure 5.1.3: HOMO of Ethene (MO 6, PM6 Method). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_ETHENE.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Ethene.chk *.chk] output.]]
|[[File:KH1015 LUMO of Ethene (MO7).png|thumb|150px|Figure 5.1.4: LUMO of Ethene (MO 7, PM6 Method). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_ETHENE.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Ethene.chk *.chk] output.]]
|-
| colspan="4"|[[File:KH1015 Chemdraw TS Molecular Orbital.png|thumb|center|400px| Figure 5.1.5: Frontier MO diagram for the formation of the TS. The numbers on the TS structure (bottom) are atom labels.]]
|-
|[[File:KH1015 HOMO-1 MO16.png|thumb|150px| Figure 5.1.6: HOMO-1 of TS (MO 16, PM6 Method). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_CYCLOHEXENE_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Cyclohexene_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 HOMO MO17.png|thumb|150px|Figure 5.1.7: HOMO of TS (MO 17, PM6 Method). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_CYCLOHEXENE_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Cyclohexene_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 LUMO MO18.png|thumb|150px|Figure 5.1.8: LUMO of TS (MO 18, PM6 Method). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_CYCLOHEXENE_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Cyclohexene_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 LUMO+1 MO19.png|thumb|150px|Figure 5.1.9: LUMO-1 of TS (MO 19, PM6 Method). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_CYCLOHEXENE_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Cyclohexene_Fragment_TS.chk *.chk] output.]]
|}

===Part 2: C-C Bond Length Evolution.===
'''Note: The carbon labels are based on the TS labels in Figure 5.1.5'''.

Referring to table 5.1.2, as the reaction progressed from reactants to product at rtp, {C<sub>1</sub>-C<sub>2</sub>, C<sub>3</sub>-C<sub>4</sub>, C<sub>5</sub>-C<sub>6</sub>} bond lengths (in Å) increased from {1.33343, 1.33343, 1.32726} to {1.37977, 1.37979, 1.38177} to {1.50084, 1.50083, 1.53457}. At the same time, the {C<sub>2</sub>-C<sub>3</sub>, C<sub>4</sub>-C<sub>5</sub>, C<sub>1</sub>-C<sub>6</sub>} bond lengths (in Å) decreased from {1.47078, NA, NA} to {1.41110, 2.11469, 2.11479} to {1.33704, 1.53714, 1.53721}. The change in bond lengths were due to change in hybridization or change in bond order or both.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.1.2: Summary of Evolution of Calculated C-C Bond Length (in Å) through the Reaction at 298.15 K and 1 atm (PM6 Method).
|- style="background: grey; color: white"
|colspan="1" rowspan="2"|'''State'''
|colspan="6"|'''C-C Bond Length (Å)'''
|- style="background: grey; color: white"
|'''C<sub>1</sub>-C<sub>2</sub>'''
|'''C<sub>2</sub>-C<sub>3</sub>'''
|'''C<sub>3</sub>-C<sub>4</sub>'''
|'''C<sub>4</sub>-C<sub>5</sub>'''
|'''C<sub>5</sub>-C<sub>6</sub>'''
|'''C<sub>1</sub>-C<sub>6</sub>'''
|-
|[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_1-4-BUTADIENE_S-CIS.LOG '''S-Cis Butadiene''']
|1.33343
|1.47078
|1.33343
|NA
|NA
|NA
|-
|'''Hybridization'''
|sp<sup>2</sup>-sp<sup>2</sup> Double Bond
|sp<sup>2</sup>-sp<sup>2</sup> Single Bond
|sp<sup>2</sup>-sp<sup>2</sup> Double Bond
|NA
|NA
|NA
|- style="background: grey; color: white"
|[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_ETHENE.LOG '''Ethene''']
|NA
|NA
|NA
|NA
|1.32726
|NA
|- style="background: grey; color: white"
|'''Hybridization'''
|NA
|NA
|NA
|NA
|sp<sup>2</sup>-sp<sup>2</sup> Double Bond
|NA
|-
|[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_CYCLOHEXENE_FRAGMENT_TS.LOG '''TS''']
|1.37977
|1.41110
|1.37979
|2.11469
|1.38177
|2.11479
|-
|'''Hybridization'''
|Not clear
|Not clear
|Not clear
|Not clear
|Not clear
|Not clear
|- style="background: grey; color: white"
|[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_CYCLOHEXENE.LOG '''Product''']
|1.50084
|1.33704
|1.50083
|1.53714
|1.53457
|1.53721
|-
|'''Hybridization'''
|sp<sup>3</sup>-sp<sup>2</sup> Single Bond
|sp<sup>2</sup>-sp<sup>2</sup> Double Bond
|sp<sup>2</sup>-sp<sup>3</sup> Single Bond
|sp<sup>3</sup>-sp<sup>3</sup> Single Bond
|sp<sup>3</sup>-sp<sup>3</sup> Single Bond
|sp<sup>3</sup>-sp<sup>3</sup> Single Bond
|}

Table 5.1.3 shows typical sp<sup>3</sup> and sp<sup>2</sup> C-C bond lengths in organic compounds at rtp. The calculated values at PM6 level show good agreement with literature values at rtp in table 5.1.3 with less than 1% difference for any given C-C bond length <ref name="C-C" />.

The average value of Van der Waals radius of C atom in literature is 1.88 <ref name="C" />. The calculated distance between the centres of two C atoms of the two fragments in the TS (about 2.115 Å) is less than the sum of their Van der Waals radii (3.76 Å). This suggests presence of partly-formed C-C bond in the TS.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.1.3: Literature Value for Average C-C Bond Length (Experimentally Measured in Å) in Organic Compounds at 298.15 K and 1 atm <ref name="C-C" />.
|-
|'''Hybridization'''
|'''sp<sup>3</sup>-sp<sup>3</sup> Single Bond'''
|'''sp<sup>3</sup>-sp<sup>2</sup> Single Bond'''
|'''sp<sup>2</sup>-sp<sup>2</sup> Double Bond'''
|-
|'''C-C Bond Length (in Å)'''
|1.54
|1.50
|1.47
|}

===Part 3: IRC and Animated Vibrations.===
Referring to Figure 5.1.10, the IRC calculation at PM6 level showed that the two C-C sigma bonds were formed in a synchronous fashion in a concerted mechanism and that the TS had been optimized.

The calculated reaction profile at PM6 suggested that the reaction was spontaneous at 298.15 K and 1 atm. The activation energy was calculated to be 171 kJ mol<sup>-1</sup> and Δ Gibbs-Free Energy was calculated to be -122 kJ mol<sup>-1</sup> at 298.15 K and 1 atm, which means that there is a very high reaction barrier to be overcome before the reaction could proceed.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:Kh1015 Cyclohexene IRC.gif|frame|Figure 5.1.10: IRC for Formation of Cyclohexene (PM6 Method).]]
|| [[File:KH1015 Cyclohexene IRC Graph.png|thumb|Figure 5.1.11: IRC Graph of Energy against Reaction Coordinate for the formation of Cyclohexene at 298.15 K and 1 atm (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Cyclohexene_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|}

Figure 5.1.12 shows the HOMO of the TS system by default (MO 17). It is possible to right-click on the Jmol and choose any MO of interest.

Figure 5.1.13 shows non-covalent interactions at the TS (Red being non-favourable interaction and Blue being favourable interaction). There was no significant non-favourable steric clash in the reaction, which meant that steric clash was not a factor contributing to the high activation barrier.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol>
<jmolApplet>
<title>Figure 5.1.12: HOMO of the TS (Default view is MO 17, PM6 Method).</title>
<color>white</color>
<size>400</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>KH1015 MO CYCLOHEXENE FRAGMENT TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Cyclohexene Fragment TS Density.png|thumb|Figure 5.1.13: Non Covalent Interactions in the Transition State of Cyclohexene Formation (PM6 Method).]]
|-
|}

Figure 5.1.14 shows an interactive vibration animation of the TS (calculation at PM6 level).

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.1.14: Interactive Vibration Animation of the TS (PM6 Method).</title>
<uploadedFileContents>KH1015 CYCLOHEXENE FRAGMENT TS.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Cyclohexene</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton>
<script>measure 1 2; measure 3 4</script>
<text>TS C-C Equilibrium Distance</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>Cyclohexene</target>
</item>
<item>
<script>frame 17; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i950/cm</text>
<target>Cyclohexene</target>
</item>
<item>
<script>frame 18; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>145/cm</text>
<target>Cyclohexene</target>
</item>
</jmolmenu>
</jmol>

=='''References.'''==
<references>
<ref name="C-C"> M. A. Fox, J. K. Whitesell, in ''''' '''Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen.'', Springer, 1995.
</ref>
<ref name="C"> J. Tsai, R. Taylor, C. Chothia, M. Gerstein, ''J Mol Biol'', 1999, '''290''', 253.</ref>
</references>

Rep:Kh1015TS

2018-03-14T10:34:18Z

Kh1015: /* Exercise 3: Reaction of 5,6-dimethylenecyclohexa-1,3-diene and Sulfur Dioxide. */

=='''1. Abstract.'''==
This paper studied eight Diels-Alder reactions and one Cheletropic reaction using two popular computational methods: PM6 and B3LYP (6-31 G(d) basis set) in GaussView 5.0. In Exercise 1-3, the MO calculation was used to identify the interacting frontier orbitals and possible secondary-orbital interactions. In Exercise 1, the C-C bond length of molecules optimized using PM6 level showed good agreement with literature with less than 1% percentage difference. IRC analysis at PM6 level in all exercises showed that the TS has been optimized. In Exercise 2 and Exercise 3, thermodynamic values (activation Gibbs-Free energy and Δ Gibbs-Free energy) were extracted from the log file output and rate constant was calculated using the activation Gibbs-Free energy based on method by D. A. McQuarrie (1997) <ref name="Rate" />.

=='''2. Aim.'''==
The aim of this study is to locate and characterize the transition states of several Diels-Alder reactions.

=='''3. Introduction.'''==

Chemical behaviour of a molecule is controlled by the electrons that participate in the chemical process <ref name="RCS Book" />. In particular, the electronic structure and properties in its stationary state could be described by the time-independent solution of Schrödinger’s equation:
<div align="center"><math>\hat{H} \psi_{A} = E_{A} \psi_{A}</math></div>
, where A labels the state of interest <ref name="RCS Book" />.

The above equation forms the foundation for quantum chemistry and modern computational methods.

For a given reaction where there is ambiguity in structure or mechanism, computational chemistry is useful in predicting the likeliest structure or mechanism. For example, in 1986, computational calculation correctly predicted and later experimentally confirmed a bent structure for methylene, which challenged the linear experimental value by Hertzberg thought to be true at the time <ref name="Methylene" />.

===A. Standard Computational Methods.===

The recurring challenge in computational method is that the Schrodinger equation can be solved exactly only for one-electron systems, while most molecules have much more than one electron in the system. To address this challenges, multiple methods have been developed to find increasingly accurate approximations to the Schrodinger equation for many-electron systems <ref name="RCS Book" />. Each of the methods has its own trade-off between accuracy and computational cost. With that in mind, two such methods had been selected in this study: semi-quantitative Parameterization Method 6 (PM6); and Density Functional Theory (DFT), Becke, 3-parameter, Lee-Yang-Parr (B3LYP).
====1) Semi Quantitative PM6 (Parameterization Method 6).====
PM6 is a modified semi-empirical method categorized under Neglect of Diatomic Differential Overlap (NDDO) <ref name="PM6" />.The main advantage of modified version of NDDO (MNDO) over its predecessors lies in the optimization of parameters to simulate molecular properties which is more accurate than calculations based on atomic properties <ref name="PM6" />. The inability of earlier MNDO to simulate hydrogen bond has been addressed in PM6 method, where the percentage difference of the average unsigned error (AUE) of a water dimer model (1.35 kcal mol<sup>-1</sup>) is 27% relative to that obtained by exhaustive analysis by Tschumper, et al. using CCSD(T) and a large basis set (5.00 kcal mol<sup>-1</sup>) <ref name="PM6" />.

====2) DFT, B3LYP (Density Functional Theory, Becke, 3-parameter, Lee-Yang-Parr).====
In general, DFT uses variational principle and one-electron density for the calculation and therefore bypasses the consideration of the many-electron wavefunction <ref name="RCS Book" />. From the Hohenberg-Kohn Theorems, it has been established that the ground state energy and all of its properties can be extracted from one-electron density alone <ref name="RCS Book" /><ref name="HKTheorem" />. DFT includes exchange-correlation functionals and self-consistent field type formalism <ref name="RCS Book" />. The basic form of DFT uses exchange and correlation terms of uniform electron gas, which is not a good approximation to the actual electron distribution in chemical systems. This error is most pronounced in two bonded atoms that have very high electronegativity difference (O-H for example), where there is a non-uniform distribution of electron density which is skewed towards the more electronegative atom. Hence, empirical inputs - such as atomic correlation energies or thermochemical databases - have been used to refine the DFT method <ref name="RCS Book" />. B3LYP is a hybrid DFT functional method whose energy term includes Slater exchange, the Hartree–Fock exchange, Becke’s exchange functional correction, the gradient-corrected correlation functional of Lee, Yang and Parr, and the local correlation functional of Vosko, Wilk and Nusair <ref name="B3LYP" /><ref name="B3LYP1" />.

===B. Finding a Stable or Transition structure in a PES.===

From the computational output, it is possible to model a potential energy surface (PES), that is dependent on one variable or more. In any given PES, there are 4 simple conditions which allow a user to find a stable structure or a transition structure <ref name="RCS Book" />:
====1) Determining Stationary Point via Gradient.====
<br><div align="center"><math>\frac{dE(\textbf{R})}{dR_{i}} = 0, i=1,2, . . . 3N_{atoms} - 6</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and R<sub>i</sub> refers to a specific member of the set.

====2) Characterizing Minimum Point via Curvature (Positive Force Constants).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{i}} > 0, i=1,2, . . . 3N_{atoms} - 6</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>i</sub> refers to a specific combination of R and bond angle (θ).

====3) Characterizing Transition Point via Curvature (One Unique Negative Force Constant corresponding to First Order Saddle Point in Reaction Coordinate (RC)).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{RC}} < 0</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>RC</sub> refers to a specific combination of R and bond angle (θ) at the lowest-possible transition state in the PES.

====4) Characterizing Transition Point via Curvature (Positive Force Constants For The Remaining Ones).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{i}} > 0, i=1,2, . . . 3N_{atoms} - 7</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>i</sub> refers to a specific combination of '''R''' and bond angle (θ).

While useful, it should be noted that the 4 conditions above '''could not differentiate between global and local stationary points''', which could impact the accuracy of geometry optimization if the geometry is trapped in a local minimum rather than global minimum.

===C.Intrinsic Reaction Coordinate (IRC).===
In 1970, Fukui proposed the concept of IRC, which is defined as the mass-weighted, vibrationless, motionless and steepest descent path on the PES from the TS or the first-order saddle point to two minima on either side of the TS <ref name="IRC" />. The descent from higher-order saddle point is called meta-IRC <ref name="IRC" />. In mathematical form, IRC is obtained by solving the following differential equation <ref name="IRC" />:
<br><div align="center"><math>\frac{d\textbf{q}(s)}{ds} = \textbf{v}(s)</math></div>
, where '''q''' is the mass-weighted Cartesian coordinates, s is the coordinate along the IRC and '''v''' is a normalized tangent vector to the IRC corresponding to the normal coordinate eigenvector with a negative eigenvalue at the TS with s=0.

At the other points, '''v''' is the unit vector parallel to the mass-weighted gradient vector '''g''' with the following relationship <ref name="IRC" />:
<br><div align="center"><math>\textbf{v} = - \frac{\textbf{g}}{|\textbf{g}|}</math> for s > 0</div>
<br><div align="center"> and </div>
<br><div align="center"><math>\textbf{v} = \frac{\textbf{g}}{|\textbf{g}|}</math> for s < 0</div>

IRC calculation has been used extensively to confirm the connection between a given TS and two minima (reactant(s) and product(s)) for a given reaction <ref name="IRC" />. In this study, IRC calculation had been done for all the reactions such that it can be used to '''independently confirm''' that the TS geometry for the given reaction had truly been optimized.

From a successful IRC calculation (Minimum-TS-Minimum), it is possible to extract the calculated activation energy (linked to a given computational method) and therefore, the calculated rate constant for a reaction via transition state theory <ref name="IRC" />.

===D. Predicting Rate of Reaction from Calculated Thermodynamic Values.===
Once the activation free-energy of a reaction is calculated, it is possible to calculate the predicted rate of reaction via the equation below <ref name="Rate" />:
<br><div align="center"><math> k(T) = \frac{k_{B}T}{hc^{o}} e^{\frac{-\Delta^{\ddagger}G^{o}}{RT}} </math></div>

, where k(T) is rate constant at a specified temperature, k<sub>B</sub> is Boltzmann constant (1.3807 x 10<sup>-23</sup> J K<sup>-1</sup>), T is temperature (in K), h is Planck's constant (6.626176 x 10<sup>-34</sup> J s), c<sup>o</sup> is concentration (taken to be 1, unitless), Δ<sup>‡</sup>G<sup>o</sup> is the activation Gibbs-Free Energy (J mol<sup>-1</sup>) and R is gas constant (8.314 J mol<sup>-1</sup> K<sup>-1</sup>).

===E. Diels-Alder Reaction as a Study Topic.===
Diels-Alder reaction is a concerted [<sub>π</sub>4<sub>s</sub> + <sub>π</sub>2<sub>s</sub>] cycloaddition between an s-cis conjugated diene and a dienophile to form a cyclohexene <ref name="DA" />. In the reaction, 3 π bonds are broken and 2 sigma bonds and 1 new π bond is formed. In a normal Diels-Alder reaction, the interaction happens between an electron-rich s-cis dienophile and an electron poor diene. In an inverse-electron-demand Diels-Alder reaction, the interaction happens between an electron-poor s-cis dienophile and an electron rich diene.

There is a strong research interest in this reaction due to its importance in biosynthetic processes, use as a protecting group and recent discovery of enzyme Diels-Alderase in nature (for example, spirotetronate cyclase AbyU), which could unlock new and efficient Diels-Alder reactions <ref name="DA" /><ref name="DA2" /><ref name="DAE1" /><ref name="DAE2" /><ref name="DAE3" /><ref name="DAE4" /><ref name="DAE5" /><ref name="DAE6" /><ref name="DAE7" /><ref name="DAE8" />. In the area of computational chemistry, there are many researches about the geometry of the transition states involved in Diels-Alder reactions and the overall reaction profiles <ref name="DA" /><ref name="DA1" /><ref name="DA2" /><ref name="DA3" />.

=='''4. Methodology.'''==
The calculation results assumed two reacting molecules in gaseous phase (in absence of solvation and other interactions with non-reacting, neighbouring molecules). The temperature and pressure settings in the calculations were 298.15 K and 1 atm (default settings). The symmetry and molecular geometries of the products and reactants were not restricted in the optimization process. All of the calculations were performed in GaussView 5.0 and the calculation grid was set to ultrafine (integral=grid=ultrafine). For TS calculations, additional keyword (opt=noeigen) was used in response to possible error in link 9999.

The non-covalent interaction plots were generated using a script by Henry Rzepa and Bob Hanson <ref name="NCI" /> using default parameters for intermolecular reaction (minimum rho cutoff set to 0.3, covalent density cutoff set to 0.07, fraction of total rho that defined intramolecular interaction set to 0.95, data scaling set to 1).

Unless stated otherwise, all of the optimization jobs were followed by frequency analysis.

===Exercise 1: Reaction of Butadiene with Ethylene.===
Cyclohexene (product) was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.2 Å at the reacting C-C termini. While freezing the coordinates of the reacting C-C termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of Butadiene and Ethylene.

Figure 4.1 shows the reaction scheme for Exercise 1.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex 1.png|thumb|400px| Figure 4.1: Exercise 1 Reaction Scheme.]]
|}

===Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole.===
The endo product was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.2 Å at the reacting C-C termini. While freezing the coordinates of the reacting C-C termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of Cyclohexadiene and 1,3-Dioxole.

The optimized structure at PM6 level was reoptimized at B3LYP/6-31G(d) level for the endo product, TS and the reactants.

The above procedures were repeated for the exo-product, with the exception of the reactants.

Figure 4.2 shows the reaction scheme for Exercise 2.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex 2.png|thumb|400px| Figure 4.2: Exercise 2 Reaction Scheme.]]
|}

===Exercise 3: Reaction of 5,6-dimethylenecyclohexa-1,3-diene and Sulfur Dioxide.===
The endo product was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.0 Å at the reacting C-O termini and 2.4 Å at the reacting C-S termini. While freezing the coordinates of the reacting termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of 5,6-dimethylenecyclohexa-1,3-diene and sulfur dioxide.

The above procedures were repeated for the exo-product, cheletropic-product and two minor Diels Alder regio-isomers, with the exception of reactants.

Figure 4.3 shows the reaction scheme for Exercise 3.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex 3.png|thumb|500px| Figure 4.3: Exercise 3 Reaction Scheme.]]
|}

=='''5. Results and Discussion.'''==
===Exercise 1: Reaction of Butadiene with Ethylene.===

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx1RD Exercise 1 Results and Discussion.]

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

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx2RD Exercise 2 Results and Discussion.]

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

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx3RD Exercise 3 Results and Discussion.]

=='''6. Conclusion.'''==
In conclusion, this paper had successfully carried out computational calculations to study eight Diels-Alder reactions and one Cheletropic reaction using two popular computational methods: PM6 and B3LYP (6-31 G(d) basis set) in GaussView 5.0. For future work, the calculated results could be shared with other teams who could carry out the experiments in the lab to verify the results.

=='''7. References.'''==
<references>
<ref name="RCS Book">J. J. W. McDouall, in ''Computational Quantum Chemistry: Molecular Structure and Properties in Silico'', Royal Society of Chemistry, 2013, ch. 1, pp. 1-62.
</ref>
<ref name="Methylene"> H. F. SCHAEFER III, ''Science'', 1986, '''231''', 1100-1107.</ref>
<ref name="NCI"> Mod:NCI, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:NCI, (accessed March 2018).</ref>
<ref name="HKTheorem"> P. Hohenberg, W. Kohn, ''Phys. Rev.'', 1964, '''136(3B)''', B864–B871.</ref>
<ref name="PM6"> J. J. P. Stewart, '' J Mol Model'', 2007, '''13''', 1173-1213.</ref>
<ref name="B3LYP"> D. Avci, A. Başoğlu, Y. Atalay, '' Z. Naturforsch.'', 2008, '''63a''', 712-720.</ref>
<ref name="B3LYP1"> S.H. Vosko, L. Wilk, and M. Nusair, '' Can. J. Phys'', 1980, '''58''', 1200.</ref>
<ref name="DA"> T. J. Brocksom, J. Nakamura, M. L. Ferreira and U. Brocksom, '' J. Braz. Chem. Soc.'', 2001, '''12''', 597-622.</ref>
<ref name="DA1"> K. N. Houk, J. Gonzalez, Y. Li, ''Acc. Chem. Res.'', 1995, '''28''', 81-90.</ref>
<ref name="DA2"> J. Chen, Q. Deng, R. Wang, K. N. Houk, D. Hilvert, ''ChemBioChem'', 2000, '''1''', 255-261.</ref>
<ref name="DA3"> D. J. Tantillo, K. N. Houk, M. E. J. Jung, ''Org. Chem.'', 2001, '''66''', 1938-1940.</ref>
<ref name="DAE1"> K. N. Houk, J. Gonzalez, Y. Li, ''Acc. Chem. Res.'', 1995, '''28''', 81-90.</ref>
<ref name="DAE2"> W. M. Bandaranayake, J. E. Banfield, D. St. C. Black, ''J. Chem. Soc., Chem. Commun.'', 1980, 902-903.</ref>
<ref name="DAE3"> K. C. Nicolaou, N. A. Petasis, in ''Strategies and Tactics in Organic Synthesis'', ed. T. Lindberg, Academic Press, 1984, ch. 6, pp. 153-170.</ref>
<ref name="DAE4"> W. R. Roush, K. Koyama, M. L. Curtin, K. J. Moriarty, ''J. Am. Chem. Soc.'', 1996, '''118''', 7502-7512.</ref>
<ref name="DAE5"> H. Oikawa, T. Kobayashi, K. Katayama, Y. Suzuki, A. Ichihara, ''J. Org. Chem.'', 1998, '''63''', 8748-8756.</ref>
<ref name="DAE6"> E. M. Stocking, J. F. Sanz-Cervera, R. M. Williams, ''J. Am. Chem. Soc.'', 2000, '''122''', 1675-1683.</ref>
<ref name="DAE7"> G. A. Wallace, C. H. Heathcock, ''J. Org. Chem.'', 2001, '''66''', 450-454.</ref>
<ref name="DAE8"> K. Auclair, A. Sutherland, J. Kennedy, D. J. Witter, J. P. Van den Heever, C. R. Hutchinson, J. C. Vederas, ''J. Am. Chem. Soc.'', 2000, '''122''', 11519-11520.</ref>
<ref name="IRC"> S. Maeda, Y. Harabuchi, Y. Ono, T. Taketsugu, K. Morokuma, ''International Journal of Quantum Chemistry'', 2015, '''115''', 258-269.</ref>
<ref name="Rate">D. A. McQuarrie, in ''Physical Chemistry : A Molecular Approach'', University Science Books, 1997.
</ref>
</references>

Rep:Kh1015TS

2018-03-14T10:33:55Z

Kh1015: /* Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole. */

=='''1. Abstract.'''==
This paper studied eight Diels-Alder reactions and one Cheletropic reaction using two popular computational methods: PM6 and B3LYP (6-31 G(d) basis set) in GaussView 5.0. In Exercise 1-3, the MO calculation was used to identify the interacting frontier orbitals and possible secondary-orbital interactions. In Exercise 1, the C-C bond length of molecules optimized using PM6 level showed good agreement with literature with less than 1% percentage difference. IRC analysis at PM6 level in all exercises showed that the TS has been optimized. In Exercise 2 and Exercise 3, thermodynamic values (activation Gibbs-Free energy and Δ Gibbs-Free energy) were extracted from the log file output and rate constant was calculated using the activation Gibbs-Free energy based on method by D. A. McQuarrie (1997) <ref name="Rate" />.

=='''2. Aim.'''==
The aim of this study is to locate and characterize the transition states of several Diels-Alder reactions.

=='''3. Introduction.'''==

Chemical behaviour of a molecule is controlled by the electrons that participate in the chemical process <ref name="RCS Book" />. In particular, the electronic structure and properties in its stationary state could be described by the time-independent solution of Schrödinger’s equation:
<div align="center"><math>\hat{H} \psi_{A} = E_{A} \psi_{A}</math></div>
, where A labels the state of interest <ref name="RCS Book" />.

The above equation forms the foundation for quantum chemistry and modern computational methods.

For a given reaction where there is ambiguity in structure or mechanism, computational chemistry is useful in predicting the likeliest structure or mechanism. For example, in 1986, computational calculation correctly predicted and later experimentally confirmed a bent structure for methylene, which challenged the linear experimental value by Hertzberg thought to be true at the time <ref name="Methylene" />.

===A. Standard Computational Methods.===

The recurring challenge in computational method is that the Schrodinger equation can be solved exactly only for one-electron systems, while most molecules have much more than one electron in the system. To address this challenges, multiple methods have been developed to find increasingly accurate approximations to the Schrodinger equation for many-electron systems <ref name="RCS Book" />. Each of the methods has its own trade-off between accuracy and computational cost. With that in mind, two such methods had been selected in this study: semi-quantitative Parameterization Method 6 (PM6); and Density Functional Theory (DFT), Becke, 3-parameter, Lee-Yang-Parr (B3LYP).
====1) Semi Quantitative PM6 (Parameterization Method 6).====
PM6 is a modified semi-empirical method categorized under Neglect of Diatomic Differential Overlap (NDDO) <ref name="PM6" />.The main advantage of modified version of NDDO (MNDO) over its predecessors lies in the optimization of parameters to simulate molecular properties which is more accurate than calculations based on atomic properties <ref name="PM6" />. The inability of earlier MNDO to simulate hydrogen bond has been addressed in PM6 method, where the percentage difference of the average unsigned error (AUE) of a water dimer model (1.35 kcal mol<sup>-1</sup>) is 27% relative to that obtained by exhaustive analysis by Tschumper, et al. using CCSD(T) and a large basis set (5.00 kcal mol<sup>-1</sup>) <ref name="PM6" />.

====2) DFT, B3LYP (Density Functional Theory, Becke, 3-parameter, Lee-Yang-Parr).====
In general, DFT uses variational principle and one-electron density for the calculation and therefore bypasses the consideration of the many-electron wavefunction <ref name="RCS Book" />. From the Hohenberg-Kohn Theorems, it has been established that the ground state energy and all of its properties can be extracted from one-electron density alone <ref name="RCS Book" /><ref name="HKTheorem" />. DFT includes exchange-correlation functionals and self-consistent field type formalism <ref name="RCS Book" />. The basic form of DFT uses exchange and correlation terms of uniform electron gas, which is not a good approximation to the actual electron distribution in chemical systems. This error is most pronounced in two bonded atoms that have very high electronegativity difference (O-H for example), where there is a non-uniform distribution of electron density which is skewed towards the more electronegative atom. Hence, empirical inputs - such as atomic correlation energies or thermochemical databases - have been used to refine the DFT method <ref name="RCS Book" />. B3LYP is a hybrid DFT functional method whose energy term includes Slater exchange, the Hartree–Fock exchange, Becke’s exchange functional correction, the gradient-corrected correlation functional of Lee, Yang and Parr, and the local correlation functional of Vosko, Wilk and Nusair <ref name="B3LYP" /><ref name="B3LYP1" />.

===B. Finding a Stable or Transition structure in a PES.===

From the computational output, it is possible to model a potential energy surface (PES), that is dependent on one variable or more. In any given PES, there are 4 simple conditions which allow a user to find a stable structure or a transition structure <ref name="RCS Book" />:
====1) Determining Stationary Point via Gradient.====
<br><div align="center"><math>\frac{dE(\textbf{R})}{dR_{i}} = 0, i=1,2, . . . 3N_{atoms} - 6</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and R<sub>i</sub> refers to a specific member of the set.

====2) Characterizing Minimum Point via Curvature (Positive Force Constants).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{i}} > 0, i=1,2, . . . 3N_{atoms} - 6</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>i</sub> refers to a specific combination of R and bond angle (θ).

====3) Characterizing Transition Point via Curvature (One Unique Negative Force Constant corresponding to First Order Saddle Point in Reaction Coordinate (RC)).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{RC}} < 0</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>RC</sub> refers to a specific combination of R and bond angle (θ) at the lowest-possible transition state in the PES.

====4) Characterizing Transition Point via Curvature (Positive Force Constants For The Remaining Ones).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{i}} > 0, i=1,2, . . . 3N_{atoms} - 7</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>i</sub> refers to a specific combination of '''R''' and bond angle (θ).

While useful, it should be noted that the 4 conditions above '''could not differentiate between global and local stationary points''', which could impact the accuracy of geometry optimization if the geometry is trapped in a local minimum rather than global minimum.

===C.Intrinsic Reaction Coordinate (IRC).===
In 1970, Fukui proposed the concept of IRC, which is defined as the mass-weighted, vibrationless, motionless and steepest descent path on the PES from the TS or the first-order saddle point to two minima on either side of the TS <ref name="IRC" />. The descent from higher-order saddle point is called meta-IRC <ref name="IRC" />. In mathematical form, IRC is obtained by solving the following differential equation <ref name="IRC" />:
<br><div align="center"><math>\frac{d\textbf{q}(s)}{ds} = \textbf{v}(s)</math></div>
, where '''q''' is the mass-weighted Cartesian coordinates, s is the coordinate along the IRC and '''v''' is a normalized tangent vector to the IRC corresponding to the normal coordinate eigenvector with a negative eigenvalue at the TS with s=0.

At the other points, '''v''' is the unit vector parallel to the mass-weighted gradient vector '''g''' with the following relationship <ref name="IRC" />:
<br><div align="center"><math>\textbf{v} = - \frac{\textbf{g}}{|\textbf{g}|}</math> for s > 0</div>
<br><div align="center"> and </div>
<br><div align="center"><math>\textbf{v} = \frac{\textbf{g}}{|\textbf{g}|}</math> for s < 0</div>

IRC calculation has been used extensively to confirm the connection between a given TS and two minima (reactant(s) and product(s)) for a given reaction <ref name="IRC" />. In this study, IRC calculation had been done for all the reactions such that it can be used to '''independently confirm''' that the TS geometry for the given reaction had truly been optimized.

From a successful IRC calculation (Minimum-TS-Minimum), it is possible to extract the calculated activation energy (linked to a given computational method) and therefore, the calculated rate constant for a reaction via transition state theory <ref name="IRC" />.

===D. Predicting Rate of Reaction from Calculated Thermodynamic Values.===
Once the activation free-energy of a reaction is calculated, it is possible to calculate the predicted rate of reaction via the equation below <ref name="Rate" />:
<br><div align="center"><math> k(T) = \frac{k_{B}T}{hc^{o}} e^{\frac{-\Delta^{\ddagger}G^{o}}{RT}} </math></div>

, where k(T) is rate constant at a specified temperature, k<sub>B</sub> is Boltzmann constant (1.3807 x 10<sup>-23</sup> J K<sup>-1</sup>), T is temperature (in K), h is Planck's constant (6.626176 x 10<sup>-34</sup> J s), c<sup>o</sup> is concentration (taken to be 1, unitless), Δ<sup>‡</sup>G<sup>o</sup> is the activation Gibbs-Free Energy (J mol<sup>-1</sup>) and R is gas constant (8.314 J mol<sup>-1</sup> K<sup>-1</sup>).

===E. Diels-Alder Reaction as a Study Topic.===
Diels-Alder reaction is a concerted [<sub>π</sub>4<sub>s</sub> + <sub>π</sub>2<sub>s</sub>] cycloaddition between an s-cis conjugated diene and a dienophile to form a cyclohexene <ref name="DA" />. In the reaction, 3 π bonds are broken and 2 sigma bonds and 1 new π bond is formed. In a normal Diels-Alder reaction, the interaction happens between an electron-rich s-cis dienophile and an electron poor diene. In an inverse-electron-demand Diels-Alder reaction, the interaction happens between an electron-poor s-cis dienophile and an electron rich diene.

There is a strong research interest in this reaction due to its importance in biosynthetic processes, use as a protecting group and recent discovery of enzyme Diels-Alderase in nature (for example, spirotetronate cyclase AbyU), which could unlock new and efficient Diels-Alder reactions <ref name="DA" /><ref name="DA2" /><ref name="DAE1" /><ref name="DAE2" /><ref name="DAE3" /><ref name="DAE4" /><ref name="DAE5" /><ref name="DAE6" /><ref name="DAE7" /><ref name="DAE8" />. In the area of computational chemistry, there are many researches about the geometry of the transition states involved in Diels-Alder reactions and the overall reaction profiles <ref name="DA" /><ref name="DA1" /><ref name="DA2" /><ref name="DA3" />.

=='''4. Methodology.'''==
The calculation results assumed two reacting molecules in gaseous phase (in absence of solvation and other interactions with non-reacting, neighbouring molecules). The temperature and pressure settings in the calculations were 298.15 K and 1 atm (default settings). The symmetry and molecular geometries of the products and reactants were not restricted in the optimization process. All of the calculations were performed in GaussView 5.0 and the calculation grid was set to ultrafine (integral=grid=ultrafine). For TS calculations, additional keyword (opt=noeigen) was used in response to possible error in link 9999.

The non-covalent interaction plots were generated using a script by Henry Rzepa and Bob Hanson <ref name="NCI" /> using default parameters for intermolecular reaction (minimum rho cutoff set to 0.3, covalent density cutoff set to 0.07, fraction of total rho that defined intramolecular interaction set to 0.95, data scaling set to 1).

Unless stated otherwise, all of the optimization jobs were followed by frequency analysis.

===Exercise 1: Reaction of Butadiene with Ethylene.===
Cyclohexene (product) was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.2 Å at the reacting C-C termini. While freezing the coordinates of the reacting C-C termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of Butadiene and Ethylene.

Figure 4.1 shows the reaction scheme for Exercise 1.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex 1.png|thumb|400px| Figure 4.1: Exercise 1 Reaction Scheme.]]
|}

===Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole.===
The endo product was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.2 Å at the reacting C-C termini. While freezing the coordinates of the reacting C-C termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of Cyclohexadiene and 1,3-Dioxole.

The optimized structure at PM6 level was reoptimized at B3LYP/6-31G(d) level for the endo product, TS and the reactants.

The above procedures were repeated for the exo-product, with the exception of the reactants.

Figure 4.2 shows the reaction scheme for Exercise 2.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex 2.png|thumb|400px| Figure 4.2: Exercise 2 Reaction Scheme.]]
|}

===Exercise 3: Reaction of 5,6-dimethylenecyclohexa-1,3-diene and Sulfur Dioxide.===
The endo product was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.0 Å at the reacting C-O termini and 2.4 Å at the reacting C-S termini. While freezing the coordinates of the reacting termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of 5,6-dimethylenecyclohexa-1,3-diene and sulfur dioxide.

The above procedures were repeated for the exo-product, cheletropic-product and two minor Diels Alder regio-isomers, with the exception of reactants.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex 3.png|thumb|500px| Figure 4.3: Exercise 3 Reaction Scheme.]]
|}

=='''5. Results and Discussion.'''==
===Exercise 1: Reaction of Butadiene with Ethylene.===

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx1RD Exercise 1 Results and Discussion.]

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

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx2RD Exercise 2 Results and Discussion.]

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

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx3RD Exercise 3 Results and Discussion.]

=='''6. Conclusion.'''==
In conclusion, this paper had successfully carried out computational calculations to study eight Diels-Alder reactions and one Cheletropic reaction using two popular computational methods: PM6 and B3LYP (6-31 G(d) basis set) in GaussView 5.0. For future work, the calculated results could be shared with other teams who could carry out the experiments in the lab to verify the results.

=='''7. References.'''==
<references>
<ref name="RCS Book">J. J. W. McDouall, in ''Computational Quantum Chemistry: Molecular Structure and Properties in Silico'', Royal Society of Chemistry, 2013, ch. 1, pp. 1-62.
</ref>
<ref name="Methylene"> H. F. SCHAEFER III, ''Science'', 1986, '''231''', 1100-1107.</ref>
<ref name="NCI"> Mod:NCI, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:NCI, (accessed March 2018).</ref>
<ref name="HKTheorem"> P. Hohenberg, W. Kohn, ''Phys. Rev.'', 1964, '''136(3B)''', B864–B871.</ref>
<ref name="PM6"> J. J. P. Stewart, '' J Mol Model'', 2007, '''13''', 1173-1213.</ref>
<ref name="B3LYP"> D. Avci, A. Başoğlu, Y. Atalay, '' Z. Naturforsch.'', 2008, '''63a''', 712-720.</ref>
<ref name="B3LYP1"> S.H. Vosko, L. Wilk, and M. Nusair, '' Can. J. Phys'', 1980, '''58''', 1200.</ref>
<ref name="DA"> T. J. Brocksom, J. Nakamura, M. L. Ferreira and U. Brocksom, '' J. Braz. Chem. Soc.'', 2001, '''12''', 597-622.</ref>
<ref name="DA1"> K. N. Houk, J. Gonzalez, Y. Li, ''Acc. Chem. Res.'', 1995, '''28''', 81-90.</ref>
<ref name="DA2"> J. Chen, Q. Deng, R. Wang, K. N. Houk, D. Hilvert, ''ChemBioChem'', 2000, '''1''', 255-261.</ref>
<ref name="DA3"> D. J. Tantillo, K. N. Houk, M. E. J. Jung, ''Org. Chem.'', 2001, '''66''', 1938-1940.</ref>
<ref name="DAE1"> K. N. Houk, J. Gonzalez, Y. Li, ''Acc. Chem. Res.'', 1995, '''28''', 81-90.</ref>
<ref name="DAE2"> W. M. Bandaranayake, J. E. Banfield, D. St. C. Black, ''J. Chem. Soc., Chem. Commun.'', 1980, 902-903.</ref>
<ref name="DAE3"> K. C. Nicolaou, N. A. Petasis, in ''Strategies and Tactics in Organic Synthesis'', ed. T. Lindberg, Academic Press, 1984, ch. 6, pp. 153-170.</ref>
<ref name="DAE4"> W. R. Roush, K. Koyama, M. L. Curtin, K. J. Moriarty, ''J. Am. Chem. Soc.'', 1996, '''118''', 7502-7512.</ref>
<ref name="DAE5"> H. Oikawa, T. Kobayashi, K. Katayama, Y. Suzuki, A. Ichihara, ''J. Org. Chem.'', 1998, '''63''', 8748-8756.</ref>
<ref name="DAE6"> E. M. Stocking, J. F. Sanz-Cervera, R. M. Williams, ''J. Am. Chem. Soc.'', 2000, '''122''', 1675-1683.</ref>
<ref name="DAE7"> G. A. Wallace, C. H. Heathcock, ''J. Org. Chem.'', 2001, '''66''', 450-454.</ref>
<ref name="DAE8"> K. Auclair, A. Sutherland, J. Kennedy, D. J. Witter, J. P. Van den Heever, C. R. Hutchinson, J. C. Vederas, ''J. Am. Chem. Soc.'', 2000, '''122''', 11519-11520.</ref>
<ref name="IRC"> S. Maeda, Y. Harabuchi, Y. Ono, T. Taketsugu, K. Morokuma, ''International Journal of Quantum Chemistry'', 2015, '''115''', 258-269.</ref>
<ref name="Rate">D. A. McQuarrie, in ''Physical Chemistry : A Molecular Approach'', University Science Books, 1997.
</ref>
</references>

Rep:Kh1015TS

2018-03-14T10:33:36Z

Kh1015: /* Exercise 1: Reaction of Butadiene with Ethylene. */

=='''1. Abstract.'''==
This paper studied eight Diels-Alder reactions and one Cheletropic reaction using two popular computational methods: PM6 and B3LYP (6-31 G(d) basis set) in GaussView 5.0. In Exercise 1-3, the MO calculation was used to identify the interacting frontier orbitals and possible secondary-orbital interactions. In Exercise 1, the C-C bond length of molecules optimized using PM6 level showed good agreement with literature with less than 1% percentage difference. IRC analysis at PM6 level in all exercises showed that the TS has been optimized. In Exercise 2 and Exercise 3, thermodynamic values (activation Gibbs-Free energy and Δ Gibbs-Free energy) were extracted from the log file output and rate constant was calculated using the activation Gibbs-Free energy based on method by D. A. McQuarrie (1997) <ref name="Rate" />.

=='''2. Aim.'''==
The aim of this study is to locate and characterize the transition states of several Diels-Alder reactions.

=='''3. Introduction.'''==

Chemical behaviour of a molecule is controlled by the electrons that participate in the chemical process <ref name="RCS Book" />. In particular, the electronic structure and properties in its stationary state could be described by the time-independent solution of Schrödinger’s equation:
<div align="center"><math>\hat{H} \psi_{A} = E_{A} \psi_{A}</math></div>
, where A labels the state of interest <ref name="RCS Book" />.

The above equation forms the foundation for quantum chemistry and modern computational methods.

For a given reaction where there is ambiguity in structure or mechanism, computational chemistry is useful in predicting the likeliest structure or mechanism. For example, in 1986, computational calculation correctly predicted and later experimentally confirmed a bent structure for methylene, which challenged the linear experimental value by Hertzberg thought to be true at the time <ref name="Methylene" />.

===A. Standard Computational Methods.===

The recurring challenge in computational method is that the Schrodinger equation can be solved exactly only for one-electron systems, while most molecules have much more than one electron in the system. To address this challenges, multiple methods have been developed to find increasingly accurate approximations to the Schrodinger equation for many-electron systems <ref name="RCS Book" />. Each of the methods has its own trade-off between accuracy and computational cost. With that in mind, two such methods had been selected in this study: semi-quantitative Parameterization Method 6 (PM6); and Density Functional Theory (DFT), Becke, 3-parameter, Lee-Yang-Parr (B3LYP).
====1) Semi Quantitative PM6 (Parameterization Method 6).====
PM6 is a modified semi-empirical method categorized under Neglect of Diatomic Differential Overlap (NDDO) <ref name="PM6" />.The main advantage of modified version of NDDO (MNDO) over its predecessors lies in the optimization of parameters to simulate molecular properties which is more accurate than calculations based on atomic properties <ref name="PM6" />. The inability of earlier MNDO to simulate hydrogen bond has been addressed in PM6 method, where the percentage difference of the average unsigned error (AUE) of a water dimer model (1.35 kcal mol<sup>-1</sup>) is 27% relative to that obtained by exhaustive analysis by Tschumper, et al. using CCSD(T) and a large basis set (5.00 kcal mol<sup>-1</sup>) <ref name="PM6" />.

====2) DFT, B3LYP (Density Functional Theory, Becke, 3-parameter, Lee-Yang-Parr).====
In general, DFT uses variational principle and one-electron density for the calculation and therefore bypasses the consideration of the many-electron wavefunction <ref name="RCS Book" />. From the Hohenberg-Kohn Theorems, it has been established that the ground state energy and all of its properties can be extracted from one-electron density alone <ref name="RCS Book" /><ref name="HKTheorem" />. DFT includes exchange-correlation functionals and self-consistent field type formalism <ref name="RCS Book" />. The basic form of DFT uses exchange and correlation terms of uniform electron gas, which is not a good approximation to the actual electron distribution in chemical systems. This error is most pronounced in two bonded atoms that have very high electronegativity difference (O-H for example), where there is a non-uniform distribution of electron density which is skewed towards the more electronegative atom. Hence, empirical inputs - such as atomic correlation energies or thermochemical databases - have been used to refine the DFT method <ref name="RCS Book" />. B3LYP is a hybrid DFT functional method whose energy term includes Slater exchange, the Hartree–Fock exchange, Becke’s exchange functional correction, the gradient-corrected correlation functional of Lee, Yang and Parr, and the local correlation functional of Vosko, Wilk and Nusair <ref name="B3LYP" /><ref name="B3LYP1" />.

===B. Finding a Stable or Transition structure in a PES.===

From the computational output, it is possible to model a potential energy surface (PES), that is dependent on one variable or more. In any given PES, there are 4 simple conditions which allow a user to find a stable structure or a transition structure <ref name="RCS Book" />:
====1) Determining Stationary Point via Gradient.====
<br><div align="center"><math>\frac{dE(\textbf{R})}{dR_{i}} = 0, i=1,2, . . . 3N_{atoms} - 6</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and R<sub>i</sub> refers to a specific member of the set.

====2) Characterizing Minimum Point via Curvature (Positive Force Constants).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{i}} > 0, i=1,2, . . . 3N_{atoms} - 6</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>i</sub> refers to a specific combination of R and bond angle (θ).

====3) Characterizing Transition Point via Curvature (One Unique Negative Force Constant corresponding to First Order Saddle Point in Reaction Coordinate (RC)).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{RC}} < 0</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>RC</sub> refers to a specific combination of R and bond angle (θ) at the lowest-possible transition state in the PES.

====4) Characterizing Transition Point via Curvature (Positive Force Constants For The Remaining Ones).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{i}} > 0, i=1,2, . . . 3N_{atoms} - 7</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>i</sub> refers to a specific combination of '''R''' and bond angle (θ).

While useful, it should be noted that the 4 conditions above '''could not differentiate between global and local stationary points''', which could impact the accuracy of geometry optimization if the geometry is trapped in a local minimum rather than global minimum.

===C.Intrinsic Reaction Coordinate (IRC).===
In 1970, Fukui proposed the concept of IRC, which is defined as the mass-weighted, vibrationless, motionless and steepest descent path on the PES from the TS or the first-order saddle point to two minima on either side of the TS <ref name="IRC" />. The descent from higher-order saddle point is called meta-IRC <ref name="IRC" />. In mathematical form, IRC is obtained by solving the following differential equation <ref name="IRC" />:
<br><div align="center"><math>\frac{d\textbf{q}(s)}{ds} = \textbf{v}(s)</math></div>
, where '''q''' is the mass-weighted Cartesian coordinates, s is the coordinate along the IRC and '''v''' is a normalized tangent vector to the IRC corresponding to the normal coordinate eigenvector with a negative eigenvalue at the TS with s=0.

At the other points, '''v''' is the unit vector parallel to the mass-weighted gradient vector '''g''' with the following relationship <ref name="IRC" />:
<br><div align="center"><math>\textbf{v} = - \frac{\textbf{g}}{|\textbf{g}|}</math> for s > 0</div>
<br><div align="center"> and </div>
<br><div align="center"><math>\textbf{v} = \frac{\textbf{g}}{|\textbf{g}|}</math> for s < 0</div>

IRC calculation has been used extensively to confirm the connection between a given TS and two minima (reactant(s) and product(s)) for a given reaction <ref name="IRC" />. In this study, IRC calculation had been done for all the reactions such that it can be used to '''independently confirm''' that the TS geometry for the given reaction had truly been optimized.

From a successful IRC calculation (Minimum-TS-Minimum), it is possible to extract the calculated activation energy (linked to a given computational method) and therefore, the calculated rate constant for a reaction via transition state theory <ref name="IRC" />.

===D. Predicting Rate of Reaction from Calculated Thermodynamic Values.===
Once the activation free-energy of a reaction is calculated, it is possible to calculate the predicted rate of reaction via the equation below <ref name="Rate" />:
<br><div align="center"><math> k(T) = \frac{k_{B}T}{hc^{o}} e^{\frac{-\Delta^{\ddagger}G^{o}}{RT}} </math></div>

, where k(T) is rate constant at a specified temperature, k<sub>B</sub> is Boltzmann constant (1.3807 x 10<sup>-23</sup> J K<sup>-1</sup>), T is temperature (in K), h is Planck's constant (6.626176 x 10<sup>-34</sup> J s), c<sup>o</sup> is concentration (taken to be 1, unitless), Δ<sup>‡</sup>G<sup>o</sup> is the activation Gibbs-Free Energy (J mol<sup>-1</sup>) and R is gas constant (8.314 J mol<sup>-1</sup> K<sup>-1</sup>).

===E. Diels-Alder Reaction as a Study Topic.===
Diels-Alder reaction is a concerted [<sub>π</sub>4<sub>s</sub> + <sub>π</sub>2<sub>s</sub>] cycloaddition between an s-cis conjugated diene and a dienophile to form a cyclohexene <ref name="DA" />. In the reaction, 3 π bonds are broken and 2 sigma bonds and 1 new π bond is formed. In a normal Diels-Alder reaction, the interaction happens between an electron-rich s-cis dienophile and an electron poor diene. In an inverse-electron-demand Diels-Alder reaction, the interaction happens between an electron-poor s-cis dienophile and an electron rich diene.

There is a strong research interest in this reaction due to its importance in biosynthetic processes, use as a protecting group and recent discovery of enzyme Diels-Alderase in nature (for example, spirotetronate cyclase AbyU), which could unlock new and efficient Diels-Alder reactions <ref name="DA" /><ref name="DA2" /><ref name="DAE1" /><ref name="DAE2" /><ref name="DAE3" /><ref name="DAE4" /><ref name="DAE5" /><ref name="DAE6" /><ref name="DAE7" /><ref name="DAE8" />. In the area of computational chemistry, there are many researches about the geometry of the transition states involved in Diels-Alder reactions and the overall reaction profiles <ref name="DA" /><ref name="DA1" /><ref name="DA2" /><ref name="DA3" />.

=='''4. Methodology.'''==
The calculation results assumed two reacting molecules in gaseous phase (in absence of solvation and other interactions with non-reacting, neighbouring molecules). The temperature and pressure settings in the calculations were 298.15 K and 1 atm (default settings). The symmetry and molecular geometries of the products and reactants were not restricted in the optimization process. All of the calculations were performed in GaussView 5.0 and the calculation grid was set to ultrafine (integral=grid=ultrafine). For TS calculations, additional keyword (opt=noeigen) was used in response to possible error in link 9999.

The non-covalent interaction plots were generated using a script by Henry Rzepa and Bob Hanson <ref name="NCI" /> using default parameters for intermolecular reaction (minimum rho cutoff set to 0.3, covalent density cutoff set to 0.07, fraction of total rho that defined intramolecular interaction set to 0.95, data scaling set to 1).

Unless stated otherwise, all of the optimization jobs were followed by frequency analysis.

===Exercise 1: Reaction of Butadiene with Ethylene.===
Cyclohexene (product) was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.2 Å at the reacting C-C termini. While freezing the coordinates of the reacting C-C termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of Butadiene and Ethylene.

Figure 4.1 shows the reaction scheme for Exercise 1.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex 1.png|thumb|400px| Figure 4.1: Exercise 1 Reaction Scheme.]]
|}

===Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole.===
The endo product was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.2 Å at the reacting C-C termini. While freezing the coordinates of the reacting C-C termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of Cyclohexadiene and 1,3-Dioxole.

The optimized structure at PM6 level was reoptimized at B3LYP/6-31G(d) level for the endo product, TS and the reactants.

The above procedures were repeated for the exo-product, with the exception of the reactants.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex 2.png|thumb|400px| Figure 4.2: Exercise 2 Reaction Scheme.]]
|}

===Exercise 3: Reaction of 5,6-dimethylenecyclohexa-1,3-diene and Sulfur Dioxide.===
The endo product was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.0 Å at the reacting C-O termini and 2.4 Å at the reacting C-S termini. While freezing the coordinates of the reacting termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of 5,6-dimethylenecyclohexa-1,3-diene and sulfur dioxide.

The above procedures were repeated for the exo-product, cheletropic-product and two minor Diels Alder regio-isomers, with the exception of reactants.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex 3.png|thumb|500px| Figure 4.3: Exercise 3 Reaction Scheme.]]
|}

=='''5. Results and Discussion.'''==
===Exercise 1: Reaction of Butadiene with Ethylene.===

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx1RD Exercise 1 Results and Discussion.]

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

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx2RD Exercise 2 Results and Discussion.]

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

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx3RD Exercise 3 Results and Discussion.]

=='''6. Conclusion.'''==
In conclusion, this paper had successfully carried out computational calculations to study eight Diels-Alder reactions and one Cheletropic reaction using two popular computational methods: PM6 and B3LYP (6-31 G(d) basis set) in GaussView 5.0. For future work, the calculated results could be shared with other teams who could carry out the experiments in the lab to verify the results.

=='''7. References.'''==
<references>
<ref name="RCS Book">J. J. W. McDouall, in ''Computational Quantum Chemistry: Molecular Structure and Properties in Silico'', Royal Society of Chemistry, 2013, ch. 1, pp. 1-62.
</ref>
<ref name="Methylene"> H. F. SCHAEFER III, ''Science'', 1986, '''231''', 1100-1107.</ref>
<ref name="NCI"> Mod:NCI, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:NCI, (accessed March 2018).</ref>
<ref name="HKTheorem"> P. Hohenberg, W. Kohn, ''Phys. Rev.'', 1964, '''136(3B)''', B864–B871.</ref>
<ref name="PM6"> J. J. P. Stewart, '' J Mol Model'', 2007, '''13''', 1173-1213.</ref>
<ref name="B3LYP"> D. Avci, A. Başoğlu, Y. Atalay, '' Z. Naturforsch.'', 2008, '''63a''', 712-720.</ref>
<ref name="B3LYP1"> S.H. Vosko, L. Wilk, and M. Nusair, '' Can. J. Phys'', 1980, '''58''', 1200.</ref>
<ref name="DA"> T. J. Brocksom, J. Nakamura, M. L. Ferreira and U. Brocksom, '' J. Braz. Chem. Soc.'', 2001, '''12''', 597-622.</ref>
<ref name="DA1"> K. N. Houk, J. Gonzalez, Y. Li, ''Acc. Chem. Res.'', 1995, '''28''', 81-90.</ref>
<ref name="DA2"> J. Chen, Q. Deng, R. Wang, K. N. Houk, D. Hilvert, ''ChemBioChem'', 2000, '''1''', 255-261.</ref>
<ref name="DA3"> D. J. Tantillo, K. N. Houk, M. E. J. Jung, ''Org. Chem.'', 2001, '''66''', 1938-1940.</ref>
<ref name="DAE1"> K. N. Houk, J. Gonzalez, Y. Li, ''Acc. Chem. Res.'', 1995, '''28''', 81-90.</ref>
<ref name="DAE2"> W. M. Bandaranayake, J. E. Banfield, D. St. C. Black, ''J. Chem. Soc., Chem. Commun.'', 1980, 902-903.</ref>
<ref name="DAE3"> K. C. Nicolaou, N. A. Petasis, in ''Strategies and Tactics in Organic Synthesis'', ed. T. Lindberg, Academic Press, 1984, ch. 6, pp. 153-170.</ref>
<ref name="DAE4"> W. R. Roush, K. Koyama, M. L. Curtin, K. J. Moriarty, ''J. Am. Chem. Soc.'', 1996, '''118''', 7502-7512.</ref>
<ref name="DAE5"> H. Oikawa, T. Kobayashi, K. Katayama, Y. Suzuki, A. Ichihara, ''J. Org. Chem.'', 1998, '''63''', 8748-8756.</ref>
<ref name="DAE6"> E. M. Stocking, J. F. Sanz-Cervera, R. M. Williams, ''J. Am. Chem. Soc.'', 2000, '''122''', 1675-1683.</ref>
<ref name="DAE7"> G. A. Wallace, C. H. Heathcock, ''J. Org. Chem.'', 2001, '''66''', 450-454.</ref>
<ref name="DAE8"> K. Auclair, A. Sutherland, J. Kennedy, D. J. Witter, J. P. Van den Heever, C. R. Hutchinson, J. C. Vederas, ''J. Am. Chem. Soc.'', 2000, '''122''', 11519-11520.</ref>
<ref name="IRC"> S. Maeda, Y. Harabuchi, Y. Ono, T. Taketsugu, K. Morokuma, ''International Journal of Quantum Chemistry'', 2015, '''115''', 258-269.</ref>
<ref name="Rate">D. A. McQuarrie, in ''Physical Chemistry : A Molecular Approach'', University Science Books, 1997.
</ref>
</references>

Rep:Kh1015TS

2018-03-14T10:33:01Z

Kh1015: /* 6. Conclusion. */

=='''1. Abstract.'''==
This paper studied eight Diels-Alder reactions and one Cheletropic reaction using two popular computational methods: PM6 and B3LYP (6-31 G(d) basis set) in GaussView 5.0. In Exercise 1-3, the MO calculation was used to identify the interacting frontier orbitals and possible secondary-orbital interactions. In Exercise 1, the C-C bond length of molecules optimized using PM6 level showed good agreement with literature with less than 1% percentage difference. IRC analysis at PM6 level in all exercises showed that the TS has been optimized. In Exercise 2 and Exercise 3, thermodynamic values (activation Gibbs-Free energy and Δ Gibbs-Free energy) were extracted from the log file output and rate constant was calculated using the activation Gibbs-Free energy based on method by D. A. McQuarrie (1997) <ref name="Rate" />.

=='''2. Aim.'''==
The aim of this study is to locate and characterize the transition states of several Diels-Alder reactions.

=='''3. Introduction.'''==

Chemical behaviour of a molecule is controlled by the electrons that participate in the chemical process <ref name="RCS Book" />. In particular, the electronic structure and properties in its stationary state could be described by the time-independent solution of Schrödinger’s equation:
<div align="center"><math>\hat{H} \psi_{A} = E_{A} \psi_{A}</math></div>
, where A labels the state of interest <ref name="RCS Book" />.

The above equation forms the foundation for quantum chemistry and modern computational methods.

For a given reaction where there is ambiguity in structure or mechanism, computational chemistry is useful in predicting the likeliest structure or mechanism. For example, in 1986, computational calculation correctly predicted and later experimentally confirmed a bent structure for methylene, which challenged the linear experimental value by Hertzberg thought to be true at the time <ref name="Methylene" />.

===A. Standard Computational Methods.===

The recurring challenge in computational method is that the Schrodinger equation can be solved exactly only for one-electron systems, while most molecules have much more than one electron in the system. To address this challenges, multiple methods have been developed to find increasingly accurate approximations to the Schrodinger equation for many-electron systems <ref name="RCS Book" />. Each of the methods has its own trade-off between accuracy and computational cost. With that in mind, two such methods had been selected in this study: semi-quantitative Parameterization Method 6 (PM6); and Density Functional Theory (DFT), Becke, 3-parameter, Lee-Yang-Parr (B3LYP).
====1) Semi Quantitative PM6 (Parameterization Method 6).====
PM6 is a modified semi-empirical method categorized under Neglect of Diatomic Differential Overlap (NDDO) <ref name="PM6" />.The main advantage of modified version of NDDO (MNDO) over its predecessors lies in the optimization of parameters to simulate molecular properties which is more accurate than calculations based on atomic properties <ref name="PM6" />. The inability of earlier MNDO to simulate hydrogen bond has been addressed in PM6 method, where the percentage difference of the average unsigned error (AUE) of a water dimer model (1.35 kcal mol<sup>-1</sup>) is 27% relative to that obtained by exhaustive analysis by Tschumper, et al. using CCSD(T) and a large basis set (5.00 kcal mol<sup>-1</sup>) <ref name="PM6" />.

====2) DFT, B3LYP (Density Functional Theory, Becke, 3-parameter, Lee-Yang-Parr).====
In general, DFT uses variational principle and one-electron density for the calculation and therefore bypasses the consideration of the many-electron wavefunction <ref name="RCS Book" />. From the Hohenberg-Kohn Theorems, it has been established that the ground state energy and all of its properties can be extracted from one-electron density alone <ref name="RCS Book" /><ref name="HKTheorem" />. DFT includes exchange-correlation functionals and self-consistent field type formalism <ref name="RCS Book" />. The basic form of DFT uses exchange and correlation terms of uniform electron gas, which is not a good approximation to the actual electron distribution in chemical systems. This error is most pronounced in two bonded atoms that have very high electronegativity difference (O-H for example), where there is a non-uniform distribution of electron density which is skewed towards the more electronegative atom. Hence, empirical inputs - such as atomic correlation energies or thermochemical databases - have been used to refine the DFT method <ref name="RCS Book" />. B3LYP is a hybrid DFT functional method whose energy term includes Slater exchange, the Hartree–Fock exchange, Becke’s exchange functional correction, the gradient-corrected correlation functional of Lee, Yang and Parr, and the local correlation functional of Vosko, Wilk and Nusair <ref name="B3LYP" /><ref name="B3LYP1" />.

===B. Finding a Stable or Transition structure in a PES.===

From the computational output, it is possible to model a potential energy surface (PES), that is dependent on one variable or more. In any given PES, there are 4 simple conditions which allow a user to find a stable structure or a transition structure <ref name="RCS Book" />:
====1) Determining Stationary Point via Gradient.====
<br><div align="center"><math>\frac{dE(\textbf{R})}{dR_{i}} = 0, i=1,2, . . . 3N_{atoms} - 6</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and R<sub>i</sub> refers to a specific member of the set.

====2) Characterizing Minimum Point via Curvature (Positive Force Constants).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{i}} > 0, i=1,2, . . . 3N_{atoms} - 6</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>i</sub> refers to a specific combination of R and bond angle (θ).

====3) Characterizing Transition Point via Curvature (One Unique Negative Force Constant corresponding to First Order Saddle Point in Reaction Coordinate (RC)).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{RC}} < 0</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>RC</sub> refers to a specific combination of R and bond angle (θ) at the lowest-possible transition state in the PES.

====4) Characterizing Transition Point via Curvature (Positive Force Constants For The Remaining Ones).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{i}} > 0, i=1,2, . . . 3N_{atoms} - 7</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>i</sub> refers to a specific combination of '''R''' and bond angle (θ).

While useful, it should be noted that the 4 conditions above '''could not differentiate between global and local stationary points''', which could impact the accuracy of geometry optimization if the geometry is trapped in a local minimum rather than global minimum.

===C.Intrinsic Reaction Coordinate (IRC).===
In 1970, Fukui proposed the concept of IRC, which is defined as the mass-weighted, vibrationless, motionless and steepest descent path on the PES from the TS or the first-order saddle point to two minima on either side of the TS <ref name="IRC" />. The descent from higher-order saddle point is called meta-IRC <ref name="IRC" />. In mathematical form, IRC is obtained by solving the following differential equation <ref name="IRC" />:
<br><div align="center"><math>\frac{d\textbf{q}(s)}{ds} = \textbf{v}(s)</math></div>
, where '''q''' is the mass-weighted Cartesian coordinates, s is the coordinate along the IRC and '''v''' is a normalized tangent vector to the IRC corresponding to the normal coordinate eigenvector with a negative eigenvalue at the TS with s=0.

At the other points, '''v''' is the unit vector parallel to the mass-weighted gradient vector '''g''' with the following relationship <ref name="IRC" />:
<br><div align="center"><math>\textbf{v} = - \frac{\textbf{g}}{|\textbf{g}|}</math> for s > 0</div>
<br><div align="center"> and </div>
<br><div align="center"><math>\textbf{v} = \frac{\textbf{g}}{|\textbf{g}|}</math> for s < 0</div>

IRC calculation has been used extensively to confirm the connection between a given TS and two minima (reactant(s) and product(s)) for a given reaction <ref name="IRC" />. In this study, IRC calculation had been done for all the reactions such that it can be used to '''independently confirm''' that the TS geometry for the given reaction had truly been optimized.

From a successful IRC calculation (Minimum-TS-Minimum), it is possible to extract the calculated activation energy (linked to a given computational method) and therefore, the calculated rate constant for a reaction via transition state theory <ref name="IRC" />.

===D. Predicting Rate of Reaction from Calculated Thermodynamic Values.===
Once the activation free-energy of a reaction is calculated, it is possible to calculate the predicted rate of reaction via the equation below <ref name="Rate" />:
<br><div align="center"><math> k(T) = \frac{k_{B}T}{hc^{o}} e^{\frac{-\Delta^{\ddagger}G^{o}}{RT}} </math></div>

, where k(T) is rate constant at a specified temperature, k<sub>B</sub> is Boltzmann constant (1.3807 x 10<sup>-23</sup> J K<sup>-1</sup>), T is temperature (in K), h is Planck's constant (6.626176 x 10<sup>-34</sup> J s), c<sup>o</sup> is concentration (taken to be 1, unitless), Δ<sup>‡</sup>G<sup>o</sup> is the activation Gibbs-Free Energy (J mol<sup>-1</sup>) and R is gas constant (8.314 J mol<sup>-1</sup> K<sup>-1</sup>).

===E. Diels-Alder Reaction as a Study Topic.===
Diels-Alder reaction is a concerted [<sub>π</sub>4<sub>s</sub> + <sub>π</sub>2<sub>s</sub>] cycloaddition between an s-cis conjugated diene and a dienophile to form a cyclohexene <ref name="DA" />. In the reaction, 3 π bonds are broken and 2 sigma bonds and 1 new π bond is formed. In a normal Diels-Alder reaction, the interaction happens between an electron-rich s-cis dienophile and an electron poor diene. In an inverse-electron-demand Diels-Alder reaction, the interaction happens between an electron-poor s-cis dienophile and an electron rich diene.

There is a strong research interest in this reaction due to its importance in biosynthetic processes, use as a protecting group and recent discovery of enzyme Diels-Alderase in nature (for example, spirotetronate cyclase AbyU), which could unlock new and efficient Diels-Alder reactions <ref name="DA" /><ref name="DA2" /><ref name="DAE1" /><ref name="DAE2" /><ref name="DAE3" /><ref name="DAE4" /><ref name="DAE5" /><ref name="DAE6" /><ref name="DAE7" /><ref name="DAE8" />. In the area of computational chemistry, there are many researches about the geometry of the transition states involved in Diels-Alder reactions and the overall reaction profiles <ref name="DA" /><ref name="DA1" /><ref name="DA2" /><ref name="DA3" />.

=='''4. Methodology.'''==
The calculation results assumed two reacting molecules in gaseous phase (in absence of solvation and other interactions with non-reacting, neighbouring molecules). The temperature and pressure settings in the calculations were 298.15 K and 1 atm (default settings). The symmetry and molecular geometries of the products and reactants were not restricted in the optimization process. All of the calculations were performed in GaussView 5.0 and the calculation grid was set to ultrafine (integral=grid=ultrafine). For TS calculations, additional keyword (opt=noeigen) was used in response to possible error in link 9999.

The non-covalent interaction plots were generated using a script by Henry Rzepa and Bob Hanson <ref name="NCI" /> using default parameters for intermolecular reaction (minimum rho cutoff set to 0.3, covalent density cutoff set to 0.07, fraction of total rho that defined intramolecular interaction set to 0.95, data scaling set to 1).

Unless stated otherwise, all of the optimization jobs were followed by frequency analysis.

===Exercise 1: Reaction of Butadiene with Ethylene.===
Cyclohexene (product) was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.2 Å at the reacting C-C termini. While freezing the coordinates of the reacting C-C termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of Butadiene and Ethylene.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex 1.png|thumb|400px| Figure 4.1: Exercise 1 Reaction Scheme.]]
|}

===Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole.===
The endo product was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.2 Å at the reacting C-C termini. While freezing the coordinates of the reacting C-C termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of Cyclohexadiene and 1,3-Dioxole.

The optimized structure at PM6 level was reoptimized at B3LYP/6-31G(d) level for the endo product, TS and the reactants.

The above procedures were repeated for the exo-product, with the exception of the reactants.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex 2.png|thumb|400px| Figure 4.2: Exercise 2 Reaction Scheme.]]
|}

===Exercise 3: Reaction of 5,6-dimethylenecyclohexa-1,3-diene and Sulfur Dioxide.===
The endo product was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.0 Å at the reacting C-O termini and 2.4 Å at the reacting C-S termini. While freezing the coordinates of the reacting termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of 5,6-dimethylenecyclohexa-1,3-diene and sulfur dioxide.

The above procedures were repeated for the exo-product, cheletropic-product and two minor Diels Alder regio-isomers, with the exception of reactants.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex 3.png|thumb|500px| Figure 4.3: Exercise 3 Reaction Scheme.]]
|}

=='''5. Results and Discussion.'''==
===Exercise 1: Reaction of Butadiene with Ethylene.===

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx1RD Exercise 1 Results and Discussion.]

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

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx2RD Exercise 2 Results and Discussion.]

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

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx3RD Exercise 3 Results and Discussion.]

=='''6. Conclusion.'''==
In conclusion, this paper had successfully carried out computational calculations to study eight Diels-Alder reactions and one Cheletropic reaction using two popular computational methods: PM6 and B3LYP (6-31 G(d) basis set) in GaussView 5.0. For future work, the calculated results could be shared with other teams who could carry out the experiments in the lab to verify the results.

=='''7. References.'''==
<references>
<ref name="RCS Book">J. J. W. McDouall, in ''Computational Quantum Chemistry: Molecular Structure and Properties in Silico'', Royal Society of Chemistry, 2013, ch. 1, pp. 1-62.
</ref>
<ref name="Methylene"> H. F. SCHAEFER III, ''Science'', 1986, '''231''', 1100-1107.</ref>
<ref name="NCI"> Mod:NCI, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:NCI, (accessed March 2018).</ref>
<ref name="HKTheorem"> P. Hohenberg, W. Kohn, ''Phys. Rev.'', 1964, '''136(3B)''', B864–B871.</ref>
<ref name="PM6"> J. J. P. Stewart, '' J Mol Model'', 2007, '''13''', 1173-1213.</ref>
<ref name="B3LYP"> D. Avci, A. Başoğlu, Y. Atalay, '' Z. Naturforsch.'', 2008, '''63a''', 712-720.</ref>
<ref name="B3LYP1"> S.H. Vosko, L. Wilk, and M. Nusair, '' Can. J. Phys'', 1980, '''58''', 1200.</ref>
<ref name="DA"> T. J. Brocksom, J. Nakamura, M. L. Ferreira and U. Brocksom, '' J. Braz. Chem. Soc.'', 2001, '''12''', 597-622.</ref>
<ref name="DA1"> K. N. Houk, J. Gonzalez, Y. Li, ''Acc. Chem. Res.'', 1995, '''28''', 81-90.</ref>
<ref name="DA2"> J. Chen, Q. Deng, R. Wang, K. N. Houk, D. Hilvert, ''ChemBioChem'', 2000, '''1''', 255-261.</ref>
<ref name="DA3"> D. J. Tantillo, K. N. Houk, M. E. J. Jung, ''Org. Chem.'', 2001, '''66''', 1938-1940.</ref>
<ref name="DAE1"> K. N. Houk, J. Gonzalez, Y. Li, ''Acc. Chem. Res.'', 1995, '''28''', 81-90.</ref>
<ref name="DAE2"> W. M. Bandaranayake, J. E. Banfield, D. St. C. Black, ''J. Chem. Soc., Chem. Commun.'', 1980, 902-903.</ref>
<ref name="DAE3"> K. C. Nicolaou, N. A. Petasis, in ''Strategies and Tactics in Organic Synthesis'', ed. T. Lindberg, Academic Press, 1984, ch. 6, pp. 153-170.</ref>
<ref name="DAE4"> W. R. Roush, K. Koyama, M. L. Curtin, K. J. Moriarty, ''J. Am. Chem. Soc.'', 1996, '''118''', 7502-7512.</ref>
<ref name="DAE5"> H. Oikawa, T. Kobayashi, K. Katayama, Y. Suzuki, A. Ichihara, ''J. Org. Chem.'', 1998, '''63''', 8748-8756.</ref>
<ref name="DAE6"> E. M. Stocking, J. F. Sanz-Cervera, R. M. Williams, ''J. Am. Chem. Soc.'', 2000, '''122''', 1675-1683.</ref>
<ref name="DAE7"> G. A. Wallace, C. H. Heathcock, ''J. Org. Chem.'', 2001, '''66''', 450-454.</ref>
<ref name="DAE8"> K. Auclair, A. Sutherland, J. Kennedy, D. J. Witter, J. P. Van den Heever, C. R. Hutchinson, J. C. Vederas, ''J. Am. Chem. Soc.'', 2000, '''122''', 11519-11520.</ref>
<ref name="IRC"> S. Maeda, Y. Harabuchi, Y. Ono, T. Taketsugu, K. Morokuma, ''International Journal of Quantum Chemistry'', 2015, '''115''', 258-269.</ref>
<ref name="Rate">D. A. McQuarrie, in ''Physical Chemistry : A Molecular Approach'', University Science Books, 1997.
</ref>
</references>

Rep:Kh1015TS

2018-03-14T10:32:43Z

Kh1015: /* 1. Abstract. */

=='''1. Abstract.'''==
This paper studied eight Diels-Alder reactions and one Cheletropic reaction using two popular computational methods: PM6 and B3LYP (6-31 G(d) basis set) in GaussView 5.0. In Exercise 1-3, the MO calculation was used to identify the interacting frontier orbitals and possible secondary-orbital interactions. In Exercise 1, the C-C bond length of molecules optimized using PM6 level showed good agreement with literature with less than 1% percentage difference. IRC analysis at PM6 level in all exercises showed that the TS has been optimized. In Exercise 2 and Exercise 3, thermodynamic values (activation Gibbs-Free energy and Δ Gibbs-Free energy) were extracted from the log file output and rate constant was calculated using the activation Gibbs-Free energy based on method by D. A. McQuarrie (1997) <ref name="Rate" />.

=='''2. Aim.'''==
The aim of this study is to locate and characterize the transition states of several Diels-Alder reactions.

=='''3. Introduction.'''==

Chemical behaviour of a molecule is controlled by the electrons that participate in the chemical process <ref name="RCS Book" />. In particular, the electronic structure and properties in its stationary state could be described by the time-independent solution of Schrödinger’s equation:
<div align="center"><math>\hat{H} \psi_{A} = E_{A} \psi_{A}</math></div>
, where A labels the state of interest <ref name="RCS Book" />.

The above equation forms the foundation for quantum chemistry and modern computational methods.

For a given reaction where there is ambiguity in structure or mechanism, computational chemistry is useful in predicting the likeliest structure or mechanism. For example, in 1986, computational calculation correctly predicted and later experimentally confirmed a bent structure for methylene, which challenged the linear experimental value by Hertzberg thought to be true at the time <ref name="Methylene" />.

===A. Standard Computational Methods.===

The recurring challenge in computational method is that the Schrodinger equation can be solved exactly only for one-electron systems, while most molecules have much more than one electron in the system. To address this challenges, multiple methods have been developed to find increasingly accurate approximations to the Schrodinger equation for many-electron systems <ref name="RCS Book" />. Each of the methods has its own trade-off between accuracy and computational cost. With that in mind, two such methods had been selected in this study: semi-quantitative Parameterization Method 6 (PM6); and Density Functional Theory (DFT), Becke, 3-parameter, Lee-Yang-Parr (B3LYP).
====1) Semi Quantitative PM6 (Parameterization Method 6).====
PM6 is a modified semi-empirical method categorized under Neglect of Diatomic Differential Overlap (NDDO) <ref name="PM6" />.The main advantage of modified version of NDDO (MNDO) over its predecessors lies in the optimization of parameters to simulate molecular properties which is more accurate than calculations based on atomic properties <ref name="PM6" />. The inability of earlier MNDO to simulate hydrogen bond has been addressed in PM6 method, where the percentage difference of the average unsigned error (AUE) of a water dimer model (1.35 kcal mol<sup>-1</sup>) is 27% relative to that obtained by exhaustive analysis by Tschumper, et al. using CCSD(T) and a large basis set (5.00 kcal mol<sup>-1</sup>) <ref name="PM6" />.

====2) DFT, B3LYP (Density Functional Theory, Becke, 3-parameter, Lee-Yang-Parr).====
In general, DFT uses variational principle and one-electron density for the calculation and therefore bypasses the consideration of the many-electron wavefunction <ref name="RCS Book" />. From the Hohenberg-Kohn Theorems, it has been established that the ground state energy and all of its properties can be extracted from one-electron density alone <ref name="RCS Book" /><ref name="HKTheorem" />. DFT includes exchange-correlation functionals and self-consistent field type formalism <ref name="RCS Book" />. The basic form of DFT uses exchange and correlation terms of uniform electron gas, which is not a good approximation to the actual electron distribution in chemical systems. This error is most pronounced in two bonded atoms that have very high electronegativity difference (O-H for example), where there is a non-uniform distribution of electron density which is skewed towards the more electronegative atom. Hence, empirical inputs - such as atomic correlation energies or thermochemical databases - have been used to refine the DFT method <ref name="RCS Book" />. B3LYP is a hybrid DFT functional method whose energy term includes Slater exchange, the Hartree–Fock exchange, Becke’s exchange functional correction, the gradient-corrected correlation functional of Lee, Yang and Parr, and the local correlation functional of Vosko, Wilk and Nusair <ref name="B3LYP" /><ref name="B3LYP1" />.

===B. Finding a Stable or Transition structure in a PES.===

From the computational output, it is possible to model a potential energy surface (PES), that is dependent on one variable or more. In any given PES, there are 4 simple conditions which allow a user to find a stable structure or a transition structure <ref name="RCS Book" />:
====1) Determining Stationary Point via Gradient.====
<br><div align="center"><math>\frac{dE(\textbf{R})}{dR_{i}} = 0, i=1,2, . . . 3N_{atoms} - 6</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and R<sub>i</sub> refers to a specific member of the set.

====2) Characterizing Minimum Point via Curvature (Positive Force Constants).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{i}} > 0, i=1,2, . . . 3N_{atoms} - 6</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>i</sub> refers to a specific combination of R and bond angle (θ).

====3) Characterizing Transition Point via Curvature (One Unique Negative Force Constant corresponding to First Order Saddle Point in Reaction Coordinate (RC)).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{RC}} < 0</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>RC</sub> refers to a specific combination of R and bond angle (θ) at the lowest-possible transition state in the PES.

====4) Characterizing Transition Point via Curvature (Positive Force Constants For The Remaining Ones).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{i}} > 0, i=1,2, . . . 3N_{atoms} - 7</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>i</sub> refers to a specific combination of '''R''' and bond angle (θ).

While useful, it should be noted that the 4 conditions above '''could not differentiate between global and local stationary points''', which could impact the accuracy of geometry optimization if the geometry is trapped in a local minimum rather than global minimum.

===C.Intrinsic Reaction Coordinate (IRC).===
In 1970, Fukui proposed the concept of IRC, which is defined as the mass-weighted, vibrationless, motionless and steepest descent path on the PES from the TS or the first-order saddle point to two minima on either side of the TS <ref name="IRC" />. The descent from higher-order saddle point is called meta-IRC <ref name="IRC" />. In mathematical form, IRC is obtained by solving the following differential equation <ref name="IRC" />:
<br><div align="center"><math>\frac{d\textbf{q}(s)}{ds} = \textbf{v}(s)</math></div>
, where '''q''' is the mass-weighted Cartesian coordinates, s is the coordinate along the IRC and '''v''' is a normalized tangent vector to the IRC corresponding to the normal coordinate eigenvector with a negative eigenvalue at the TS with s=0.

At the other points, '''v''' is the unit vector parallel to the mass-weighted gradient vector '''g''' with the following relationship <ref name="IRC" />:
<br><div align="center"><math>\textbf{v} = - \frac{\textbf{g}}{|\textbf{g}|}</math> for s > 0</div>
<br><div align="center"> and </div>
<br><div align="center"><math>\textbf{v} = \frac{\textbf{g}}{|\textbf{g}|}</math> for s < 0</div>

IRC calculation has been used extensively to confirm the connection between a given TS and two minima (reactant(s) and product(s)) for a given reaction <ref name="IRC" />. In this study, IRC calculation had been done for all the reactions such that it can be used to '''independently confirm''' that the TS geometry for the given reaction had truly been optimized.

From a successful IRC calculation (Minimum-TS-Minimum), it is possible to extract the calculated activation energy (linked to a given computational method) and therefore, the calculated rate constant for a reaction via transition state theory <ref name="IRC" />.

===D. Predicting Rate of Reaction from Calculated Thermodynamic Values.===
Once the activation free-energy of a reaction is calculated, it is possible to calculate the predicted rate of reaction via the equation below <ref name="Rate" />:
<br><div align="center"><math> k(T) = \frac{k_{B}T}{hc^{o}} e^{\frac{-\Delta^{\ddagger}G^{o}}{RT}} </math></div>

, where k(T) is rate constant at a specified temperature, k<sub>B</sub> is Boltzmann constant (1.3807 x 10<sup>-23</sup> J K<sup>-1</sup>), T is temperature (in K), h is Planck's constant (6.626176 x 10<sup>-34</sup> J s), c<sup>o</sup> is concentration (taken to be 1, unitless), Δ<sup>‡</sup>G<sup>o</sup> is the activation Gibbs-Free Energy (J mol<sup>-1</sup>) and R is gas constant (8.314 J mol<sup>-1</sup> K<sup>-1</sup>).

===E. Diels-Alder Reaction as a Study Topic.===
Diels-Alder reaction is a concerted [<sub>π</sub>4<sub>s</sub> + <sub>π</sub>2<sub>s</sub>] cycloaddition between an s-cis conjugated diene and a dienophile to form a cyclohexene <ref name="DA" />. In the reaction, 3 π bonds are broken and 2 sigma bonds and 1 new π bond is formed. In a normal Diels-Alder reaction, the interaction happens between an electron-rich s-cis dienophile and an electron poor diene. In an inverse-electron-demand Diels-Alder reaction, the interaction happens between an electron-poor s-cis dienophile and an electron rich diene.

There is a strong research interest in this reaction due to its importance in biosynthetic processes, use as a protecting group and recent discovery of enzyme Diels-Alderase in nature (for example, spirotetronate cyclase AbyU), which could unlock new and efficient Diels-Alder reactions <ref name="DA" /><ref name="DA2" /><ref name="DAE1" /><ref name="DAE2" /><ref name="DAE3" /><ref name="DAE4" /><ref name="DAE5" /><ref name="DAE6" /><ref name="DAE7" /><ref name="DAE8" />. In the area of computational chemistry, there are many researches about the geometry of the transition states involved in Diels-Alder reactions and the overall reaction profiles <ref name="DA" /><ref name="DA1" /><ref name="DA2" /><ref name="DA3" />.

=='''4. Methodology.'''==
The calculation results assumed two reacting molecules in gaseous phase (in absence of solvation and other interactions with non-reacting, neighbouring molecules). The temperature and pressure settings in the calculations were 298.15 K and 1 atm (default settings). The symmetry and molecular geometries of the products and reactants were not restricted in the optimization process. All of the calculations were performed in GaussView 5.0 and the calculation grid was set to ultrafine (integral=grid=ultrafine). For TS calculations, additional keyword (opt=noeigen) was used in response to possible error in link 9999.

The non-covalent interaction plots were generated using a script by Henry Rzepa and Bob Hanson <ref name="NCI" /> using default parameters for intermolecular reaction (minimum rho cutoff set to 0.3, covalent density cutoff set to 0.07, fraction of total rho that defined intramolecular interaction set to 0.95, data scaling set to 1).

Unless stated otherwise, all of the optimization jobs were followed by frequency analysis.

===Exercise 1: Reaction of Butadiene with Ethylene.===
Cyclohexene (product) was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.2 Å at the reacting C-C termini. While freezing the coordinates of the reacting C-C termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of Butadiene and Ethylene.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex 1.png|thumb|400px| Figure 4.1: Exercise 1 Reaction Scheme.]]
|}

===Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole.===
The endo product was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.2 Å at the reacting C-C termini. While freezing the coordinates of the reacting C-C termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of Cyclohexadiene and 1,3-Dioxole.

The optimized structure at PM6 level was reoptimized at B3LYP/6-31G(d) level for the endo product, TS and the reactants.

The above procedures were repeated for the exo-product, with the exception of the reactants.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex 2.png|thumb|400px| Figure 4.2: Exercise 2 Reaction Scheme.]]
|}

===Exercise 3: Reaction of 5,6-dimethylenecyclohexa-1,3-diene and Sulfur Dioxide.===
The endo product was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.0 Å at the reacting C-O termini and 2.4 Å at the reacting C-S termini. While freezing the coordinates of the reacting termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of 5,6-dimethylenecyclohexa-1,3-diene and sulfur dioxide.

The above procedures were repeated for the exo-product, cheletropic-product and two minor Diels Alder regio-isomers, with the exception of reactants.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex 3.png|thumb|500px| Figure 4.3: Exercise 3 Reaction Scheme.]]
|}

=='''5. Results and Discussion.'''==
===Exercise 1: Reaction of Butadiene with Ethylene.===

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx1RD Exercise 1 Results and Discussion.]

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

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx2RD Exercise 2 Results and Discussion.]

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

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx3RD Exercise 3 Results and Discussion.]

=='''6. Conclusion.'''==
In conclusion, this paper had successfully carried out computational calculations to study six Diels-Alder reactions and one Cheletropic reaction using two popular computational methods: PM6 and B3LYP (6-31 G(d) basis set) in GaussView 5.0. For future work, the calculated results could be shared with other teams who could carry out the experiments in the lab to verify the results.

=='''7. References.'''==
<references>
<ref name="RCS Book">J. J. W. McDouall, in ''Computational Quantum Chemistry: Molecular Structure and Properties in Silico'', Royal Society of Chemistry, 2013, ch. 1, pp. 1-62.
</ref>
<ref name="Methylene"> H. F. SCHAEFER III, ''Science'', 1986, '''231''', 1100-1107.</ref>
<ref name="NCI"> Mod:NCI, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:NCI, (accessed March 2018).</ref>
<ref name="HKTheorem"> P. Hohenberg, W. Kohn, ''Phys. Rev.'', 1964, '''136(3B)''', B864–B871.</ref>
<ref name="PM6"> J. J. P. Stewart, '' J Mol Model'', 2007, '''13''', 1173-1213.</ref>
<ref name="B3LYP"> D. Avci, A. Başoğlu, Y. Atalay, '' Z. Naturforsch.'', 2008, '''63a''', 712-720.</ref>
<ref name="B3LYP1"> S.H. Vosko, L. Wilk, and M. Nusair, '' Can. J. Phys'', 1980, '''58''', 1200.</ref>
<ref name="DA"> T. J. Brocksom, J. Nakamura, M. L. Ferreira and U. Brocksom, '' J. Braz. Chem. Soc.'', 2001, '''12''', 597-622.</ref>
<ref name="DA1"> K. N. Houk, J. Gonzalez, Y. Li, ''Acc. Chem. Res.'', 1995, '''28''', 81-90.</ref>
<ref name="DA2"> J. Chen, Q. Deng, R. Wang, K. N. Houk, D. Hilvert, ''ChemBioChem'', 2000, '''1''', 255-261.</ref>
<ref name="DA3"> D. J. Tantillo, K. N. Houk, M. E. J. Jung, ''Org. Chem.'', 2001, '''66''', 1938-1940.</ref>
<ref name="DAE1"> K. N. Houk, J. Gonzalez, Y. Li, ''Acc. Chem. Res.'', 1995, '''28''', 81-90.</ref>
<ref name="DAE2"> W. M. Bandaranayake, J. E. Banfield, D. St. C. Black, ''J. Chem. Soc., Chem. Commun.'', 1980, 902-903.</ref>
<ref name="DAE3"> K. C. Nicolaou, N. A. Petasis, in ''Strategies and Tactics in Organic Synthesis'', ed. T. Lindberg, Academic Press, 1984, ch. 6, pp. 153-170.</ref>
<ref name="DAE4"> W. R. Roush, K. Koyama, M. L. Curtin, K. J. Moriarty, ''J. Am. Chem. Soc.'', 1996, '''118''', 7502-7512.</ref>
<ref name="DAE5"> H. Oikawa, T. Kobayashi, K. Katayama, Y. Suzuki, A. Ichihara, ''J. Org. Chem.'', 1998, '''63''', 8748-8756.</ref>
<ref name="DAE6"> E. M. Stocking, J. F. Sanz-Cervera, R. M. Williams, ''J. Am. Chem. Soc.'', 2000, '''122''', 1675-1683.</ref>
<ref name="DAE7"> G. A. Wallace, C. H. Heathcock, ''J. Org. Chem.'', 2001, '''66''', 450-454.</ref>
<ref name="DAE8"> K. Auclair, A. Sutherland, J. Kennedy, D. J. Witter, J. P. Van den Heever, C. R. Hutchinson, J. C. Vederas, ''J. Am. Chem. Soc.'', 2000, '''122''', 11519-11520.</ref>
<ref name="IRC"> S. Maeda, Y. Harabuchi, Y. Ono, T. Taketsugu, K. Morokuma, ''International Journal of Quantum Chemistry'', 2015, '''115''', 258-269.</ref>
<ref name="Rate">D. A. McQuarrie, in ''Physical Chemistry : A Molecular Approach'', University Science Books, 1997.
</ref>
</references>

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Kh1015: /* Exercise 3: Reaction of 5,6-dimethylenecyclohexa-1,3-diene and Sulfur Dioxide. */

=='''1. Abstract.'''==
This paper studied six Diels-Alder reactions and one Cheletropic reaction using two popular computational methods: PM6 and B3LYP (6-31 G(d) basis set) in GaussView 5.0. In Exercise 1-3, the MO calculation was used to identify the interacting frontier orbitals and possible secondary-orbital interactions. In Exercise 1, the C-C bond length of molecules optimized using PM6 level showed good agreement with literature with less than 1% percentage difference. IRC analysis at PM6 level in all exercises showed that the TS has been optimized. In Exercise 2 and Exercise 3, thermodynamic values (activation Gibbs-Free energy and Δ Gibbs-Free energy) were extracted from the log file output and rate constant was calculated using the activation Gibbs-Free energy based on method by D. A. McQuarrie (1997) <ref name="Rate" />.

=='''2. Aim.'''==
The aim of this study is to locate and characterize the transition states of several Diels-Alder reactions.

=='''3. Introduction.'''==

Chemical behaviour of a molecule is controlled by the electrons that participate in the chemical process <ref name="RCS Book" />. In particular, the electronic structure and properties in its stationary state could be described by the time-independent solution of Schrödinger’s equation:
<div align="center"><math>\hat{H} \psi_{A} = E_{A} \psi_{A}</math></div>
, where A labels the state of interest <ref name="RCS Book" />.

The above equation forms the foundation for quantum chemistry and modern computational methods.

For a given reaction where there is ambiguity in structure or mechanism, computational chemistry is useful in predicting the likeliest structure or mechanism. For example, in 1986, computational calculation correctly predicted and later experimentally confirmed a bent structure for methylene, which challenged the linear experimental value by Hertzberg thought to be true at the time <ref name="Methylene" />.

===A. Standard Computational Methods.===

The recurring challenge in computational method is that the Schrodinger equation can be solved exactly only for one-electron systems, while most molecules have much more than one electron in the system. To address this challenges, multiple methods have been developed to find increasingly accurate approximations to the Schrodinger equation for many-electron systems <ref name="RCS Book" />. Each of the methods has its own trade-off between accuracy and computational cost. With that in mind, two such methods had been selected in this study: semi-quantitative Parameterization Method 6 (PM6); and Density Functional Theory (DFT), Becke, 3-parameter, Lee-Yang-Parr (B3LYP).
====1) Semi Quantitative PM6 (Parameterization Method 6).====
PM6 is a modified semi-empirical method categorized under Neglect of Diatomic Differential Overlap (NDDO) <ref name="PM6" />.The main advantage of modified version of NDDO (MNDO) over its predecessors lies in the optimization of parameters to simulate molecular properties which is more accurate than calculations based on atomic properties <ref name="PM6" />. The inability of earlier MNDO to simulate hydrogen bond has been addressed in PM6 method, where the percentage difference of the average unsigned error (AUE) of a water dimer model (1.35 kcal mol<sup>-1</sup>) is 27% relative to that obtained by exhaustive analysis by Tschumper, et al. using CCSD(T) and a large basis set (5.00 kcal mol<sup>-1</sup>) <ref name="PM6" />.

====2) DFT, B3LYP (Density Functional Theory, Becke, 3-parameter, Lee-Yang-Parr).====
In general, DFT uses variational principle and one-electron density for the calculation and therefore bypasses the consideration of the many-electron wavefunction <ref name="RCS Book" />. From the Hohenberg-Kohn Theorems, it has been established that the ground state energy and all of its properties can be extracted from one-electron density alone <ref name="RCS Book" /><ref name="HKTheorem" />. DFT includes exchange-correlation functionals and self-consistent field type formalism <ref name="RCS Book" />. The basic form of DFT uses exchange and correlation terms of uniform electron gas, which is not a good approximation to the actual electron distribution in chemical systems. This error is most pronounced in two bonded atoms that have very high electronegativity difference (O-H for example), where there is a non-uniform distribution of electron density which is skewed towards the more electronegative atom. Hence, empirical inputs - such as atomic correlation energies or thermochemical databases - have been used to refine the DFT method <ref name="RCS Book" />. B3LYP is a hybrid DFT functional method whose energy term includes Slater exchange, the Hartree–Fock exchange, Becke’s exchange functional correction, the gradient-corrected correlation functional of Lee, Yang and Parr, and the local correlation functional of Vosko, Wilk and Nusair <ref name="B3LYP" /><ref name="B3LYP1" />.

===B. Finding a Stable or Transition structure in a PES.===

From the computational output, it is possible to model a potential energy surface (PES), that is dependent on one variable or more. In any given PES, there are 4 simple conditions which allow a user to find a stable structure or a transition structure <ref name="RCS Book" />:
====1) Determining Stationary Point via Gradient.====
<br><div align="center"><math>\frac{dE(\textbf{R})}{dR_{i}} = 0, i=1,2, . . . 3N_{atoms} - 6</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and R<sub>i</sub> refers to a specific member of the set.

====2) Characterizing Minimum Point via Curvature (Positive Force Constants).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{i}} > 0, i=1,2, . . . 3N_{atoms} - 6</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>i</sub> refers to a specific combination of R and bond angle (θ).

====3) Characterizing Transition Point via Curvature (One Unique Negative Force Constant corresponding to First Order Saddle Point in Reaction Coordinate (RC)).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{RC}} < 0</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>RC</sub> refers to a specific combination of R and bond angle (θ) at the lowest-possible transition state in the PES.

====4) Characterizing Transition Point via Curvature (Positive Force Constants For The Remaining Ones).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{i}} > 0, i=1,2, . . . 3N_{atoms} - 7</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>i</sub> refers to a specific combination of '''R''' and bond angle (θ).

While useful, it should be noted that the 4 conditions above '''could not differentiate between global and local stationary points''', which could impact the accuracy of geometry optimization if the geometry is trapped in a local minimum rather than global minimum.

===C.Intrinsic Reaction Coordinate (IRC).===
In 1970, Fukui proposed the concept of IRC, which is defined as the mass-weighted, vibrationless, motionless and steepest descent path on the PES from the TS or the first-order saddle point to two minima on either side of the TS <ref name="IRC" />. The descent from higher-order saddle point is called meta-IRC <ref name="IRC" />. In mathematical form, IRC is obtained by solving the following differential equation <ref name="IRC" />:
<br><div align="center"><math>\frac{d\textbf{q}(s)}{ds} = \textbf{v}(s)</math></div>
, where '''q''' is the mass-weighted Cartesian coordinates, s is the coordinate along the IRC and '''v''' is a normalized tangent vector to the IRC corresponding to the normal coordinate eigenvector with a negative eigenvalue at the TS with s=0.

At the other points, '''v''' is the unit vector parallel to the mass-weighted gradient vector '''g''' with the following relationship <ref name="IRC" />:
<br><div align="center"><math>\textbf{v} = - \frac{\textbf{g}}{|\textbf{g}|}</math> for s > 0</div>
<br><div align="center"> and </div>
<br><div align="center"><math>\textbf{v} = \frac{\textbf{g}}{|\textbf{g}|}</math> for s < 0</div>

IRC calculation has been used extensively to confirm the connection between a given TS and two minima (reactant(s) and product(s)) for a given reaction <ref name="IRC" />. In this study, IRC calculation had been done for all the reactions such that it can be used to '''independently confirm''' that the TS geometry for the given reaction had truly been optimized.

From a successful IRC calculation (Minimum-TS-Minimum), it is possible to extract the calculated activation energy (linked to a given computational method) and therefore, the calculated rate constant for a reaction via transition state theory <ref name="IRC" />.

===D. Predicting Rate of Reaction from Calculated Thermodynamic Values.===
Once the activation free-energy of a reaction is calculated, it is possible to calculate the predicted rate of reaction via the equation below <ref name="Rate" />:
<br><div align="center"><math> k(T) = \frac{k_{B}T}{hc^{o}} e^{\frac{-\Delta^{\ddagger}G^{o}}{RT}} </math></div>

, where k(T) is rate constant at a specified temperature, k<sub>B</sub> is Boltzmann constant (1.3807 x 10<sup>-23</sup> J K<sup>-1</sup>), T is temperature (in K), h is Planck's constant (6.626176 x 10<sup>-34</sup> J s), c<sup>o</sup> is concentration (taken to be 1, unitless), Δ<sup>‡</sup>G<sup>o</sup> is the activation Gibbs-Free Energy (J mol<sup>-1</sup>) and R is gas constant (8.314 J mol<sup>-1</sup> K<sup>-1</sup>).

===E. Diels-Alder Reaction as a Study Topic.===
Diels-Alder reaction is a concerted [<sub>π</sub>4<sub>s</sub> + <sub>π</sub>2<sub>s</sub>] cycloaddition between an s-cis conjugated diene and a dienophile to form a cyclohexene <ref name="DA" />. In the reaction, 3 π bonds are broken and 2 sigma bonds and 1 new π bond is formed. In a normal Diels-Alder reaction, the interaction happens between an electron-rich s-cis dienophile and an electron poor diene. In an inverse-electron-demand Diels-Alder reaction, the interaction happens between an electron-poor s-cis dienophile and an electron rich diene.

There is a strong research interest in this reaction due to its importance in biosynthetic processes, use as a protecting group and recent discovery of enzyme Diels-Alderase in nature (for example, spirotetronate cyclase AbyU), which could unlock new and efficient Diels-Alder reactions <ref name="DA" /><ref name="DA2" /><ref name="DAE1" /><ref name="DAE2" /><ref name="DAE3" /><ref name="DAE4" /><ref name="DAE5" /><ref name="DAE6" /><ref name="DAE7" /><ref name="DAE8" />. In the area of computational chemistry, there are many researches about the geometry of the transition states involved in Diels-Alder reactions and the overall reaction profiles <ref name="DA" /><ref name="DA1" /><ref name="DA2" /><ref name="DA3" />.

=='''4. Methodology.'''==
The calculation results assumed two reacting molecules in gaseous phase (in absence of solvation and other interactions with non-reacting, neighbouring molecules). The temperature and pressure settings in the calculations were 298.15 K and 1 atm (default settings). The symmetry and molecular geometries of the products and reactants were not restricted in the optimization process. All of the calculations were performed in GaussView 5.0 and the calculation grid was set to ultrafine (integral=grid=ultrafine). For TS calculations, additional keyword (opt=noeigen) was used in response to possible error in link 9999.

The non-covalent interaction plots were generated using a script by Henry Rzepa and Bob Hanson <ref name="NCI" /> using default parameters for intermolecular reaction (minimum rho cutoff set to 0.3, covalent density cutoff set to 0.07, fraction of total rho that defined intramolecular interaction set to 0.95, data scaling set to 1).

Unless stated otherwise, all of the optimization jobs were followed by frequency analysis.

===Exercise 1: Reaction of Butadiene with Ethylene.===
Cyclohexene (product) was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.2 Å at the reacting C-C termini. While freezing the coordinates of the reacting C-C termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of Butadiene and Ethylene.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex 1.png|thumb|400px| Figure 4.1: Exercise 1 Reaction Scheme.]]
|}

===Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole.===
The endo product was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.2 Å at the reacting C-C termini. While freezing the coordinates of the reacting C-C termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of Cyclohexadiene and 1,3-Dioxole.

The optimized structure at PM6 level was reoptimized at B3LYP/6-31G(d) level for the endo product, TS and the reactants.

The above procedures were repeated for the exo-product, with the exception of the reactants.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex 2.png|thumb|400px| Figure 4.2: Exercise 2 Reaction Scheme.]]
|}

===Exercise 3: Reaction of 5,6-dimethylenecyclohexa-1,3-diene and Sulfur Dioxide.===
The endo product was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.0 Å at the reacting C-O termini and 2.4 Å at the reacting C-S termini. While freezing the coordinates of the reacting termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of 5,6-dimethylenecyclohexa-1,3-diene and sulfur dioxide.

The above procedures were repeated for the exo-product, cheletropic-product and two minor Diels Alder regio-isomers, with the exception of reactants.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex 3.png|thumb|500px| Figure 4.3: Exercise 3 Reaction Scheme.]]
|}

=='''5. Results and Discussion.'''==
===Exercise 1: Reaction of Butadiene with Ethylene.===

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx1RD Exercise 1 Results and Discussion.]

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

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx2RD Exercise 2 Results and Discussion.]

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

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx3RD Exercise 3 Results and Discussion.]

=='''6. Conclusion.'''==
In conclusion, this paper had successfully carried out computational calculations to study six Diels-Alder reactions and one Cheletropic reaction using two popular computational methods: PM6 and B3LYP (6-31 G(d) basis set) in GaussView 5.0. For future work, the calculated results could be shared with other teams who could carry out the experiments in the lab to verify the results.

=='''7. References.'''==
<references>
<ref name="RCS Book">J. J. W. McDouall, in ''Computational Quantum Chemistry: Molecular Structure and Properties in Silico'', Royal Society of Chemistry, 2013, ch. 1, pp. 1-62.
</ref>
<ref name="Methylene"> H. F. SCHAEFER III, ''Science'', 1986, '''231''', 1100-1107.</ref>
<ref name="NCI"> Mod:NCI, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:NCI, (accessed March 2018).</ref>
<ref name="HKTheorem"> P. Hohenberg, W. Kohn, ''Phys. Rev.'', 1964, '''136(3B)''', B864–B871.</ref>
<ref name="PM6"> J. J. P. Stewart, '' J Mol Model'', 2007, '''13''', 1173-1213.</ref>
<ref name="B3LYP"> D. Avci, A. Başoğlu, Y. Atalay, '' Z. Naturforsch.'', 2008, '''63a''', 712-720.</ref>
<ref name="B3LYP1"> S.H. Vosko, L. Wilk, and M. Nusair, '' Can. J. Phys'', 1980, '''58''', 1200.</ref>
<ref name="DA"> T. J. Brocksom, J. Nakamura, M. L. Ferreira and U. Brocksom, '' J. Braz. Chem. Soc.'', 2001, '''12''', 597-622.</ref>
<ref name="DA1"> K. N. Houk, J. Gonzalez, Y. Li, ''Acc. Chem. Res.'', 1995, '''28''', 81-90.</ref>
<ref name="DA2"> J. Chen, Q. Deng, R. Wang, K. N. Houk, D. Hilvert, ''ChemBioChem'', 2000, '''1''', 255-261.</ref>
<ref name="DA3"> D. J. Tantillo, K. N. Houk, M. E. J. Jung, ''Org. Chem.'', 2001, '''66''', 1938-1940.</ref>
<ref name="DAE1"> K. N. Houk, J. Gonzalez, Y. Li, ''Acc. Chem. Res.'', 1995, '''28''', 81-90.</ref>
<ref name="DAE2"> W. M. Bandaranayake, J. E. Banfield, D. St. C. Black, ''J. Chem. Soc., Chem. Commun.'', 1980, 902-903.</ref>
<ref name="DAE3"> K. C. Nicolaou, N. A. Petasis, in ''Strategies and Tactics in Organic Synthesis'', ed. T. Lindberg, Academic Press, 1984, ch. 6, pp. 153-170.</ref>
<ref name="DAE4"> W. R. Roush, K. Koyama, M. L. Curtin, K. J. Moriarty, ''J. Am. Chem. Soc.'', 1996, '''118''', 7502-7512.</ref>
<ref name="DAE5"> H. Oikawa, T. Kobayashi, K. Katayama, Y. Suzuki, A. Ichihara, ''J. Org. Chem.'', 1998, '''63''', 8748-8756.</ref>
<ref name="DAE6"> E. M. Stocking, J. F. Sanz-Cervera, R. M. Williams, ''J. Am. Chem. Soc.'', 2000, '''122''', 1675-1683.</ref>
<ref name="DAE7"> G. A. Wallace, C. H. Heathcock, ''J. Org. Chem.'', 2001, '''66''', 450-454.</ref>
<ref name="DAE8"> K. Auclair, A. Sutherland, J. Kennedy, D. J. Witter, J. P. Van den Heever, C. R. Hutchinson, J. C. Vederas, ''J. Am. Chem. Soc.'', 2000, '''122''', 11519-11520.</ref>
<ref name="IRC"> S. Maeda, Y. Harabuchi, Y. Ono, T. Taketsugu, K. Morokuma, ''International Journal of Quantum Chemistry'', 2015, '''115''', 258-269.</ref>
<ref name="Rate">D. A. McQuarrie, in ''Physical Chemistry : A Molecular Approach'', University Science Books, 1997.
</ref>
</references>

File:KH1015 Ex 1.png

2018-03-14T10:06:53Z

Kh1015: Kh1015 uploaded a new version of File:KH1015 Ex 1.png

Rep:Kh1015TS

2018-03-14T10:05:30Z

Kh1015: /* Exercise 3: Reaction of 5,6-dimethylenecyclohexa-1,3-diene and Sulfur Dioxide. */

=='''1. Abstract.'''==
This paper studied six Diels-Alder reactions and one Cheletropic reaction using two popular computational methods: PM6 and B3LYP (6-31 G(d) basis set) in GaussView 5.0. In Exercise 1-3, the MO calculation was used to identify the interacting frontier orbitals and possible secondary-orbital interactions. In Exercise 1, the C-C bond length of molecules optimized using PM6 level showed good agreement with literature with less than 1% percentage difference. IRC analysis at PM6 level in all exercises showed that the TS has been optimized. In Exercise 2 and Exercise 3, thermodynamic values (activation Gibbs-Free energy and Δ Gibbs-Free energy) were extracted from the log file output and rate constant was calculated using the activation Gibbs-Free energy based on method by D. A. McQuarrie (1997) <ref name="Rate" />.

=='''2. Aim.'''==
The aim of this study is to locate and characterize the transition states of several Diels-Alder reactions.

=='''3. Introduction.'''==

Chemical behaviour of a molecule is controlled by the electrons that participate in the chemical process <ref name="RCS Book" />. In particular, the electronic structure and properties in its stationary state could be described by the time-independent solution of Schrödinger’s equation:
<div align="center"><math>\hat{H} \psi_{A} = E_{A} \psi_{A}</math></div>
, where A labels the state of interest <ref name="RCS Book" />.

The above equation forms the foundation for quantum chemistry and modern computational methods.

For a given reaction where there is ambiguity in structure or mechanism, computational chemistry is useful in predicting the likeliest structure or mechanism. For example, in 1986, computational calculation correctly predicted and later experimentally confirmed a bent structure for methylene, which challenged the linear experimental value by Hertzberg thought to be true at the time <ref name="Methylene" />.

===A. Standard Computational Methods.===

The recurring challenge in computational method is that the Schrodinger equation can be solved exactly only for one-electron systems, while most molecules have much more than one electron in the system. To address this challenges, multiple methods have been developed to find increasingly accurate approximations to the Schrodinger equation for many-electron systems <ref name="RCS Book" />. Each of the methods has its own trade-off between accuracy and computational cost. With that in mind, two such methods had been selected in this study: semi-quantitative Parameterization Method 6 (PM6); and Density Functional Theory (DFT), Becke, 3-parameter, Lee-Yang-Parr (B3LYP).
====1) Semi Quantitative PM6 (Parameterization Method 6).====
PM6 is a modified semi-empirical method categorized under Neglect of Diatomic Differential Overlap (NDDO) <ref name="PM6" />.The main advantage of modified version of NDDO (MNDO) over its predecessors lies in the optimization of parameters to simulate molecular properties which is more accurate than calculations based on atomic properties <ref name="PM6" />. The inability of earlier MNDO to simulate hydrogen bond has been addressed in PM6 method, where the percentage difference of the average unsigned error (AUE) of a water dimer model (1.35 kcal mol<sup>-1</sup>) is 27% relative to that obtained by exhaustive analysis by Tschumper, et al. using CCSD(T) and a large basis set (5.00 kcal mol<sup>-1</sup>) <ref name="PM6" />.

====2) DFT, B3LYP (Density Functional Theory, Becke, 3-parameter, Lee-Yang-Parr).====
In general, DFT uses variational principle and one-electron density for the calculation and therefore bypasses the consideration of the many-electron wavefunction <ref name="RCS Book" />. From the Hohenberg-Kohn Theorems, it has been established that the ground state energy and all of its properties can be extracted from one-electron density alone <ref name="RCS Book" /><ref name="HKTheorem" />. DFT includes exchange-correlation functionals and self-consistent field type formalism <ref name="RCS Book" />. The basic form of DFT uses exchange and correlation terms of uniform electron gas, which is not a good approximation to the actual electron distribution in chemical systems. This error is most pronounced in two bonded atoms that have very high electronegativity difference (O-H for example), where there is a non-uniform distribution of electron density which is skewed towards the more electronegative atom. Hence, empirical inputs - such as atomic correlation energies or thermochemical databases - have been used to refine the DFT method <ref name="RCS Book" />. B3LYP is a hybrid DFT functional method whose energy term includes Slater exchange, the Hartree–Fock exchange, Becke’s exchange functional correction, the gradient-corrected correlation functional of Lee, Yang and Parr, and the local correlation functional of Vosko, Wilk and Nusair <ref name="B3LYP" /><ref name="B3LYP1" />.

===B. Finding a Stable or Transition structure in a PES.===

From the computational output, it is possible to model a potential energy surface (PES), that is dependent on one variable or more. In any given PES, there are 4 simple conditions which allow a user to find a stable structure or a transition structure <ref name="RCS Book" />:
====1) Determining Stationary Point via Gradient.====
<br><div align="center"><math>\frac{dE(\textbf{R})}{dR_{i}} = 0, i=1,2, . . . 3N_{atoms} - 6</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and R<sub>i</sub> refers to a specific member of the set.

====2) Characterizing Minimum Point via Curvature (Positive Force Constants).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{i}} > 0, i=1,2, . . . 3N_{atoms} - 6</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>i</sub> refers to a specific combination of R and bond angle (θ).

====3) Characterizing Transition Point via Curvature (One Unique Negative Force Constant corresponding to First Order Saddle Point in Reaction Coordinate (RC)).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{RC}} < 0</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>RC</sub> refers to a specific combination of R and bond angle (θ) at the lowest-possible transition state in the PES.

====4) Characterizing Transition Point via Curvature (Positive Force Constants For The Remaining Ones).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{i}} > 0, i=1,2, . . . 3N_{atoms} - 7</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>i</sub> refers to a specific combination of '''R''' and bond angle (θ).

While useful, it should be noted that the 4 conditions above '''could not differentiate between global and local stationary points''', which could impact the accuracy of geometry optimization if the geometry is trapped in a local minimum rather than global minimum.

===C.Intrinsic Reaction Coordinate (IRC).===
In 1970, Fukui proposed the concept of IRC, which is defined as the mass-weighted, vibrationless, motionless and steepest descent path on the PES from the TS or the first-order saddle point to two minima on either side of the TS <ref name="IRC" />. The descent from higher-order saddle point is called meta-IRC <ref name="IRC" />. In mathematical form, IRC is obtained by solving the following differential equation <ref name="IRC" />:
<br><div align="center"><math>\frac{d\textbf{q}(s)}{ds} = \textbf{v}(s)</math></div>
, where '''q''' is the mass-weighted Cartesian coordinates, s is the coordinate along the IRC and '''v''' is a normalized tangent vector to the IRC corresponding to the normal coordinate eigenvector with a negative eigenvalue at the TS with s=0.

At the other points, '''v''' is the unit vector parallel to the mass-weighted gradient vector '''g''' with the following relationship <ref name="IRC" />:
<br><div align="center"><math>\textbf{v} = - \frac{\textbf{g}}{|\textbf{g}|}</math> for s > 0</div>
<br><div align="center"> and </div>
<br><div align="center"><math>\textbf{v} = \frac{\textbf{g}}{|\textbf{g}|}</math> for s < 0</div>

IRC calculation has been used extensively to confirm the connection between a given TS and two minima (reactant(s) and product(s)) for a given reaction <ref name="IRC" />. In this study, IRC calculation had been done for all the reactions such that it can be used to '''independently confirm''' that the TS geometry for the given reaction had truly been optimized.

From a successful IRC calculation (Minimum-TS-Minimum), it is possible to extract the calculated activation energy (linked to a given computational method) and therefore, the calculated rate constant for a reaction via transition state theory <ref name="IRC" />.

===D. Predicting Rate of Reaction from Calculated Thermodynamic Values.===
Once the activation free-energy of a reaction is calculated, it is possible to calculate the predicted rate of reaction via the equation below <ref name="Rate" />:
<br><div align="center"><math> k(T) = \frac{k_{B}T}{hc^{o}} e^{\frac{-\Delta^{\ddagger}G^{o}}{RT}} </math></div>

, where k(T) is rate constant at a specified temperature, k<sub>B</sub> is Boltzmann constant (1.3807 x 10<sup>-23</sup> J K<sup>-1</sup>), T is temperature (in K), h is Planck's constant (6.626176 x 10<sup>-34</sup> J s), c<sup>o</sup> is concentration (taken to be 1, unitless), Δ<sup>‡</sup>G<sup>o</sup> is the activation Gibbs-Free Energy (J mol<sup>-1</sup>) and R is gas constant (8.314 J mol<sup>-1</sup> K<sup>-1</sup>).

===E. Diels-Alder Reaction as a Study Topic.===
Diels-Alder reaction is a concerted [<sub>π</sub>4<sub>s</sub> + <sub>π</sub>2<sub>s</sub>] cycloaddition between an s-cis conjugated diene and a dienophile to form a cyclohexene <ref name="DA" />. In the reaction, 3 π bonds are broken and 2 sigma bonds and 1 new π bond is formed. In a normal Diels-Alder reaction, the interaction happens between an electron-rich s-cis dienophile and an electron poor diene. In an inverse-electron-demand Diels-Alder reaction, the interaction happens between an electron-poor s-cis dienophile and an electron rich diene.

There is a strong research interest in this reaction due to its importance in biosynthetic processes, use as a protecting group and recent discovery of enzyme Diels-Alderase in nature (for example, spirotetronate cyclase AbyU), which could unlock new and efficient Diels-Alder reactions <ref name="DA" /><ref name="DA2" /><ref name="DAE1" /><ref name="DAE2" /><ref name="DAE3" /><ref name="DAE4" /><ref name="DAE5" /><ref name="DAE6" /><ref name="DAE7" /><ref name="DAE8" />. In the area of computational chemistry, there are many researches about the geometry of the transition states involved in Diels-Alder reactions and the overall reaction profiles <ref name="DA" /><ref name="DA1" /><ref name="DA2" /><ref name="DA3" />.

=='''4. Methodology.'''==
The calculation results assumed two reacting molecules in gaseous phase (in absence of solvation and other interactions with non-reacting, neighbouring molecules). The temperature and pressure settings in the calculations were 298.15 K and 1 atm (default settings). The symmetry and molecular geometries of the products and reactants were not restricted in the optimization process. All of the calculations were performed in GaussView 5.0 and the calculation grid was set to ultrafine (integral=grid=ultrafine). For TS calculations, additional keyword (opt=noeigen) was used in response to possible error in link 9999.

The non-covalent interaction plots were generated using a script by Henry Rzepa and Bob Hanson <ref name="NCI" /> using default parameters for intermolecular reaction (minimum rho cutoff set to 0.3, covalent density cutoff set to 0.07, fraction of total rho that defined intramolecular interaction set to 0.95, data scaling set to 1).

Unless stated otherwise, all of the optimization jobs were followed by frequency analysis.

===Exercise 1: Reaction of Butadiene with Ethylene.===
Cyclohexene (product) was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.2 Å at the reacting C-C termini. While freezing the coordinates of the reacting C-C termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of Butadiene and Ethylene.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex 1.png|thumb|400px| Figure 4.1: Exercise 1 Reaction Scheme.]]
|}

===Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole.===
The endo product was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.2 Å at the reacting C-C termini. While freezing the coordinates of the reacting C-C termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of Cyclohexadiene and 1,3-Dioxole.

The optimized structure at PM6 level was reoptimized at B3LYP/6-31G(d) level for the endo product, TS and the reactants.

The above procedures were repeated for the exo-product, with the exception of the reactants.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex 2.png|thumb|400px| Figure 4.2: Exercise 2 Reaction Scheme.]]
|}

===Exercise 3: Reaction of 5,6-dimethylenecyclohexa-1,3-diene and Sulfur Dioxide.===
The endo product was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.0 Å at the reacting C-O termini and 2.4 Å at the reacting C-S termini. While freezing the coordinates of the reacting termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of 5,6-dimethylenecyclohexa-1,3-diene and sulfur dioxide.

The above procedures were repeated for the exo-product, cheletropic-product and two minor Diels Alder regio-isomers, with the exception of reactants.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex 3.png|thumb|400px| Figure 4.3: Exercise 3 Reaction Scheme.]]
|}

=='''5. Results and Discussion.'''==
===Exercise 1: Reaction of Butadiene with Ethylene.===

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx1RD Exercise 1 Results and Discussion.]

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

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx2RD Exercise 2 Results and Discussion.]

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

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx3RD Exercise 3 Results and Discussion.]

=='''6. Conclusion.'''==
In conclusion, this paper had successfully carried out computational calculations to study six Diels-Alder reactions and one Cheletropic reaction using two popular computational methods: PM6 and B3LYP (6-31 G(d) basis set) in GaussView 5.0. For future work, the calculated results could be shared with other teams who could carry out the experiments in the lab to verify the results.

=='''7. References.'''==
<references>
<ref name="RCS Book">J. J. W. McDouall, in ''Computational Quantum Chemistry: Molecular Structure and Properties in Silico'', Royal Society of Chemistry, 2013, ch. 1, pp. 1-62.
</ref>
<ref name="Methylene"> H. F. SCHAEFER III, ''Science'', 1986, '''231''', 1100-1107.</ref>
<ref name="NCI"> Mod:NCI, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:NCI, (accessed March 2018).</ref>
<ref name="HKTheorem"> P. Hohenberg, W. Kohn, ''Phys. Rev.'', 1964, '''136(3B)''', B864–B871.</ref>
<ref name="PM6"> J. J. P. Stewart, '' J Mol Model'', 2007, '''13''', 1173-1213.</ref>
<ref name="B3LYP"> D. Avci, A. Başoğlu, Y. Atalay, '' Z. Naturforsch.'', 2008, '''63a''', 712-720.</ref>
<ref name="B3LYP1"> S.H. Vosko, L. Wilk, and M. Nusair, '' Can. J. Phys'', 1980, '''58''', 1200.</ref>
<ref name="DA"> T. J. Brocksom, J. Nakamura, M. L. Ferreira and U. Brocksom, '' J. Braz. Chem. Soc.'', 2001, '''12''', 597-622.</ref>
<ref name="DA1"> K. N. Houk, J. Gonzalez, Y. Li, ''Acc. Chem. Res.'', 1995, '''28''', 81-90.</ref>
<ref name="DA2"> J. Chen, Q. Deng, R. Wang, K. N. Houk, D. Hilvert, ''ChemBioChem'', 2000, '''1''', 255-261.</ref>
<ref name="DA3"> D. J. Tantillo, K. N. Houk, M. E. J. Jung, ''Org. Chem.'', 2001, '''66''', 1938-1940.</ref>
<ref name="DAE1"> K. N. Houk, J. Gonzalez, Y. Li, ''Acc. Chem. Res.'', 1995, '''28''', 81-90.</ref>
<ref name="DAE2"> W. M. Bandaranayake, J. E. Banfield, D. St. C. Black, ''J. Chem. Soc., Chem. Commun.'', 1980, 902-903.</ref>
<ref name="DAE3"> K. C. Nicolaou, N. A. Petasis, in ''Strategies and Tactics in Organic Synthesis'', ed. T. Lindberg, Academic Press, 1984, ch. 6, pp. 153-170.</ref>
<ref name="DAE4"> W. R. Roush, K. Koyama, M. L. Curtin, K. J. Moriarty, ''J. Am. Chem. Soc.'', 1996, '''118''', 7502-7512.</ref>
<ref name="DAE5"> H. Oikawa, T. Kobayashi, K. Katayama, Y. Suzuki, A. Ichihara, ''J. Org. Chem.'', 1998, '''63''', 8748-8756.</ref>
<ref name="DAE6"> E. M. Stocking, J. F. Sanz-Cervera, R. M. Williams, ''J. Am. Chem. Soc.'', 2000, '''122''', 1675-1683.</ref>
<ref name="DAE7"> G. A. Wallace, C. H. Heathcock, ''J. Org. Chem.'', 2001, '''66''', 450-454.</ref>
<ref name="DAE8"> K. Auclair, A. Sutherland, J. Kennedy, D. J. Witter, J. P. Van den Heever, C. R. Hutchinson, J. C. Vederas, ''J. Am. Chem. Soc.'', 2000, '''122''', 11519-11520.</ref>
<ref name="IRC"> S. Maeda, Y. Harabuchi, Y. Ono, T. Taketsugu, K. Morokuma, ''International Journal of Quantum Chemistry'', 2015, '''115''', 258-269.</ref>
<ref name="Rate">D. A. McQuarrie, in ''Physical Chemistry : A Molecular Approach'', University Science Books, 1997.
</ref>
</references>

File:KH1015 Ex 3.png

2018-03-14T10:05:03Z

Kh1015:

Rep:Kh1015TS

2018-03-14T10:03:52Z

Kh1015: /* Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole. */

=='''1. Abstract.'''==
This paper studied six Diels-Alder reactions and one Cheletropic reaction using two popular computational methods: PM6 and B3LYP (6-31 G(d) basis set) in GaussView 5.0. In Exercise 1-3, the MO calculation was used to identify the interacting frontier orbitals and possible secondary-orbital interactions. In Exercise 1, the C-C bond length of molecules optimized using PM6 level showed good agreement with literature with less than 1% percentage difference. IRC analysis at PM6 level in all exercises showed that the TS has been optimized. In Exercise 2 and Exercise 3, thermodynamic values (activation Gibbs-Free energy and Δ Gibbs-Free energy) were extracted from the log file output and rate constant was calculated using the activation Gibbs-Free energy based on method by D. A. McQuarrie (1997) <ref name="Rate" />.

=='''2. Aim.'''==
The aim of this study is to locate and characterize the transition states of several Diels-Alder reactions.

=='''3. Introduction.'''==

Chemical behaviour of a molecule is controlled by the electrons that participate in the chemical process <ref name="RCS Book" />. In particular, the electronic structure and properties in its stationary state could be described by the time-independent solution of Schrödinger’s equation:
<div align="center"><math>\hat{H} \psi_{A} = E_{A} \psi_{A}</math></div>
, where A labels the state of interest <ref name="RCS Book" />.

The above equation forms the foundation for quantum chemistry and modern computational methods.

For a given reaction where there is ambiguity in structure or mechanism, computational chemistry is useful in predicting the likeliest structure or mechanism. For example, in 1986, computational calculation correctly predicted and later experimentally confirmed a bent structure for methylene, which challenged the linear experimental value by Hertzberg thought to be true at the time <ref name="Methylene" />.

===A. Standard Computational Methods.===

The recurring challenge in computational method is that the Schrodinger equation can be solved exactly only for one-electron systems, while most molecules have much more than one electron in the system. To address this challenges, multiple methods have been developed to find increasingly accurate approximations to the Schrodinger equation for many-electron systems <ref name="RCS Book" />. Each of the methods has its own trade-off between accuracy and computational cost. With that in mind, two such methods had been selected in this study: semi-quantitative Parameterization Method 6 (PM6); and Density Functional Theory (DFT), Becke, 3-parameter, Lee-Yang-Parr (B3LYP).
====1) Semi Quantitative PM6 (Parameterization Method 6).====
PM6 is a modified semi-empirical method categorized under Neglect of Diatomic Differential Overlap (NDDO) <ref name="PM6" />.The main advantage of modified version of NDDO (MNDO) over its predecessors lies in the optimization of parameters to simulate molecular properties which is more accurate than calculations based on atomic properties <ref name="PM6" />. The inability of earlier MNDO to simulate hydrogen bond has been addressed in PM6 method, where the percentage difference of the average unsigned error (AUE) of a water dimer model (1.35 kcal mol<sup>-1</sup>) is 27% relative to that obtained by exhaustive analysis by Tschumper, et al. using CCSD(T) and a large basis set (5.00 kcal mol<sup>-1</sup>) <ref name="PM6" />.

====2) DFT, B3LYP (Density Functional Theory, Becke, 3-parameter, Lee-Yang-Parr).====
In general, DFT uses variational principle and one-electron density for the calculation and therefore bypasses the consideration of the many-electron wavefunction <ref name="RCS Book" />. From the Hohenberg-Kohn Theorems, it has been established that the ground state energy and all of its properties can be extracted from one-electron density alone <ref name="RCS Book" /><ref name="HKTheorem" />. DFT includes exchange-correlation functionals and self-consistent field type formalism <ref name="RCS Book" />. The basic form of DFT uses exchange and correlation terms of uniform electron gas, which is not a good approximation to the actual electron distribution in chemical systems. This error is most pronounced in two bonded atoms that have very high electronegativity difference (O-H for example), where there is a non-uniform distribution of electron density which is skewed towards the more electronegative atom. Hence, empirical inputs - such as atomic correlation energies or thermochemical databases - have been used to refine the DFT method <ref name="RCS Book" />. B3LYP is a hybrid DFT functional method whose energy term includes Slater exchange, the Hartree–Fock exchange, Becke’s exchange functional correction, the gradient-corrected correlation functional of Lee, Yang and Parr, and the local correlation functional of Vosko, Wilk and Nusair <ref name="B3LYP" /><ref name="B3LYP1" />.

===B. Finding a Stable or Transition structure in a PES.===

From the computational output, it is possible to model a potential energy surface (PES), that is dependent on one variable or more. In any given PES, there are 4 simple conditions which allow a user to find a stable structure or a transition structure <ref name="RCS Book" />:
====1) Determining Stationary Point via Gradient.====
<br><div align="center"><math>\frac{dE(\textbf{R})}{dR_{i}} = 0, i=1,2, . . . 3N_{atoms} - 6</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and R<sub>i</sub> refers to a specific member of the set.

====2) Characterizing Minimum Point via Curvature (Positive Force Constants).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{i}} > 0, i=1,2, . . . 3N_{atoms} - 6</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>i</sub> refers to a specific combination of R and bond angle (θ).

====3) Characterizing Transition Point via Curvature (One Unique Negative Force Constant corresponding to First Order Saddle Point in Reaction Coordinate (RC)).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{RC}} < 0</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>RC</sub> refers to a specific combination of R and bond angle (θ) at the lowest-possible transition state in the PES.

====4) Characterizing Transition Point via Curvature (Positive Force Constants For The Remaining Ones).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{i}} > 0, i=1,2, . . . 3N_{atoms} - 7</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>i</sub> refers to a specific combination of '''R''' and bond angle (θ).

While useful, it should be noted that the 4 conditions above '''could not differentiate between global and local stationary points''', which could impact the accuracy of geometry optimization if the geometry is trapped in a local minimum rather than global minimum.

===C.Intrinsic Reaction Coordinate (IRC).===
In 1970, Fukui proposed the concept of IRC, which is defined as the mass-weighted, vibrationless, motionless and steepest descent path on the PES from the TS or the first-order saddle point to two minima on either side of the TS <ref name="IRC" />. The descent from higher-order saddle point is called meta-IRC <ref name="IRC" />. In mathematical form, IRC is obtained by solving the following differential equation <ref name="IRC" />:
<br><div align="center"><math>\frac{d\textbf{q}(s)}{ds} = \textbf{v}(s)</math></div>
, where '''q''' is the mass-weighted Cartesian coordinates, s is the coordinate along the IRC and '''v''' is a normalized tangent vector to the IRC corresponding to the normal coordinate eigenvector with a negative eigenvalue at the TS with s=0.

At the other points, '''v''' is the unit vector parallel to the mass-weighted gradient vector '''g''' with the following relationship <ref name="IRC" />:
<br><div align="center"><math>\textbf{v} = - \frac{\textbf{g}}{|\textbf{g}|}</math> for s > 0</div>
<br><div align="center"> and </div>
<br><div align="center"><math>\textbf{v} = \frac{\textbf{g}}{|\textbf{g}|}</math> for s < 0</div>

IRC calculation has been used extensively to confirm the connection between a given TS and two minima (reactant(s) and product(s)) for a given reaction <ref name="IRC" />. In this study, IRC calculation had been done for all the reactions such that it can be used to '''independently confirm''' that the TS geometry for the given reaction had truly been optimized.

From a successful IRC calculation (Minimum-TS-Minimum), it is possible to extract the calculated activation energy (linked to a given computational method) and therefore, the calculated rate constant for a reaction via transition state theory <ref name="IRC" />.

===D. Predicting Rate of Reaction from Calculated Thermodynamic Values.===
Once the activation free-energy of a reaction is calculated, it is possible to calculate the predicted rate of reaction via the equation below <ref name="Rate" />:
<br><div align="center"><math> k(T) = \frac{k_{B}T}{hc^{o}} e^{\frac{-\Delta^{\ddagger}G^{o}}{RT}} </math></div>

, where k(T) is rate constant at a specified temperature, k<sub>B</sub> is Boltzmann constant (1.3807 x 10<sup>-23</sup> J K<sup>-1</sup>), T is temperature (in K), h is Planck's constant (6.626176 x 10<sup>-34</sup> J s), c<sup>o</sup> is concentration (taken to be 1, unitless), Δ<sup>‡</sup>G<sup>o</sup> is the activation Gibbs-Free Energy (J mol<sup>-1</sup>) and R is gas constant (8.314 J mol<sup>-1</sup> K<sup>-1</sup>).

===E. Diels-Alder Reaction as a Study Topic.===
Diels-Alder reaction is a concerted [<sub>π</sub>4<sub>s</sub> + <sub>π</sub>2<sub>s</sub>] cycloaddition between an s-cis conjugated diene and a dienophile to form a cyclohexene <ref name="DA" />. In the reaction, 3 π bonds are broken and 2 sigma bonds and 1 new π bond is formed. In a normal Diels-Alder reaction, the interaction happens between an electron-rich s-cis dienophile and an electron poor diene. In an inverse-electron-demand Diels-Alder reaction, the interaction happens between an electron-poor s-cis dienophile and an electron rich diene.

There is a strong research interest in this reaction due to its importance in biosynthetic processes, use as a protecting group and recent discovery of enzyme Diels-Alderase in nature (for example, spirotetronate cyclase AbyU), which could unlock new and efficient Diels-Alder reactions <ref name="DA" /><ref name="DA2" /><ref name="DAE1" /><ref name="DAE2" /><ref name="DAE3" /><ref name="DAE4" /><ref name="DAE5" /><ref name="DAE6" /><ref name="DAE7" /><ref name="DAE8" />. In the area of computational chemistry, there are many researches about the geometry of the transition states involved in Diels-Alder reactions and the overall reaction profiles <ref name="DA" /><ref name="DA1" /><ref name="DA2" /><ref name="DA3" />.

=='''4. Methodology.'''==
The calculation results assumed two reacting molecules in gaseous phase (in absence of solvation and other interactions with non-reacting, neighbouring molecules). The temperature and pressure settings in the calculations were 298.15 K and 1 atm (default settings). The symmetry and molecular geometries of the products and reactants were not restricted in the optimization process. All of the calculations were performed in GaussView 5.0 and the calculation grid was set to ultrafine (integral=grid=ultrafine). For TS calculations, additional keyword (opt=noeigen) was used in response to possible error in link 9999.

The non-covalent interaction plots were generated using a script by Henry Rzepa and Bob Hanson <ref name="NCI" /> using default parameters for intermolecular reaction (minimum rho cutoff set to 0.3, covalent density cutoff set to 0.07, fraction of total rho that defined intramolecular interaction set to 0.95, data scaling set to 1).

Unless stated otherwise, all of the optimization jobs were followed by frequency analysis.

===Exercise 1: Reaction of Butadiene with Ethylene.===
Cyclohexene (product) was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.2 Å at the reacting C-C termini. While freezing the coordinates of the reacting C-C termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of Butadiene and Ethylene.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex 1.png|thumb|400px| Figure 4.1: Exercise 1 Reaction Scheme.]]
|}

===Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole.===
The endo product was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.2 Å at the reacting C-C termini. While freezing the coordinates of the reacting C-C termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of Cyclohexadiene and 1,3-Dioxole.

The optimized structure at PM6 level was reoptimized at B3LYP/6-31G(d) level for the endo product, TS and the reactants.

The above procedures were repeated for the exo-product, with the exception of the reactants.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex 2.png|thumb|400px| Figure 4.2: Exercise 2 Reaction Scheme.]]
|}

===Exercise 3: Reaction of 5,6-dimethylenecyclohexa-1,3-diene and Sulfur Dioxide.===
The endo product was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.0 Å at the reacting C-O termini and 2.4 Å at the reacting C-S termini. While freezing the coordinates of the reacting termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of 5,6-dimethylenecyclohexa-1,3-diene and sulfur dioxide.

The above procedures were repeated for the exo-product, cheletropic-product and two minor Diels Alder regio-isomers, with the exception of reactants.

=='''5. Results and Discussion.'''==
===Exercise 1: Reaction of Butadiene with Ethylene.===

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx1RD Exercise 1 Results and Discussion.]

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

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx2RD Exercise 2 Results and Discussion.]

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

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx3RD Exercise 3 Results and Discussion.]

=='''6. Conclusion.'''==
In conclusion, this paper had successfully carried out computational calculations to study six Diels-Alder reactions and one Cheletropic reaction using two popular computational methods: PM6 and B3LYP (6-31 G(d) basis set) in GaussView 5.0. For future work, the calculated results could be shared with other teams who could carry out the experiments in the lab to verify the results.

=='''7. References.'''==
<references>
<ref name="RCS Book">J. J. W. McDouall, in ''Computational Quantum Chemistry: Molecular Structure and Properties in Silico'', Royal Society of Chemistry, 2013, ch. 1, pp. 1-62.
</ref>
<ref name="Methylene"> H. F. SCHAEFER III, ''Science'', 1986, '''231''', 1100-1107.</ref>
<ref name="NCI"> Mod:NCI, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:NCI, (accessed March 2018).</ref>
<ref name="HKTheorem"> P. Hohenberg, W. Kohn, ''Phys. Rev.'', 1964, '''136(3B)''', B864–B871.</ref>
<ref name="PM6"> J. J. P. Stewart, '' J Mol Model'', 2007, '''13''', 1173-1213.</ref>
<ref name="B3LYP"> D. Avci, A. Başoğlu, Y. Atalay, '' Z. Naturforsch.'', 2008, '''63a''', 712-720.</ref>
<ref name="B3LYP1"> S.H. Vosko, L. Wilk, and M. Nusair, '' Can. J. Phys'', 1980, '''58''', 1200.</ref>
<ref name="DA"> T. J. Brocksom, J. Nakamura, M. L. Ferreira and U. Brocksom, '' J. Braz. Chem. Soc.'', 2001, '''12''', 597-622.</ref>
<ref name="DA1"> K. N. Houk, J. Gonzalez, Y. Li, ''Acc. Chem. Res.'', 1995, '''28''', 81-90.</ref>
<ref name="DA2"> J. Chen, Q. Deng, R. Wang, K. N. Houk, D. Hilvert, ''ChemBioChem'', 2000, '''1''', 255-261.</ref>
<ref name="DA3"> D. J. Tantillo, K. N. Houk, M. E. J. Jung, ''Org. Chem.'', 2001, '''66''', 1938-1940.</ref>
<ref name="DAE1"> K. N. Houk, J. Gonzalez, Y. Li, ''Acc. Chem. Res.'', 1995, '''28''', 81-90.</ref>
<ref name="DAE2"> W. M. Bandaranayake, J. E. Banfield, D. St. C. Black, ''J. Chem. Soc., Chem. Commun.'', 1980, 902-903.</ref>
<ref name="DAE3"> K. C. Nicolaou, N. A. Petasis, in ''Strategies and Tactics in Organic Synthesis'', ed. T. Lindberg, Academic Press, 1984, ch. 6, pp. 153-170.</ref>
<ref name="DAE4"> W. R. Roush, K. Koyama, M. L. Curtin, K. J. Moriarty, ''J. Am. Chem. Soc.'', 1996, '''118''', 7502-7512.</ref>
<ref name="DAE5"> H. Oikawa, T. Kobayashi, K. Katayama, Y. Suzuki, A. Ichihara, ''J. Org. Chem.'', 1998, '''63''', 8748-8756.</ref>
<ref name="DAE6"> E. M. Stocking, J. F. Sanz-Cervera, R. M. Williams, ''J. Am. Chem. Soc.'', 2000, '''122''', 1675-1683.</ref>
<ref name="DAE7"> G. A. Wallace, C. H. Heathcock, ''J. Org. Chem.'', 2001, '''66''', 450-454.</ref>
<ref name="DAE8"> K. Auclair, A. Sutherland, J. Kennedy, D. J. Witter, J. P. Van den Heever, C. R. Hutchinson, J. C. Vederas, ''J. Am. Chem. Soc.'', 2000, '''122''', 11519-11520.</ref>
<ref name="IRC"> S. Maeda, Y. Harabuchi, Y. Ono, T. Taketsugu, K. Morokuma, ''International Journal of Quantum Chemistry'', 2015, '''115''', 258-269.</ref>
<ref name="Rate">D. A. McQuarrie, in ''Physical Chemistry : A Molecular Approach'', University Science Books, 1997.
</ref>
</references>

File:KH1015 Ex 2.png

2018-03-14T10:03:26Z

Kh1015:

Rep:Kh1015TS

2018-03-14T10:02:42Z

Kh1015: /* Exercise 1: Reaction of Butadiene with Ethylene. */

=='''1. Abstract.'''==
This paper studied six Diels-Alder reactions and one Cheletropic reaction using two popular computational methods: PM6 and B3LYP (6-31 G(d) basis set) in GaussView 5.0. In Exercise 1-3, the MO calculation was used to identify the interacting frontier orbitals and possible secondary-orbital interactions. In Exercise 1, the C-C bond length of molecules optimized using PM6 level showed good agreement with literature with less than 1% percentage difference. IRC analysis at PM6 level in all exercises showed that the TS has been optimized. In Exercise 2 and Exercise 3, thermodynamic values (activation Gibbs-Free energy and Δ Gibbs-Free energy) were extracted from the log file output and rate constant was calculated using the activation Gibbs-Free energy based on method by D. A. McQuarrie (1997) <ref name="Rate" />.

=='''2. Aim.'''==
The aim of this study is to locate and characterize the transition states of several Diels-Alder reactions.

=='''3. Introduction.'''==

Chemical behaviour of a molecule is controlled by the electrons that participate in the chemical process <ref name="RCS Book" />. In particular, the electronic structure and properties in its stationary state could be described by the time-independent solution of Schrödinger’s equation:
<div align="center"><math>\hat{H} \psi_{A} = E_{A} \psi_{A}</math></div>
, where A labels the state of interest <ref name="RCS Book" />.

The above equation forms the foundation for quantum chemistry and modern computational methods.

For a given reaction where there is ambiguity in structure or mechanism, computational chemistry is useful in predicting the likeliest structure or mechanism. For example, in 1986, computational calculation correctly predicted and later experimentally confirmed a bent structure for methylene, which challenged the linear experimental value by Hertzberg thought to be true at the time <ref name="Methylene" />.

===A. Standard Computational Methods.===

The recurring challenge in computational method is that the Schrodinger equation can be solved exactly only for one-electron systems, while most molecules have much more than one electron in the system. To address this challenges, multiple methods have been developed to find increasingly accurate approximations to the Schrodinger equation for many-electron systems <ref name="RCS Book" />. Each of the methods has its own trade-off between accuracy and computational cost. With that in mind, two such methods had been selected in this study: semi-quantitative Parameterization Method 6 (PM6); and Density Functional Theory (DFT), Becke, 3-parameter, Lee-Yang-Parr (B3LYP).
====1) Semi Quantitative PM6 (Parameterization Method 6).====
PM6 is a modified semi-empirical method categorized under Neglect of Diatomic Differential Overlap (NDDO) <ref name="PM6" />.The main advantage of modified version of NDDO (MNDO) over its predecessors lies in the optimization of parameters to simulate molecular properties which is more accurate than calculations based on atomic properties <ref name="PM6" />. The inability of earlier MNDO to simulate hydrogen bond has been addressed in PM6 method, where the percentage difference of the average unsigned error (AUE) of a water dimer model (1.35 kcal mol<sup>-1</sup>) is 27% relative to that obtained by exhaustive analysis by Tschumper, et al. using CCSD(T) and a large basis set (5.00 kcal mol<sup>-1</sup>) <ref name="PM6" />.

====2) DFT, B3LYP (Density Functional Theory, Becke, 3-parameter, Lee-Yang-Parr).====
In general, DFT uses variational principle and one-electron density for the calculation and therefore bypasses the consideration of the many-electron wavefunction <ref name="RCS Book" />. From the Hohenberg-Kohn Theorems, it has been established that the ground state energy and all of its properties can be extracted from one-electron density alone <ref name="RCS Book" /><ref name="HKTheorem" />. DFT includes exchange-correlation functionals and self-consistent field type formalism <ref name="RCS Book" />. The basic form of DFT uses exchange and correlation terms of uniform electron gas, which is not a good approximation to the actual electron distribution in chemical systems. This error is most pronounced in two bonded atoms that have very high electronegativity difference (O-H for example), where there is a non-uniform distribution of electron density which is skewed towards the more electronegative atom. Hence, empirical inputs - such as atomic correlation energies or thermochemical databases - have been used to refine the DFT method <ref name="RCS Book" />. B3LYP is a hybrid DFT functional method whose energy term includes Slater exchange, the Hartree–Fock exchange, Becke’s exchange functional correction, the gradient-corrected correlation functional of Lee, Yang and Parr, and the local correlation functional of Vosko, Wilk and Nusair <ref name="B3LYP" /><ref name="B3LYP1" />.

===B. Finding a Stable or Transition structure in a PES.===

From the computational output, it is possible to model a potential energy surface (PES), that is dependent on one variable or more. In any given PES, there are 4 simple conditions which allow a user to find a stable structure or a transition structure <ref name="RCS Book" />:
====1) Determining Stationary Point via Gradient.====
<br><div align="center"><math>\frac{dE(\textbf{R})}{dR_{i}} = 0, i=1,2, . . . 3N_{atoms} - 6</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and R<sub>i</sub> refers to a specific member of the set.

====2) Characterizing Minimum Point via Curvature (Positive Force Constants).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{i}} > 0, i=1,2, . . . 3N_{atoms} - 6</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>i</sub> refers to a specific combination of R and bond angle (θ).

====3) Characterizing Transition Point via Curvature (One Unique Negative Force Constant corresponding to First Order Saddle Point in Reaction Coordinate (RC)).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{RC}} < 0</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>RC</sub> refers to a specific combination of R and bond angle (θ) at the lowest-possible transition state in the PES.

====4) Characterizing Transition Point via Curvature (Positive Force Constants For The Remaining Ones).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{i}} > 0, i=1,2, . . . 3N_{atoms} - 7</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>i</sub> refers to a specific combination of '''R''' and bond angle (θ).

While useful, it should be noted that the 4 conditions above '''could not differentiate between global and local stationary points''', which could impact the accuracy of geometry optimization if the geometry is trapped in a local minimum rather than global minimum.

===C.Intrinsic Reaction Coordinate (IRC).===
In 1970, Fukui proposed the concept of IRC, which is defined as the mass-weighted, vibrationless, motionless and steepest descent path on the PES from the TS or the first-order saddle point to two minima on either side of the TS <ref name="IRC" />. The descent from higher-order saddle point is called meta-IRC <ref name="IRC" />. In mathematical form, IRC is obtained by solving the following differential equation <ref name="IRC" />:
<br><div align="center"><math>\frac{d\textbf{q}(s)}{ds} = \textbf{v}(s)</math></div>
, where '''q''' is the mass-weighted Cartesian coordinates, s is the coordinate along the IRC and '''v''' is a normalized tangent vector to the IRC corresponding to the normal coordinate eigenvector with a negative eigenvalue at the TS with s=0.

At the other points, '''v''' is the unit vector parallel to the mass-weighted gradient vector '''g''' with the following relationship <ref name="IRC" />:
<br><div align="center"><math>\textbf{v} = - \frac{\textbf{g}}{|\textbf{g}|}</math> for s > 0</div>
<br><div align="center"> and </div>
<br><div align="center"><math>\textbf{v} = \frac{\textbf{g}}{|\textbf{g}|}</math> for s < 0</div>

IRC calculation has been used extensively to confirm the connection between a given TS and two minima (reactant(s) and product(s)) for a given reaction <ref name="IRC" />. In this study, IRC calculation had been done for all the reactions such that it can be used to '''independently confirm''' that the TS geometry for the given reaction had truly been optimized.

From a successful IRC calculation (Minimum-TS-Minimum), it is possible to extract the calculated activation energy (linked to a given computational method) and therefore, the calculated rate constant for a reaction via transition state theory <ref name="IRC" />.

===D. Predicting Rate of Reaction from Calculated Thermodynamic Values.===
Once the activation free-energy of a reaction is calculated, it is possible to calculate the predicted rate of reaction via the equation below <ref name="Rate" />:
<br><div align="center"><math> k(T) = \frac{k_{B}T}{hc^{o}} e^{\frac{-\Delta^{\ddagger}G^{o}}{RT}} </math></div>

, where k(T) is rate constant at a specified temperature, k<sub>B</sub> is Boltzmann constant (1.3807 x 10<sup>-23</sup> J K<sup>-1</sup>), T is temperature (in K), h is Planck's constant (6.626176 x 10<sup>-34</sup> J s), c<sup>o</sup> is concentration (taken to be 1, unitless), Δ<sup>‡</sup>G<sup>o</sup> is the activation Gibbs-Free Energy (J mol<sup>-1</sup>) and R is gas constant (8.314 J mol<sup>-1</sup> K<sup>-1</sup>).

===E. Diels-Alder Reaction as a Study Topic.===
Diels-Alder reaction is a concerted [<sub>π</sub>4<sub>s</sub> + <sub>π</sub>2<sub>s</sub>] cycloaddition between an s-cis conjugated diene and a dienophile to form a cyclohexene <ref name="DA" />. In the reaction, 3 π bonds are broken and 2 sigma bonds and 1 new π bond is formed. In a normal Diels-Alder reaction, the interaction happens between an electron-rich s-cis dienophile and an electron poor diene. In an inverse-electron-demand Diels-Alder reaction, the interaction happens between an electron-poor s-cis dienophile and an electron rich diene.

There is a strong research interest in this reaction due to its importance in biosynthetic processes, use as a protecting group and recent discovery of enzyme Diels-Alderase in nature (for example, spirotetronate cyclase AbyU), which could unlock new and efficient Diels-Alder reactions <ref name="DA" /><ref name="DA2" /><ref name="DAE1" /><ref name="DAE2" /><ref name="DAE3" /><ref name="DAE4" /><ref name="DAE5" /><ref name="DAE6" /><ref name="DAE7" /><ref name="DAE8" />. In the area of computational chemistry, there are many researches about the geometry of the transition states involved in Diels-Alder reactions and the overall reaction profiles <ref name="DA" /><ref name="DA1" /><ref name="DA2" /><ref name="DA3" />.

=='''4. Methodology.'''==
The calculation results assumed two reacting molecules in gaseous phase (in absence of solvation and other interactions with non-reacting, neighbouring molecules). The temperature and pressure settings in the calculations were 298.15 K and 1 atm (default settings). The symmetry and molecular geometries of the products and reactants were not restricted in the optimization process. All of the calculations were performed in GaussView 5.0 and the calculation grid was set to ultrafine (integral=grid=ultrafine). For TS calculations, additional keyword (opt=noeigen) was used in response to possible error in link 9999.

The non-covalent interaction plots were generated using a script by Henry Rzepa and Bob Hanson <ref name="NCI" /> using default parameters for intermolecular reaction (minimum rho cutoff set to 0.3, covalent density cutoff set to 0.07, fraction of total rho that defined intramolecular interaction set to 0.95, data scaling set to 1).

Unless stated otherwise, all of the optimization jobs were followed by frequency analysis.

===Exercise 1: Reaction of Butadiene with Ethylene.===
Cyclohexene (product) was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.2 Å at the reacting C-C termini. While freezing the coordinates of the reacting C-C termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of Butadiene and Ethylene.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex 1.png|thumb|400px| Figure 4.1: Exercise 1 Reaction Scheme.]]
|}

===Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole.===
The endo product was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.2 Å at the reacting C-C termini. While freezing the coordinates of the reacting C-C termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of Cyclohexadiene and 1,3-Dioxole.

The optimized structure at PM6 level was reoptimized at B3LYP/6-31G(d) level for the endo product, TS and the reactants.

The above procedures were repeated for the exo-product, with the exception of the reactants.

===Exercise 3: Reaction of 5,6-dimethylenecyclohexa-1,3-diene and Sulfur Dioxide.===
The endo product was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.0 Å at the reacting C-O termini and 2.4 Å at the reacting C-S termini. While freezing the coordinates of the reacting termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of 5,6-dimethylenecyclohexa-1,3-diene and sulfur dioxide.

The above procedures were repeated for the exo-product, cheletropic-product and two minor Diels Alder regio-isomers, with the exception of reactants.

=='''5. Results and Discussion.'''==
===Exercise 1: Reaction of Butadiene with Ethylene.===

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx1RD Exercise 1 Results and Discussion.]

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

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx2RD Exercise 2 Results and Discussion.]

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

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx3RD Exercise 3 Results and Discussion.]

=='''6. Conclusion.'''==
In conclusion, this paper had successfully carried out computational calculations to study six Diels-Alder reactions and one Cheletropic reaction using two popular computational methods: PM6 and B3LYP (6-31 G(d) basis set) in GaussView 5.0. For future work, the calculated results could be shared with other teams who could carry out the experiments in the lab to verify the results.

=='''7. References.'''==
<references>
<ref name="RCS Book">J. J. W. McDouall, in ''Computational Quantum Chemistry: Molecular Structure and Properties in Silico'', Royal Society of Chemistry, 2013, ch. 1, pp. 1-62.
</ref>
<ref name="Methylene"> H. F. SCHAEFER III, ''Science'', 1986, '''231''', 1100-1107.</ref>
<ref name="NCI"> Mod:NCI, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:NCI, (accessed March 2018).</ref>
<ref name="HKTheorem"> P. Hohenberg, W. Kohn, ''Phys. Rev.'', 1964, '''136(3B)''', B864–B871.</ref>
<ref name="PM6"> J. J. P. Stewart, '' J Mol Model'', 2007, '''13''', 1173-1213.</ref>
<ref name="B3LYP"> D. Avci, A. Başoğlu, Y. Atalay, '' Z. Naturforsch.'', 2008, '''63a''', 712-720.</ref>
<ref name="B3LYP1"> S.H. Vosko, L. Wilk, and M. Nusair, '' Can. J. Phys'', 1980, '''58''', 1200.</ref>
<ref name="DA"> T. J. Brocksom, J. Nakamura, M. L. Ferreira and U. Brocksom, '' J. Braz. Chem. Soc.'', 2001, '''12''', 597-622.</ref>
<ref name="DA1"> K. N. Houk, J. Gonzalez, Y. Li, ''Acc. Chem. Res.'', 1995, '''28''', 81-90.</ref>
<ref name="DA2"> J. Chen, Q. Deng, R. Wang, K. N. Houk, D. Hilvert, ''ChemBioChem'', 2000, '''1''', 255-261.</ref>
<ref name="DA3"> D. J. Tantillo, K. N. Houk, M. E. J. Jung, ''Org. Chem.'', 2001, '''66''', 1938-1940.</ref>
<ref name="DAE1"> K. N. Houk, J. Gonzalez, Y. Li, ''Acc. Chem. Res.'', 1995, '''28''', 81-90.</ref>
<ref name="DAE2"> W. M. Bandaranayake, J. E. Banfield, D. St. C. Black, ''J. Chem. Soc., Chem. Commun.'', 1980, 902-903.</ref>
<ref name="DAE3"> K. C. Nicolaou, N. A. Petasis, in ''Strategies and Tactics in Organic Synthesis'', ed. T. Lindberg, Academic Press, 1984, ch. 6, pp. 153-170.</ref>
<ref name="DAE4"> W. R. Roush, K. Koyama, M. L. Curtin, K. J. Moriarty, ''J. Am. Chem. Soc.'', 1996, '''118''', 7502-7512.</ref>
<ref name="DAE5"> H. Oikawa, T. Kobayashi, K. Katayama, Y. Suzuki, A. Ichihara, ''J. Org. Chem.'', 1998, '''63''', 8748-8756.</ref>
<ref name="DAE6"> E. M. Stocking, J. F. Sanz-Cervera, R. M. Williams, ''J. Am. Chem. Soc.'', 2000, '''122''', 1675-1683.</ref>
<ref name="DAE7"> G. A. Wallace, C. H. Heathcock, ''J. Org. Chem.'', 2001, '''66''', 450-454.</ref>
<ref name="DAE8"> K. Auclair, A. Sutherland, J. Kennedy, D. J. Witter, J. P. Van den Heever, C. R. Hutchinson, J. C. Vederas, ''J. Am. Chem. Soc.'', 2000, '''122''', 11519-11520.</ref>
<ref name="IRC"> S. Maeda, Y. Harabuchi, Y. Ono, T. Taketsugu, K. Morokuma, ''International Journal of Quantum Chemistry'', 2015, '''115''', 258-269.</ref>
<ref name="Rate">D. A. McQuarrie, in ''Physical Chemistry : A Molecular Approach'', University Science Books, 1997.
</ref>
</references>

Rep:Kh1015TS

2018-03-14T10:02:17Z

Kh1015: /* Exercise 1: Reaction of Butadiene with Ethylene. */

=='''1. Abstract.'''==
This paper studied six Diels-Alder reactions and one Cheletropic reaction using two popular computational methods: PM6 and B3LYP (6-31 G(d) basis set) in GaussView 5.0. In Exercise 1-3, the MO calculation was used to identify the interacting frontier orbitals and possible secondary-orbital interactions. In Exercise 1, the C-C bond length of molecules optimized using PM6 level showed good agreement with literature with less than 1% percentage difference. IRC analysis at PM6 level in all exercises showed that the TS has been optimized. In Exercise 2 and Exercise 3, thermodynamic values (activation Gibbs-Free energy and Δ Gibbs-Free energy) were extracted from the log file output and rate constant was calculated using the activation Gibbs-Free energy based on method by D. A. McQuarrie (1997) <ref name="Rate" />.

=='''2. Aim.'''==
The aim of this study is to locate and characterize the transition states of several Diels-Alder reactions.

=='''3. Introduction.'''==

Chemical behaviour of a molecule is controlled by the electrons that participate in the chemical process <ref name="RCS Book" />. In particular, the electronic structure and properties in its stationary state could be described by the time-independent solution of Schrödinger’s equation:
<div align="center"><math>\hat{H} \psi_{A} = E_{A} \psi_{A}</math></div>
, where A labels the state of interest <ref name="RCS Book" />.

The above equation forms the foundation for quantum chemistry and modern computational methods.

For a given reaction where there is ambiguity in structure or mechanism, computational chemistry is useful in predicting the likeliest structure or mechanism. For example, in 1986, computational calculation correctly predicted and later experimentally confirmed a bent structure for methylene, which challenged the linear experimental value by Hertzberg thought to be true at the time <ref name="Methylene" />.

===A. Standard Computational Methods.===

The recurring challenge in computational method is that the Schrodinger equation can be solved exactly only for one-electron systems, while most molecules have much more than one electron in the system. To address this challenges, multiple methods have been developed to find increasingly accurate approximations to the Schrodinger equation for many-electron systems <ref name="RCS Book" />. Each of the methods has its own trade-off between accuracy and computational cost. With that in mind, two such methods had been selected in this study: semi-quantitative Parameterization Method 6 (PM6); and Density Functional Theory (DFT), Becke, 3-parameter, Lee-Yang-Parr (B3LYP).
====1) Semi Quantitative PM6 (Parameterization Method 6).====
PM6 is a modified semi-empirical method categorized under Neglect of Diatomic Differential Overlap (NDDO) <ref name="PM6" />.The main advantage of modified version of NDDO (MNDO) over its predecessors lies in the optimization of parameters to simulate molecular properties which is more accurate than calculations based on atomic properties <ref name="PM6" />. The inability of earlier MNDO to simulate hydrogen bond has been addressed in PM6 method, where the percentage difference of the average unsigned error (AUE) of a water dimer model (1.35 kcal mol<sup>-1</sup>) is 27% relative to that obtained by exhaustive analysis by Tschumper, et al. using CCSD(T) and a large basis set (5.00 kcal mol<sup>-1</sup>) <ref name="PM6" />.

====2) DFT, B3LYP (Density Functional Theory, Becke, 3-parameter, Lee-Yang-Parr).====
In general, DFT uses variational principle and one-electron density for the calculation and therefore bypasses the consideration of the many-electron wavefunction <ref name="RCS Book" />. From the Hohenberg-Kohn Theorems, it has been established that the ground state energy and all of its properties can be extracted from one-electron density alone <ref name="RCS Book" /><ref name="HKTheorem" />. DFT includes exchange-correlation functionals and self-consistent field type formalism <ref name="RCS Book" />. The basic form of DFT uses exchange and correlation terms of uniform electron gas, which is not a good approximation to the actual electron distribution in chemical systems. This error is most pronounced in two bonded atoms that have very high electronegativity difference (O-H for example), where there is a non-uniform distribution of electron density which is skewed towards the more electronegative atom. Hence, empirical inputs - such as atomic correlation energies or thermochemical databases - have been used to refine the DFT method <ref name="RCS Book" />. B3LYP is a hybrid DFT functional method whose energy term includes Slater exchange, the Hartree–Fock exchange, Becke’s exchange functional correction, the gradient-corrected correlation functional of Lee, Yang and Parr, and the local correlation functional of Vosko, Wilk and Nusair <ref name="B3LYP" /><ref name="B3LYP1" />.

===B. Finding a Stable or Transition structure in a PES.===

From the computational output, it is possible to model a potential energy surface (PES), that is dependent on one variable or more. In any given PES, there are 4 simple conditions which allow a user to find a stable structure or a transition structure <ref name="RCS Book" />:
====1) Determining Stationary Point via Gradient.====
<br><div align="center"><math>\frac{dE(\textbf{R})}{dR_{i}} = 0, i=1,2, . . . 3N_{atoms} - 6</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and R<sub>i</sub> refers to a specific member of the set.

====2) Characterizing Minimum Point via Curvature (Positive Force Constants).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{i}} > 0, i=1,2, . . . 3N_{atoms} - 6</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>i</sub> refers to a specific combination of R and bond angle (θ).

====3) Characterizing Transition Point via Curvature (One Unique Negative Force Constant corresponding to First Order Saddle Point in Reaction Coordinate (RC)).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{RC}} < 0</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>RC</sub> refers to a specific combination of R and bond angle (θ) at the lowest-possible transition state in the PES.

====4) Characterizing Transition Point via Curvature (Positive Force Constants For The Remaining Ones).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{i}} > 0, i=1,2, . . . 3N_{atoms} - 7</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>i</sub> refers to a specific combination of '''R''' and bond angle (θ).

While useful, it should be noted that the 4 conditions above '''could not differentiate between global and local stationary points''', which could impact the accuracy of geometry optimization if the geometry is trapped in a local minimum rather than global minimum.

===C.Intrinsic Reaction Coordinate (IRC).===
In 1970, Fukui proposed the concept of IRC, which is defined as the mass-weighted, vibrationless, motionless and steepest descent path on the PES from the TS or the first-order saddle point to two minima on either side of the TS <ref name="IRC" />. The descent from higher-order saddle point is called meta-IRC <ref name="IRC" />. In mathematical form, IRC is obtained by solving the following differential equation <ref name="IRC" />:
<br><div align="center"><math>\frac{d\textbf{q}(s)}{ds} = \textbf{v}(s)</math></div>
, where '''q''' is the mass-weighted Cartesian coordinates, s is the coordinate along the IRC and '''v''' is a normalized tangent vector to the IRC corresponding to the normal coordinate eigenvector with a negative eigenvalue at the TS with s=0.

At the other points, '''v''' is the unit vector parallel to the mass-weighted gradient vector '''g''' with the following relationship <ref name="IRC" />:
<br><div align="center"><math>\textbf{v} = - \frac{\textbf{g}}{|\textbf{g}|}</math> for s > 0</div>
<br><div align="center"> and </div>
<br><div align="center"><math>\textbf{v} = \frac{\textbf{g}}{|\textbf{g}|}</math> for s < 0</div>

IRC calculation has been used extensively to confirm the connection between a given TS and two minima (reactant(s) and product(s)) for a given reaction <ref name="IRC" />. In this study, IRC calculation had been done for all the reactions such that it can be used to '''independently confirm''' that the TS geometry for the given reaction had truly been optimized.

From a successful IRC calculation (Minimum-TS-Minimum), it is possible to extract the calculated activation energy (linked to a given computational method) and therefore, the calculated rate constant for a reaction via transition state theory <ref name="IRC" />.

===D. Predicting Rate of Reaction from Calculated Thermodynamic Values.===
Once the activation free-energy of a reaction is calculated, it is possible to calculate the predicted rate of reaction via the equation below <ref name="Rate" />:
<br><div align="center"><math> k(T) = \frac{k_{B}T}{hc^{o}} e^{\frac{-\Delta^{\ddagger}G^{o}}{RT}} </math></div>

, where k(T) is rate constant at a specified temperature, k<sub>B</sub> is Boltzmann constant (1.3807 x 10<sup>-23</sup> J K<sup>-1</sup>), T is temperature (in K), h is Planck's constant (6.626176 x 10<sup>-34</sup> J s), c<sup>o</sup> is concentration (taken to be 1, unitless), Δ<sup>‡</sup>G<sup>o</sup> is the activation Gibbs-Free Energy (J mol<sup>-1</sup>) and R is gas constant (8.314 J mol<sup>-1</sup> K<sup>-1</sup>).

===E. Diels-Alder Reaction as a Study Topic.===
Diels-Alder reaction is a concerted [<sub>π</sub>4<sub>s</sub> + <sub>π</sub>2<sub>s</sub>] cycloaddition between an s-cis conjugated diene and a dienophile to form a cyclohexene <ref name="DA" />. In the reaction, 3 π bonds are broken and 2 sigma bonds and 1 new π bond is formed. In a normal Diels-Alder reaction, the interaction happens between an electron-rich s-cis dienophile and an electron poor diene. In an inverse-electron-demand Diels-Alder reaction, the interaction happens between an electron-poor s-cis dienophile and an electron rich diene.

There is a strong research interest in this reaction due to its importance in biosynthetic processes, use as a protecting group and recent discovery of enzyme Diels-Alderase in nature (for example, spirotetronate cyclase AbyU), which could unlock new and efficient Diels-Alder reactions <ref name="DA" /><ref name="DA2" /><ref name="DAE1" /><ref name="DAE2" /><ref name="DAE3" /><ref name="DAE4" /><ref name="DAE5" /><ref name="DAE6" /><ref name="DAE7" /><ref name="DAE8" />. In the area of computational chemistry, there are many researches about the geometry of the transition states involved in Diels-Alder reactions and the overall reaction profiles <ref name="DA" /><ref name="DA1" /><ref name="DA2" /><ref name="DA3" />.

=='''4. Methodology.'''==
The calculation results assumed two reacting molecules in gaseous phase (in absence of solvation and other interactions with non-reacting, neighbouring molecules). The temperature and pressure settings in the calculations were 298.15 K and 1 atm (default settings). The symmetry and molecular geometries of the products and reactants were not restricted in the optimization process. All of the calculations were performed in GaussView 5.0 and the calculation grid was set to ultrafine (integral=grid=ultrafine). For TS calculations, additional keyword (opt=noeigen) was used in response to possible error in link 9999.

The non-covalent interaction plots were generated using a script by Henry Rzepa and Bob Hanson <ref name="NCI" /> using default parameters for intermolecular reaction (minimum rho cutoff set to 0.3, covalent density cutoff set to 0.07, fraction of total rho that defined intramolecular interaction set to 0.95, data scaling set to 1).

Unless stated otherwise, all of the optimization jobs were followed by frequency analysis.

===Exercise 1: Reaction of Butadiene with Ethylene.===
Cyclohexene (product) was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.2 Å at the reacting C-C termini. While freezing the coordinates of the reacting C-C termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of Butadiene and Ethylene.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex 1.png|frame| Figure 4.1: Exercise 1 Reaction Scheme.]]
|}

===Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole.===
The endo product was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.2 Å at the reacting C-C termini. While freezing the coordinates of the reacting C-C termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of Cyclohexadiene and 1,3-Dioxole.

The optimized structure at PM6 level was reoptimized at B3LYP/6-31G(d) level for the endo product, TS and the reactants.

The above procedures were repeated for the exo-product, with the exception of the reactants.

===Exercise 3: Reaction of 5,6-dimethylenecyclohexa-1,3-diene and Sulfur Dioxide.===
The endo product was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.0 Å at the reacting C-O termini and 2.4 Å at the reacting C-S termini. While freezing the coordinates of the reacting termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of 5,6-dimethylenecyclohexa-1,3-diene and sulfur dioxide.

The above procedures were repeated for the exo-product, cheletropic-product and two minor Diels Alder regio-isomers, with the exception of reactants.

=='''5. Results and Discussion.'''==
===Exercise 1: Reaction of Butadiene with Ethylene.===

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx1RD Exercise 1 Results and Discussion.]

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

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx2RD Exercise 2 Results and Discussion.]

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

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx3RD Exercise 3 Results and Discussion.]

=='''6. Conclusion.'''==
In conclusion, this paper had successfully carried out computational calculations to study six Diels-Alder reactions and one Cheletropic reaction using two popular computational methods: PM6 and B3LYP (6-31 G(d) basis set) in GaussView 5.0. For future work, the calculated results could be shared with other teams who could carry out the experiments in the lab to verify the results.

=='''7. References.'''==
<references>
<ref name="RCS Book">J. J. W. McDouall, in ''Computational Quantum Chemistry: Molecular Structure and Properties in Silico'', Royal Society of Chemistry, 2013, ch. 1, pp. 1-62.
</ref>
<ref name="Methylene"> H. F. SCHAEFER III, ''Science'', 1986, '''231''', 1100-1107.</ref>
<ref name="NCI"> Mod:NCI, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:NCI, (accessed March 2018).</ref>
<ref name="HKTheorem"> P. Hohenberg, W. Kohn, ''Phys. Rev.'', 1964, '''136(3B)''', B864–B871.</ref>
<ref name="PM6"> J. J. P. Stewart, '' J Mol Model'', 2007, '''13''', 1173-1213.</ref>
<ref name="B3LYP"> D. Avci, A. Başoğlu, Y. Atalay, '' Z. Naturforsch.'', 2008, '''63a''', 712-720.</ref>
<ref name="B3LYP1"> S.H. Vosko, L. Wilk, and M. Nusair, '' Can. J. Phys'', 1980, '''58''', 1200.</ref>
<ref name="DA"> T. J. Brocksom, J. Nakamura, M. L. Ferreira and U. Brocksom, '' J. Braz. Chem. Soc.'', 2001, '''12''', 597-622.</ref>
<ref name="DA1"> K. N. Houk, J. Gonzalez, Y. Li, ''Acc. Chem. Res.'', 1995, '''28''', 81-90.</ref>
<ref name="DA2"> J. Chen, Q. Deng, R. Wang, K. N. Houk, D. Hilvert, ''ChemBioChem'', 2000, '''1''', 255-261.</ref>
<ref name="DA3"> D. J. Tantillo, K. N. Houk, M. E. J. Jung, ''Org. Chem.'', 2001, '''66''', 1938-1940.</ref>
<ref name="DAE1"> K. N. Houk, J. Gonzalez, Y. Li, ''Acc. Chem. Res.'', 1995, '''28''', 81-90.</ref>
<ref name="DAE2"> W. M. Bandaranayake, J. E. Banfield, D. St. C. Black, ''J. Chem. Soc., Chem. Commun.'', 1980, 902-903.</ref>
<ref name="DAE3"> K. C. Nicolaou, N. A. Petasis, in ''Strategies and Tactics in Organic Synthesis'', ed. T. Lindberg, Academic Press, 1984, ch. 6, pp. 153-170.</ref>
<ref name="DAE4"> W. R. Roush, K. Koyama, M. L. Curtin, K. J. Moriarty, ''J. Am. Chem. Soc.'', 1996, '''118''', 7502-7512.</ref>
<ref name="DAE5"> H. Oikawa, T. Kobayashi, K. Katayama, Y. Suzuki, A. Ichihara, ''J. Org. Chem.'', 1998, '''63''', 8748-8756.</ref>
<ref name="DAE6"> E. M. Stocking, J. F. Sanz-Cervera, R. M. Williams, ''J. Am. Chem. Soc.'', 2000, '''122''', 1675-1683.</ref>
<ref name="DAE7"> G. A. Wallace, C. H. Heathcock, ''J. Org. Chem.'', 2001, '''66''', 450-454.</ref>
<ref name="DAE8"> K. Auclair, A. Sutherland, J. Kennedy, D. J. Witter, J. P. Van den Heever, C. R. Hutchinson, J. C. Vederas, ''J. Am. Chem. Soc.'', 2000, '''122''', 11519-11520.</ref>
<ref name="IRC"> S. Maeda, Y. Harabuchi, Y. Ono, T. Taketsugu, K. Morokuma, ''International Journal of Quantum Chemistry'', 2015, '''115''', 258-269.</ref>
<ref name="Rate">D. A. McQuarrie, in ''Physical Chemistry : A Molecular Approach'', University Science Books, 1997.
</ref>
</references>

Rep:Kh1015TS

2018-03-14T10:02:01Z

Kh1015: /* Exercise 1: Reaction of Butadiene with Ethylene. */

=='''1. Abstract.'''==
This paper studied six Diels-Alder reactions and one Cheletropic reaction using two popular computational methods: PM6 and B3LYP (6-31 G(d) basis set) in GaussView 5.0. In Exercise 1-3, the MO calculation was used to identify the interacting frontier orbitals and possible secondary-orbital interactions. In Exercise 1, the C-C bond length of molecules optimized using PM6 level showed good agreement with literature with less than 1% percentage difference. IRC analysis at PM6 level in all exercises showed that the TS has been optimized. In Exercise 2 and Exercise 3, thermodynamic values (activation Gibbs-Free energy and Δ Gibbs-Free energy) were extracted from the log file output and rate constant was calculated using the activation Gibbs-Free energy based on method by D. A. McQuarrie (1997) <ref name="Rate" />.

=='''2. Aim.'''==
The aim of this study is to locate and characterize the transition states of several Diels-Alder reactions.

=='''3. Introduction.'''==

Chemical behaviour of a molecule is controlled by the electrons that participate in the chemical process <ref name="RCS Book" />. In particular, the electronic structure and properties in its stationary state could be described by the time-independent solution of Schrödinger’s equation:
<div align="center"><math>\hat{H} \psi_{A} = E_{A} \psi_{A}</math></div>
, where A labels the state of interest <ref name="RCS Book" />.

The above equation forms the foundation for quantum chemistry and modern computational methods.

For a given reaction where there is ambiguity in structure or mechanism, computational chemistry is useful in predicting the likeliest structure or mechanism. For example, in 1986, computational calculation correctly predicted and later experimentally confirmed a bent structure for methylene, which challenged the linear experimental value by Hertzberg thought to be true at the time <ref name="Methylene" />.

===A. Standard Computational Methods.===

The recurring challenge in computational method is that the Schrodinger equation can be solved exactly only for one-electron systems, while most molecules have much more than one electron in the system. To address this challenges, multiple methods have been developed to find increasingly accurate approximations to the Schrodinger equation for many-electron systems <ref name="RCS Book" />. Each of the methods has its own trade-off between accuracy and computational cost. With that in mind, two such methods had been selected in this study: semi-quantitative Parameterization Method 6 (PM6); and Density Functional Theory (DFT), Becke, 3-parameter, Lee-Yang-Parr (B3LYP).
====1) Semi Quantitative PM6 (Parameterization Method 6).====
PM6 is a modified semi-empirical method categorized under Neglect of Diatomic Differential Overlap (NDDO) <ref name="PM6" />.The main advantage of modified version of NDDO (MNDO) over its predecessors lies in the optimization of parameters to simulate molecular properties which is more accurate than calculations based on atomic properties <ref name="PM6" />. The inability of earlier MNDO to simulate hydrogen bond has been addressed in PM6 method, where the percentage difference of the average unsigned error (AUE) of a water dimer model (1.35 kcal mol<sup>-1</sup>) is 27% relative to that obtained by exhaustive analysis by Tschumper, et al. using CCSD(T) and a large basis set (5.00 kcal mol<sup>-1</sup>) <ref name="PM6" />.

====2) DFT, B3LYP (Density Functional Theory, Becke, 3-parameter, Lee-Yang-Parr).====
In general, DFT uses variational principle and one-electron density for the calculation and therefore bypasses the consideration of the many-electron wavefunction <ref name="RCS Book" />. From the Hohenberg-Kohn Theorems, it has been established that the ground state energy and all of its properties can be extracted from one-electron density alone <ref name="RCS Book" /><ref name="HKTheorem" />. DFT includes exchange-correlation functionals and self-consistent field type formalism <ref name="RCS Book" />. The basic form of DFT uses exchange and correlation terms of uniform electron gas, which is not a good approximation to the actual electron distribution in chemical systems. This error is most pronounced in two bonded atoms that have very high electronegativity difference (O-H for example), where there is a non-uniform distribution of electron density which is skewed towards the more electronegative atom. Hence, empirical inputs - such as atomic correlation energies or thermochemical databases - have been used to refine the DFT method <ref name="RCS Book" />. B3LYP is a hybrid DFT functional method whose energy term includes Slater exchange, the Hartree–Fock exchange, Becke’s exchange functional correction, the gradient-corrected correlation functional of Lee, Yang and Parr, and the local correlation functional of Vosko, Wilk and Nusair <ref name="B3LYP" /><ref name="B3LYP1" />.

===B. Finding a Stable or Transition structure in a PES.===

From the computational output, it is possible to model a potential energy surface (PES), that is dependent on one variable or more. In any given PES, there are 4 simple conditions which allow a user to find a stable structure or a transition structure <ref name="RCS Book" />:
====1) Determining Stationary Point via Gradient.====
<br><div align="center"><math>\frac{dE(\textbf{R})}{dR_{i}} = 0, i=1,2, . . . 3N_{atoms} - 6</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and R<sub>i</sub> refers to a specific member of the set.

====2) Characterizing Minimum Point via Curvature (Positive Force Constants).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{i}} > 0, i=1,2, . . . 3N_{atoms} - 6</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>i</sub> refers to a specific combination of R and bond angle (θ).

====3) Characterizing Transition Point via Curvature (One Unique Negative Force Constant corresponding to First Order Saddle Point in Reaction Coordinate (RC)).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{RC}} < 0</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>RC</sub> refers to a specific combination of R and bond angle (θ) at the lowest-possible transition state in the PES.

====4) Characterizing Transition Point via Curvature (Positive Force Constants For The Remaining Ones).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{i}} > 0, i=1,2, . . . 3N_{atoms} - 7</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>i</sub> refers to a specific combination of '''R''' and bond angle (θ).

While useful, it should be noted that the 4 conditions above '''could not differentiate between global and local stationary points''', which could impact the accuracy of geometry optimization if the geometry is trapped in a local minimum rather than global minimum.

===C.Intrinsic Reaction Coordinate (IRC).===
In 1970, Fukui proposed the concept of IRC, which is defined as the mass-weighted, vibrationless, motionless and steepest descent path on the PES from the TS or the first-order saddle point to two minima on either side of the TS <ref name="IRC" />. The descent from higher-order saddle point is called meta-IRC <ref name="IRC" />. In mathematical form, IRC is obtained by solving the following differential equation <ref name="IRC" />:
<br><div align="center"><math>\frac{d\textbf{q}(s)}{ds} = \textbf{v}(s)</math></div>
, where '''q''' is the mass-weighted Cartesian coordinates, s is the coordinate along the IRC and '''v''' is a normalized tangent vector to the IRC corresponding to the normal coordinate eigenvector with a negative eigenvalue at the TS with s=0.

At the other points, '''v''' is the unit vector parallel to the mass-weighted gradient vector '''g''' with the following relationship <ref name="IRC" />:
<br><div align="center"><math>\textbf{v} = - \frac{\textbf{g}}{|\textbf{g}|}</math> for s > 0</div>
<br><div align="center"> and </div>
<br><div align="center"><math>\textbf{v} = \frac{\textbf{g}}{|\textbf{g}|}</math> for s < 0</div>

IRC calculation has been used extensively to confirm the connection between a given TS and two minima (reactant(s) and product(s)) for a given reaction <ref name="IRC" />. In this study, IRC calculation had been done for all the reactions such that it can be used to '''independently confirm''' that the TS geometry for the given reaction had truly been optimized.

From a successful IRC calculation (Minimum-TS-Minimum), it is possible to extract the calculated activation energy (linked to a given computational method) and therefore, the calculated rate constant for a reaction via transition state theory <ref name="IRC" />.

===D. Predicting Rate of Reaction from Calculated Thermodynamic Values.===
Once the activation free-energy of a reaction is calculated, it is possible to calculate the predicted rate of reaction via the equation below <ref name="Rate" />:
<br><div align="center"><math> k(T) = \frac{k_{B}T}{hc^{o}} e^{\frac{-\Delta^{\ddagger}G^{o}}{RT}} </math></div>

, where k(T) is rate constant at a specified temperature, k<sub>B</sub> is Boltzmann constant (1.3807 x 10<sup>-23</sup> J K<sup>-1</sup>), T is temperature (in K), h is Planck's constant (6.626176 x 10<sup>-34</sup> J s), c<sup>o</sup> is concentration (taken to be 1, unitless), Δ<sup>‡</sup>G<sup>o</sup> is the activation Gibbs-Free Energy (J mol<sup>-1</sup>) and R is gas constant (8.314 J mol<sup>-1</sup> K<sup>-1</sup>).

===E. Diels-Alder Reaction as a Study Topic.===
Diels-Alder reaction is a concerted [<sub>π</sub>4<sub>s</sub> + <sub>π</sub>2<sub>s</sub>] cycloaddition between an s-cis conjugated diene and a dienophile to form a cyclohexene <ref name="DA" />. In the reaction, 3 π bonds are broken and 2 sigma bonds and 1 new π bond is formed. In a normal Diels-Alder reaction, the interaction happens between an electron-rich s-cis dienophile and an electron poor diene. In an inverse-electron-demand Diels-Alder reaction, the interaction happens between an electron-poor s-cis dienophile and an electron rich diene.

There is a strong research interest in this reaction due to its importance in biosynthetic processes, use as a protecting group and recent discovery of enzyme Diels-Alderase in nature (for example, spirotetronate cyclase AbyU), which could unlock new and efficient Diels-Alder reactions <ref name="DA" /><ref name="DA2" /><ref name="DAE1" /><ref name="DAE2" /><ref name="DAE3" /><ref name="DAE4" /><ref name="DAE5" /><ref name="DAE6" /><ref name="DAE7" /><ref name="DAE8" />. In the area of computational chemistry, there are many researches about the geometry of the transition states involved in Diels-Alder reactions and the overall reaction profiles <ref name="DA" /><ref name="DA1" /><ref name="DA2" /><ref name="DA3" />.

=='''4. Methodology.'''==
The calculation results assumed two reacting molecules in gaseous phase (in absence of solvation and other interactions with non-reacting, neighbouring molecules). The temperature and pressure settings in the calculations were 298.15 K and 1 atm (default settings). The symmetry and molecular geometries of the products and reactants were not restricted in the optimization process. All of the calculations were performed in GaussView 5.0 and the calculation grid was set to ultrafine (integral=grid=ultrafine). For TS calculations, additional keyword (opt=noeigen) was used in response to possible error in link 9999.

The non-covalent interaction plots were generated using a script by Henry Rzepa and Bob Hanson <ref name="NCI" /> using default parameters for intermolecular reaction (minimum rho cutoff set to 0.3, covalent density cutoff set to 0.07, fraction of total rho that defined intramolecular interaction set to 0.95, data scaling set to 1).

Unless stated otherwise, all of the optimization jobs were followed by frequency analysis.

===Exercise 1: Reaction of Butadiene with Ethylene.===
Cyclohexene (product) was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.2 Å at the reacting C-C termini. While freezing the coordinates of the reacting C-C termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of Butadiene and Ethylene.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex 1.png|thumb|200px| Figure 4.1: Exercise 1 Reaction Scheme.]]
|}

===Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole.===
The endo product was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.2 Å at the reacting C-C termini. While freezing the coordinates of the reacting C-C termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of Cyclohexadiene and 1,3-Dioxole.

The optimized structure at PM6 level was reoptimized at B3LYP/6-31G(d) level for the endo product, TS and the reactants.

The above procedures were repeated for the exo-product, with the exception of the reactants.

===Exercise 3: Reaction of 5,6-dimethylenecyclohexa-1,3-diene and Sulfur Dioxide.===
The endo product was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.0 Å at the reacting C-O termini and 2.4 Å at the reacting C-S termini. While freezing the coordinates of the reacting termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of 5,6-dimethylenecyclohexa-1,3-diene and sulfur dioxide.

The above procedures were repeated for the exo-product, cheletropic-product and two minor Diels Alder regio-isomers, with the exception of reactants.

=='''5. Results and Discussion.'''==
===Exercise 1: Reaction of Butadiene with Ethylene.===

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx1RD Exercise 1 Results and Discussion.]

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

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx2RD Exercise 2 Results and Discussion.]

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

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx3RD Exercise 3 Results and Discussion.]

=='''6. Conclusion.'''==
In conclusion, this paper had successfully carried out computational calculations to study six Diels-Alder reactions and one Cheletropic reaction using two popular computational methods: PM6 and B3LYP (6-31 G(d) basis set) in GaussView 5.0. For future work, the calculated results could be shared with other teams who could carry out the experiments in the lab to verify the results.

=='''7. References.'''==
<references>
<ref name="RCS Book">J. J. W. McDouall, in ''Computational Quantum Chemistry: Molecular Structure and Properties in Silico'', Royal Society of Chemistry, 2013, ch. 1, pp. 1-62.
</ref>
<ref name="Methylene"> H. F. SCHAEFER III, ''Science'', 1986, '''231''', 1100-1107.</ref>
<ref name="NCI"> Mod:NCI, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:NCI, (accessed March 2018).</ref>
<ref name="HKTheorem"> P. Hohenberg, W. Kohn, ''Phys. Rev.'', 1964, '''136(3B)''', B864–B871.</ref>
<ref name="PM6"> J. J. P. Stewart, '' J Mol Model'', 2007, '''13''', 1173-1213.</ref>
<ref name="B3LYP"> D. Avci, A. Başoğlu, Y. Atalay, '' Z. Naturforsch.'', 2008, '''63a''', 712-720.</ref>
<ref name="B3LYP1"> S.H. Vosko, L. Wilk, and M. Nusair, '' Can. J. Phys'', 1980, '''58''', 1200.</ref>
<ref name="DA"> T. J. Brocksom, J. Nakamura, M. L. Ferreira and U. Brocksom, '' J. Braz. Chem. Soc.'', 2001, '''12''', 597-622.</ref>
<ref name="DA1"> K. N. Houk, J. Gonzalez, Y. Li, ''Acc. Chem. Res.'', 1995, '''28''', 81-90.</ref>
<ref name="DA2"> J. Chen, Q. Deng, R. Wang, K. N. Houk, D. Hilvert, ''ChemBioChem'', 2000, '''1''', 255-261.</ref>
<ref name="DA3"> D. J. Tantillo, K. N. Houk, M. E. J. Jung, ''Org. Chem.'', 2001, '''66''', 1938-1940.</ref>
<ref name="DAE1"> K. N. Houk, J. Gonzalez, Y. Li, ''Acc. Chem. Res.'', 1995, '''28''', 81-90.</ref>
<ref name="DAE2"> W. M. Bandaranayake, J. E. Banfield, D. St. C. Black, ''J. Chem. Soc., Chem. Commun.'', 1980, 902-903.</ref>
<ref name="DAE3"> K. C. Nicolaou, N. A. Petasis, in ''Strategies and Tactics in Organic Synthesis'', ed. T. Lindberg, Academic Press, 1984, ch. 6, pp. 153-170.</ref>
<ref name="DAE4"> W. R. Roush, K. Koyama, M. L. Curtin, K. J. Moriarty, ''J. Am. Chem. Soc.'', 1996, '''118''', 7502-7512.</ref>
<ref name="DAE5"> H. Oikawa, T. Kobayashi, K. Katayama, Y. Suzuki, A. Ichihara, ''J. Org. Chem.'', 1998, '''63''', 8748-8756.</ref>
<ref name="DAE6"> E. M. Stocking, J. F. Sanz-Cervera, R. M. Williams, ''J. Am. Chem. Soc.'', 2000, '''122''', 1675-1683.</ref>
<ref name="DAE7"> G. A. Wallace, C. H. Heathcock, ''J. Org. Chem.'', 2001, '''66''', 450-454.</ref>
<ref name="DAE8"> K. Auclair, A. Sutherland, J. Kennedy, D. J. Witter, J. P. Van den Heever, C. R. Hutchinson, J. C. Vederas, ''J. Am. Chem. Soc.'', 2000, '''122''', 11519-11520.</ref>
<ref name="IRC"> S. Maeda, Y. Harabuchi, Y. Ono, T. Taketsugu, K. Morokuma, ''International Journal of Quantum Chemistry'', 2015, '''115''', 258-269.</ref>
<ref name="Rate">D. A. McQuarrie, in ''Physical Chemistry : A Molecular Approach'', University Science Books, 1997.
</ref>
</references>

File:KH1015 Ex 1.png

2018-03-14T10:01:34Z

Kh1015:

Rep:Kh1015TS

2018-03-14T10:01:04Z

Kh1015: /* Exercise 1: Reaction of Butadiene with Ethylene. */

=='''1. Abstract.'''==
This paper studied six Diels-Alder reactions and one Cheletropic reaction using two popular computational methods: PM6 and B3LYP (6-31 G(d) basis set) in GaussView 5.0. In Exercise 1-3, the MO calculation was used to identify the interacting frontier orbitals and possible secondary-orbital interactions. In Exercise 1, the C-C bond length of molecules optimized using PM6 level showed good agreement with literature with less than 1% percentage difference. IRC analysis at PM6 level in all exercises showed that the TS has been optimized. In Exercise 2 and Exercise 3, thermodynamic values (activation Gibbs-Free energy and Δ Gibbs-Free energy) were extracted from the log file output and rate constant was calculated using the activation Gibbs-Free energy based on method by D. A. McQuarrie (1997) <ref name="Rate" />.

=='''2. Aim.'''==
The aim of this study is to locate and characterize the transition states of several Diels-Alder reactions.

=='''3. Introduction.'''==

Chemical behaviour of a molecule is controlled by the electrons that participate in the chemical process <ref name="RCS Book" />. In particular, the electronic structure and properties in its stationary state could be described by the time-independent solution of Schrödinger’s equation:
<div align="center"><math>\hat{H} \psi_{A} = E_{A} \psi_{A}</math></div>
, where A labels the state of interest <ref name="RCS Book" />.

The above equation forms the foundation for quantum chemistry and modern computational methods.

For a given reaction where there is ambiguity in structure or mechanism, computational chemistry is useful in predicting the likeliest structure or mechanism. For example, in 1986, computational calculation correctly predicted and later experimentally confirmed a bent structure for methylene, which challenged the linear experimental value by Hertzberg thought to be true at the time <ref name="Methylene" />.

===A. Standard Computational Methods.===

The recurring challenge in computational method is that the Schrodinger equation can be solved exactly only for one-electron systems, while most molecules have much more than one electron in the system. To address this challenges, multiple methods have been developed to find increasingly accurate approximations to the Schrodinger equation for many-electron systems <ref name="RCS Book" />. Each of the methods has its own trade-off between accuracy and computational cost. With that in mind, two such methods had been selected in this study: semi-quantitative Parameterization Method 6 (PM6); and Density Functional Theory (DFT), Becke, 3-parameter, Lee-Yang-Parr (B3LYP).
====1) Semi Quantitative PM6 (Parameterization Method 6).====
PM6 is a modified semi-empirical method categorized under Neglect of Diatomic Differential Overlap (NDDO) <ref name="PM6" />.The main advantage of modified version of NDDO (MNDO) over its predecessors lies in the optimization of parameters to simulate molecular properties which is more accurate than calculations based on atomic properties <ref name="PM6" />. The inability of earlier MNDO to simulate hydrogen bond has been addressed in PM6 method, where the percentage difference of the average unsigned error (AUE) of a water dimer model (1.35 kcal mol<sup>-1</sup>) is 27% relative to that obtained by exhaustive analysis by Tschumper, et al. using CCSD(T) and a large basis set (5.00 kcal mol<sup>-1</sup>) <ref name="PM6" />.

====2) DFT, B3LYP (Density Functional Theory, Becke, 3-parameter, Lee-Yang-Parr).====
In general, DFT uses variational principle and one-electron density for the calculation and therefore bypasses the consideration of the many-electron wavefunction <ref name="RCS Book" />. From the Hohenberg-Kohn Theorems, it has been established that the ground state energy and all of its properties can be extracted from one-electron density alone <ref name="RCS Book" /><ref name="HKTheorem" />. DFT includes exchange-correlation functionals and self-consistent field type formalism <ref name="RCS Book" />. The basic form of DFT uses exchange and correlation terms of uniform electron gas, which is not a good approximation to the actual electron distribution in chemical systems. This error is most pronounced in two bonded atoms that have very high electronegativity difference (O-H for example), where there is a non-uniform distribution of electron density which is skewed towards the more electronegative atom. Hence, empirical inputs - such as atomic correlation energies or thermochemical databases - have been used to refine the DFT method <ref name="RCS Book" />. B3LYP is a hybrid DFT functional method whose energy term includes Slater exchange, the Hartree–Fock exchange, Becke’s exchange functional correction, the gradient-corrected correlation functional of Lee, Yang and Parr, and the local correlation functional of Vosko, Wilk and Nusair <ref name="B3LYP" /><ref name="B3LYP1" />.

===B. Finding a Stable or Transition structure in a PES.===

From the computational output, it is possible to model a potential energy surface (PES), that is dependent on one variable or more. In any given PES, there are 4 simple conditions which allow a user to find a stable structure or a transition structure <ref name="RCS Book" />:
====1) Determining Stationary Point via Gradient.====
<br><div align="center"><math>\frac{dE(\textbf{R})}{dR_{i}} = 0, i=1,2, . . . 3N_{atoms} - 6</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and R<sub>i</sub> refers to a specific member of the set.

====2) Characterizing Minimum Point via Curvature (Positive Force Constants).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{i}} > 0, i=1,2, . . . 3N_{atoms} - 6</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>i</sub> refers to a specific combination of R and bond angle (θ).

====3) Characterizing Transition Point via Curvature (One Unique Negative Force Constant corresponding to First Order Saddle Point in Reaction Coordinate (RC)).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{RC}} < 0</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>RC</sub> refers to a specific combination of R and bond angle (θ) at the lowest-possible transition state in the PES.

====4) Characterizing Transition Point via Curvature (Positive Force Constants For The Remaining Ones).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{i}} > 0, i=1,2, . . . 3N_{atoms} - 7</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>i</sub> refers to a specific combination of '''R''' and bond angle (θ).

While useful, it should be noted that the 4 conditions above '''could not differentiate between global and local stationary points''', which could impact the accuracy of geometry optimization if the geometry is trapped in a local minimum rather than global minimum.

===C.Intrinsic Reaction Coordinate (IRC).===
In 1970, Fukui proposed the concept of IRC, which is defined as the mass-weighted, vibrationless, motionless and steepest descent path on the PES from the TS or the first-order saddle point to two minima on either side of the TS <ref name="IRC" />. The descent from higher-order saddle point is called meta-IRC <ref name="IRC" />. In mathematical form, IRC is obtained by solving the following differential equation <ref name="IRC" />:
<br><div align="center"><math>\frac{d\textbf{q}(s)}{ds} = \textbf{v}(s)</math></div>
, where '''q''' is the mass-weighted Cartesian coordinates, s is the coordinate along the IRC and '''v''' is a normalized tangent vector to the IRC corresponding to the normal coordinate eigenvector with a negative eigenvalue at the TS with s=0.

At the other points, '''v''' is the unit vector parallel to the mass-weighted gradient vector '''g''' with the following relationship <ref name="IRC" />:
<br><div align="center"><math>\textbf{v} = - \frac{\textbf{g}}{|\textbf{g}|}</math> for s > 0</div>
<br><div align="center"> and </div>
<br><div align="center"><math>\textbf{v} = \frac{\textbf{g}}{|\textbf{g}|}</math> for s < 0</div>

IRC calculation has been used extensively to confirm the connection between a given TS and two minima (reactant(s) and product(s)) for a given reaction <ref name="IRC" />. In this study, IRC calculation had been done for all the reactions such that it can be used to '''independently confirm''' that the TS geometry for the given reaction had truly been optimized.

From a successful IRC calculation (Minimum-TS-Minimum), it is possible to extract the calculated activation energy (linked to a given computational method) and therefore, the calculated rate constant for a reaction via transition state theory <ref name="IRC" />.

===D. Predicting Rate of Reaction from Calculated Thermodynamic Values.===
Once the activation free-energy of a reaction is calculated, it is possible to calculate the predicted rate of reaction via the equation below <ref name="Rate" />:
<br><div align="center"><math> k(T) = \frac{k_{B}T}{hc^{o}} e^{\frac{-\Delta^{\ddagger}G^{o}}{RT}} </math></div>

, where k(T) is rate constant at a specified temperature, k<sub>B</sub> is Boltzmann constant (1.3807 x 10<sup>-23</sup> J K<sup>-1</sup>), T is temperature (in K), h is Planck's constant (6.626176 x 10<sup>-34</sup> J s), c<sup>o</sup> is concentration (taken to be 1, unitless), Δ<sup>‡</sup>G<sup>o</sup> is the activation Gibbs-Free Energy (J mol<sup>-1</sup>) and R is gas constant (8.314 J mol<sup>-1</sup> K<sup>-1</sup>).

===E. Diels-Alder Reaction as a Study Topic.===
Diels-Alder reaction is a concerted [<sub>π</sub>4<sub>s</sub> + <sub>π</sub>2<sub>s</sub>] cycloaddition between an s-cis conjugated diene and a dienophile to form a cyclohexene <ref name="DA" />. In the reaction, 3 π bonds are broken and 2 sigma bonds and 1 new π bond is formed. In a normal Diels-Alder reaction, the interaction happens between an electron-rich s-cis dienophile and an electron poor diene. In an inverse-electron-demand Diels-Alder reaction, the interaction happens between an electron-poor s-cis dienophile and an electron rich diene.

There is a strong research interest in this reaction due to its importance in biosynthetic processes, use as a protecting group and recent discovery of enzyme Diels-Alderase in nature (for example, spirotetronate cyclase AbyU), which could unlock new and efficient Diels-Alder reactions <ref name="DA" /><ref name="DA2" /><ref name="DAE1" /><ref name="DAE2" /><ref name="DAE3" /><ref name="DAE4" /><ref name="DAE5" /><ref name="DAE6" /><ref name="DAE7" /><ref name="DAE8" />. In the area of computational chemistry, there are many researches about the geometry of the transition states involved in Diels-Alder reactions and the overall reaction profiles <ref name="DA" /><ref name="DA1" /><ref name="DA2" /><ref name="DA3" />.

=='''4. Methodology.'''==
The calculation results assumed two reacting molecules in gaseous phase (in absence of solvation and other interactions with non-reacting, neighbouring molecules). The temperature and pressure settings in the calculations were 298.15 K and 1 atm (default settings). The symmetry and molecular geometries of the products and reactants were not restricted in the optimization process. All of the calculations were performed in GaussView 5.0 and the calculation grid was set to ultrafine (integral=grid=ultrafine). For TS calculations, additional keyword (opt=noeigen) was used in response to possible error in link 9999.

The non-covalent interaction plots were generated using a script by Henry Rzepa and Bob Hanson <ref name="NCI" /> using default parameters for intermolecular reaction (minimum rho cutoff set to 0.3, covalent density cutoff set to 0.07, fraction of total rho that defined intramolecular interaction set to 0.95, data scaling set to 1).

Unless stated otherwise, all of the optimization jobs were followed by frequency analysis.

===Exercise 1: Reaction of Butadiene with Ethylene.===
Cyclohexene (product) was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.2 Å at the reacting C-C termini. While freezing the coordinates of the reacting C-C termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of Butadiene and Ethylene.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 HOMO of S-Cis Butadiene (MO11).png|thumb|150px| Figure 4.1: Exercise 1 Reaction Scheme.]]
|}

===Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole.===
The endo product was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.2 Å at the reacting C-C termini. While freezing the coordinates of the reacting C-C termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of Cyclohexadiene and 1,3-Dioxole.

The optimized structure at PM6 level was reoptimized at B3LYP/6-31G(d) level for the endo product, TS and the reactants.

The above procedures were repeated for the exo-product, with the exception of the reactants.

===Exercise 3: Reaction of 5,6-dimethylenecyclohexa-1,3-diene and Sulfur Dioxide.===
The endo product was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.0 Å at the reacting C-O termini and 2.4 Å at the reacting C-S termini. While freezing the coordinates of the reacting termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of 5,6-dimethylenecyclohexa-1,3-diene and sulfur dioxide.

The above procedures were repeated for the exo-product, cheletropic-product and two minor Diels Alder regio-isomers, with the exception of reactants.

=='''5. Results and Discussion.'''==
===Exercise 1: Reaction of Butadiene with Ethylene.===

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx1RD Exercise 1 Results and Discussion.]

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

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx2RD Exercise 2 Results and Discussion.]

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

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx3RD Exercise 3 Results and Discussion.]

=='''6. Conclusion.'''==
In conclusion, this paper had successfully carried out computational calculations to study six Diels-Alder reactions and one Cheletropic reaction using two popular computational methods: PM6 and B3LYP (6-31 G(d) basis set) in GaussView 5.0. For future work, the calculated results could be shared with other teams who could carry out the experiments in the lab to verify the results.

=='''7. References.'''==
<references>
<ref name="RCS Book">J. J. W. McDouall, in ''Computational Quantum Chemistry: Molecular Structure and Properties in Silico'', Royal Society of Chemistry, 2013, ch. 1, pp. 1-62.
</ref>
<ref name="Methylene"> H. F. SCHAEFER III, ''Science'', 1986, '''231''', 1100-1107.</ref>
<ref name="NCI"> Mod:NCI, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:NCI, (accessed March 2018).</ref>
<ref name="HKTheorem"> P. Hohenberg, W. Kohn, ''Phys. Rev.'', 1964, '''136(3B)''', B864–B871.</ref>
<ref name="PM6"> J. J. P. Stewart, '' J Mol Model'', 2007, '''13''', 1173-1213.</ref>
<ref name="B3LYP"> D. Avci, A. Başoğlu, Y. Atalay, '' Z. Naturforsch.'', 2008, '''63a''', 712-720.</ref>
<ref name="B3LYP1"> S.H. Vosko, L. Wilk, and M. Nusair, '' Can. J. Phys'', 1980, '''58''', 1200.</ref>
<ref name="DA"> T. J. Brocksom, J. Nakamura, M. L. Ferreira and U. Brocksom, '' J. Braz. Chem. Soc.'', 2001, '''12''', 597-622.</ref>
<ref name="DA1"> K. N. Houk, J. Gonzalez, Y. Li, ''Acc. Chem. Res.'', 1995, '''28''', 81-90.</ref>
<ref name="DA2"> J. Chen, Q. Deng, R. Wang, K. N. Houk, D. Hilvert, ''ChemBioChem'', 2000, '''1''', 255-261.</ref>
<ref name="DA3"> D. J. Tantillo, K. N. Houk, M. E. J. Jung, ''Org. Chem.'', 2001, '''66''', 1938-1940.</ref>
<ref name="DAE1"> K. N. Houk, J. Gonzalez, Y. Li, ''Acc. Chem. Res.'', 1995, '''28''', 81-90.</ref>
<ref name="DAE2"> W. M. Bandaranayake, J. E. Banfield, D. St. C. Black, ''J. Chem. Soc., Chem. Commun.'', 1980, 902-903.</ref>
<ref name="DAE3"> K. C. Nicolaou, N. A. Petasis, in ''Strategies and Tactics in Organic Synthesis'', ed. T. Lindberg, Academic Press, 1984, ch. 6, pp. 153-170.</ref>
<ref name="DAE4"> W. R. Roush, K. Koyama, M. L. Curtin, K. J. Moriarty, ''J. Am. Chem. Soc.'', 1996, '''118''', 7502-7512.</ref>
<ref name="DAE5"> H. Oikawa, T. Kobayashi, K. Katayama, Y. Suzuki, A. Ichihara, ''J. Org. Chem.'', 1998, '''63''', 8748-8756.</ref>
<ref name="DAE6"> E. M. Stocking, J. F. Sanz-Cervera, R. M. Williams, ''J. Am. Chem. Soc.'', 2000, '''122''', 1675-1683.</ref>
<ref name="DAE7"> G. A. Wallace, C. H. Heathcock, ''J. Org. Chem.'', 2001, '''66''', 450-454.</ref>
<ref name="DAE8"> K. Auclair, A. Sutherland, J. Kennedy, D. J. Witter, J. P. Van den Heever, C. R. Hutchinson, J. C. Vederas, ''J. Am. Chem. Soc.'', 2000, '''122''', 11519-11520.</ref>
<ref name="IRC"> S. Maeda, Y. Harabuchi, Y. Ono, T. Taketsugu, K. Morokuma, ''International Journal of Quantum Chemistry'', 2015, '''115''', 258-269.</ref>
<ref name="Rate">D. A. McQuarrie, in ''Physical Chemistry : A Molecular Approach'', University Science Books, 1997.
</ref>
</references>

Rep:Kh1015TS

2018-03-14T10:00:00Z

Kh1015: /* Exercise 1: Reaction of Butadiene with Ethylene. */

=='''1. Abstract.'''==
This paper studied six Diels-Alder reactions and one Cheletropic reaction using two popular computational methods: PM6 and B3LYP (6-31 G(d) basis set) in GaussView 5.0. In Exercise 1-3, the MO calculation was used to identify the interacting frontier orbitals and possible secondary-orbital interactions. In Exercise 1, the C-C bond length of molecules optimized using PM6 level showed good agreement with literature with less than 1% percentage difference. IRC analysis at PM6 level in all exercises showed that the TS has been optimized. In Exercise 2 and Exercise 3, thermodynamic values (activation Gibbs-Free energy and Δ Gibbs-Free energy) were extracted from the log file output and rate constant was calculated using the activation Gibbs-Free energy based on method by D. A. McQuarrie (1997) <ref name="Rate" />.

=='''2. Aim.'''==
The aim of this study is to locate and characterize the transition states of several Diels-Alder reactions.

=='''3. Introduction.'''==

Chemical behaviour of a molecule is controlled by the electrons that participate in the chemical process <ref name="RCS Book" />. In particular, the electronic structure and properties in its stationary state could be described by the time-independent solution of Schrödinger’s equation:
<div align="center"><math>\hat{H} \psi_{A} = E_{A} \psi_{A}</math></div>
, where A labels the state of interest <ref name="RCS Book" />.

The above equation forms the foundation for quantum chemistry and modern computational methods.

For a given reaction where there is ambiguity in structure or mechanism, computational chemistry is useful in predicting the likeliest structure or mechanism. For example, in 1986, computational calculation correctly predicted and later experimentally confirmed a bent structure for methylene, which challenged the linear experimental value by Hertzberg thought to be true at the time <ref name="Methylene" />.

===A. Standard Computational Methods.===

The recurring challenge in computational method is that the Schrodinger equation can be solved exactly only for one-electron systems, while most molecules have much more than one electron in the system. To address this challenges, multiple methods have been developed to find increasingly accurate approximations to the Schrodinger equation for many-electron systems <ref name="RCS Book" />. Each of the methods has its own trade-off between accuracy and computational cost. With that in mind, two such methods had been selected in this study: semi-quantitative Parameterization Method 6 (PM6); and Density Functional Theory (DFT), Becke, 3-parameter, Lee-Yang-Parr (B3LYP).
====1) Semi Quantitative PM6 (Parameterization Method 6).====
PM6 is a modified semi-empirical method categorized under Neglect of Diatomic Differential Overlap (NDDO) <ref name="PM6" />.The main advantage of modified version of NDDO (MNDO) over its predecessors lies in the optimization of parameters to simulate molecular properties which is more accurate than calculations based on atomic properties <ref name="PM6" />. The inability of earlier MNDO to simulate hydrogen bond has been addressed in PM6 method, where the percentage difference of the average unsigned error (AUE) of a water dimer model (1.35 kcal mol<sup>-1</sup>) is 27% relative to that obtained by exhaustive analysis by Tschumper, et al. using CCSD(T) and a large basis set (5.00 kcal mol<sup>-1</sup>) <ref name="PM6" />.

====2) DFT, B3LYP (Density Functional Theory, Becke, 3-parameter, Lee-Yang-Parr).====
In general, DFT uses variational principle and one-electron density for the calculation and therefore bypasses the consideration of the many-electron wavefunction <ref name="RCS Book" />. From the Hohenberg-Kohn Theorems, it has been established that the ground state energy and all of its properties can be extracted from one-electron density alone <ref name="RCS Book" /><ref name="HKTheorem" />. DFT includes exchange-correlation functionals and self-consistent field type formalism <ref name="RCS Book" />. The basic form of DFT uses exchange and correlation terms of uniform electron gas, which is not a good approximation to the actual electron distribution in chemical systems. This error is most pronounced in two bonded atoms that have very high electronegativity difference (O-H for example), where there is a non-uniform distribution of electron density which is skewed towards the more electronegative atom. Hence, empirical inputs - such as atomic correlation energies or thermochemical databases - have been used to refine the DFT method <ref name="RCS Book" />. B3LYP is a hybrid DFT functional method whose energy term includes Slater exchange, the Hartree–Fock exchange, Becke’s exchange functional correction, the gradient-corrected correlation functional of Lee, Yang and Parr, and the local correlation functional of Vosko, Wilk and Nusair <ref name="B3LYP" /><ref name="B3LYP1" />.

===B. Finding a Stable or Transition structure in a PES.===

From the computational output, it is possible to model a potential energy surface (PES), that is dependent on one variable or more. In any given PES, there are 4 simple conditions which allow a user to find a stable structure or a transition structure <ref name="RCS Book" />:
====1) Determining Stationary Point via Gradient.====
<br><div align="center"><math>\frac{dE(\textbf{R})}{dR_{i}} = 0, i=1,2, . . . 3N_{atoms} - 6</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and R<sub>i</sub> refers to a specific member of the set.

====2) Characterizing Minimum Point via Curvature (Positive Force Constants).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{i}} > 0, i=1,2, . . . 3N_{atoms} - 6</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>i</sub> refers to a specific combination of R and bond angle (θ).

====3) Characterizing Transition Point via Curvature (One Unique Negative Force Constant corresponding to First Order Saddle Point in Reaction Coordinate (RC)).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{RC}} < 0</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>RC</sub> refers to a specific combination of R and bond angle (θ) at the lowest-possible transition state in the PES.

====4) Characterizing Transition Point via Curvature (Positive Force Constants For The Remaining Ones).====
<br><div align="center"><math>\frac{d^2E(\textbf{R})}{dq^2_{i}} > 0, i=1,2, . . . 3N_{atoms} - 7</math></div>
, where E('''R''') refers to the total energy of the system, '''R''' in E('''R''') refers to the set of all nuclear coordinates and q<sub>i</sub> refers to a specific combination of '''R''' and bond angle (θ).

While useful, it should be noted that the 4 conditions above '''could not differentiate between global and local stationary points''', which could impact the accuracy of geometry optimization if the geometry is trapped in a local minimum rather than global minimum.

===C.Intrinsic Reaction Coordinate (IRC).===
In 1970, Fukui proposed the concept of IRC, which is defined as the mass-weighted, vibrationless, motionless and steepest descent path on the PES from the TS or the first-order saddle point to two minima on either side of the TS <ref name="IRC" />. The descent from higher-order saddle point is called meta-IRC <ref name="IRC" />. In mathematical form, IRC is obtained by solving the following differential equation <ref name="IRC" />:
<br><div align="center"><math>\frac{d\textbf{q}(s)}{ds} = \textbf{v}(s)</math></div>
, where '''q''' is the mass-weighted Cartesian coordinates, s is the coordinate along the IRC and '''v''' is a normalized tangent vector to the IRC corresponding to the normal coordinate eigenvector with a negative eigenvalue at the TS with s=0.

At the other points, '''v''' is the unit vector parallel to the mass-weighted gradient vector '''g''' with the following relationship <ref name="IRC" />:
<br><div align="center"><math>\textbf{v} = - \frac{\textbf{g}}{|\textbf{g}|}</math> for s > 0</div>
<br><div align="center"> and </div>
<br><div align="center"><math>\textbf{v} = \frac{\textbf{g}}{|\textbf{g}|}</math> for s < 0</div>

IRC calculation has been used extensively to confirm the connection between a given TS and two minima (reactant(s) and product(s)) for a given reaction <ref name="IRC" />. In this study, IRC calculation had been done for all the reactions such that it can be used to '''independently confirm''' that the TS geometry for the given reaction had truly been optimized.

From a successful IRC calculation (Minimum-TS-Minimum), it is possible to extract the calculated activation energy (linked to a given computational method) and therefore, the calculated rate constant for a reaction via transition state theory <ref name="IRC" />.

===D. Predicting Rate of Reaction from Calculated Thermodynamic Values.===
Once the activation free-energy of a reaction is calculated, it is possible to calculate the predicted rate of reaction via the equation below <ref name="Rate" />:
<br><div align="center"><math> k(T) = \frac{k_{B}T}{hc^{o}} e^{\frac{-\Delta^{\ddagger}G^{o}}{RT}} </math></div>

, where k(T) is rate constant at a specified temperature, k<sub>B</sub> is Boltzmann constant (1.3807 x 10<sup>-23</sup> J K<sup>-1</sup>), T is temperature (in K), h is Planck's constant (6.626176 x 10<sup>-34</sup> J s), c<sup>o</sup> is concentration (taken to be 1, unitless), Δ<sup>‡</sup>G<sup>o</sup> is the activation Gibbs-Free Energy (J mol<sup>-1</sup>) and R is gas constant (8.314 J mol<sup>-1</sup> K<sup>-1</sup>).

===E. Diels-Alder Reaction as a Study Topic.===
Diels-Alder reaction is a concerted [<sub>π</sub>4<sub>s</sub> + <sub>π</sub>2<sub>s</sub>] cycloaddition between an s-cis conjugated diene and a dienophile to form a cyclohexene <ref name="DA" />. In the reaction, 3 π bonds are broken and 2 sigma bonds and 1 new π bond is formed. In a normal Diels-Alder reaction, the interaction happens between an electron-rich s-cis dienophile and an electron poor diene. In an inverse-electron-demand Diels-Alder reaction, the interaction happens between an electron-poor s-cis dienophile and an electron rich diene.

There is a strong research interest in this reaction due to its importance in biosynthetic processes, use as a protecting group and recent discovery of enzyme Diels-Alderase in nature (for example, spirotetronate cyclase AbyU), which could unlock new and efficient Diels-Alder reactions <ref name="DA" /><ref name="DA2" /><ref name="DAE1" /><ref name="DAE2" /><ref name="DAE3" /><ref name="DAE4" /><ref name="DAE5" /><ref name="DAE6" /><ref name="DAE7" /><ref name="DAE8" />. In the area of computational chemistry, there are many researches about the geometry of the transition states involved in Diels-Alder reactions and the overall reaction profiles <ref name="DA" /><ref name="DA1" /><ref name="DA2" /><ref name="DA3" />.

=='''4. Methodology.'''==
The calculation results assumed two reacting molecules in gaseous phase (in absence of solvation and other interactions with non-reacting, neighbouring molecules). The temperature and pressure settings in the calculations were 298.15 K and 1 atm (default settings). The symmetry and molecular geometries of the products and reactants were not restricted in the optimization process. All of the calculations were performed in GaussView 5.0 and the calculation grid was set to ultrafine (integral=grid=ultrafine). For TS calculations, additional keyword (opt=noeigen) was used in response to possible error in link 9999.

The non-covalent interaction plots were generated using a script by Henry Rzepa and Bob Hanson <ref name="NCI" /> using default parameters for intermolecular reaction (minimum rho cutoff set to 0.3, covalent density cutoff set to 0.07, fraction of total rho that defined intramolecular interaction set to 0.95, data scaling set to 1).

Unless stated otherwise, all of the optimization jobs were followed by frequency analysis.

===Exercise 1: Reaction of Butadiene with Ethylene.===
Cyclohexene (product) was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.2 Å at the reacting C-C termini. While freezing the coordinates of the reacting C-C termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of Butadiene and Ethylene.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|
|}

===Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole.===
The endo product was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.2 Å at the reacting C-C termini. While freezing the coordinates of the reacting C-C termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of Cyclohexadiene and 1,3-Dioxole.

The optimized structure at PM6 level was reoptimized at B3LYP/6-31G(d) level for the endo product, TS and the reactants.

The above procedures were repeated for the exo-product, with the exception of the reactants.

===Exercise 3: Reaction of 5,6-dimethylenecyclohexa-1,3-diene and Sulfur Dioxide.===
The endo product was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.0 Å at the reacting C-O termini and 2.4 Å at the reacting C-S termini. While freezing the coordinates of the reacting termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of 5,6-dimethylenecyclohexa-1,3-diene and sulfur dioxide.

The above procedures were repeated for the exo-product, cheletropic-product and two minor Diels Alder regio-isomers, with the exception of reactants.

=='''5. Results and Discussion.'''==
===Exercise 1: Reaction of Butadiene with Ethylene.===

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx1RD Exercise 1 Results and Discussion.]

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

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx2RD Exercise 2 Results and Discussion.]

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

[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Kh1015TSEx3RD Exercise 3 Results and Discussion.]

=='''6. Conclusion.'''==
In conclusion, this paper had successfully carried out computational calculations to study six Diels-Alder reactions and one Cheletropic reaction using two popular computational methods: PM6 and B3LYP (6-31 G(d) basis set) in GaussView 5.0. For future work, the calculated results could be shared with other teams who could carry out the experiments in the lab to verify the results.

=='''7. References.'''==
<references>
<ref name="RCS Book">J. J. W. McDouall, in ''Computational Quantum Chemistry: Molecular Structure and Properties in Silico'', Royal Society of Chemistry, 2013, ch. 1, pp. 1-62.
</ref>
<ref name="Methylene"> H. F. SCHAEFER III, ''Science'', 1986, '''231''', 1100-1107.</ref>
<ref name="NCI"> Mod:NCI, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:NCI, (accessed March 2018).</ref>
<ref name="HKTheorem"> P. Hohenberg, W. Kohn, ''Phys. Rev.'', 1964, '''136(3B)''', B864–B871.</ref>
<ref name="PM6"> J. J. P. Stewart, '' J Mol Model'', 2007, '''13''', 1173-1213.</ref>
<ref name="B3LYP"> D. Avci, A. Başoğlu, Y. Atalay, '' Z. Naturforsch.'', 2008, '''63a''', 712-720.</ref>
<ref name="B3LYP1"> S.H. Vosko, L. Wilk, and M. Nusair, '' Can. J. Phys'', 1980, '''58''', 1200.</ref>
<ref name="DA"> T. J. Brocksom, J. Nakamura, M. L. Ferreira and U. Brocksom, '' J. Braz. Chem. Soc.'', 2001, '''12''', 597-622.</ref>
<ref name="DA1"> K. N. Houk, J. Gonzalez, Y. Li, ''Acc. Chem. Res.'', 1995, '''28''', 81-90.</ref>
<ref name="DA2"> J. Chen, Q. Deng, R. Wang, K. N. Houk, D. Hilvert, ''ChemBioChem'', 2000, '''1''', 255-261.</ref>
<ref name="DA3"> D. J. Tantillo, K. N. Houk, M. E. J. Jung, ''Org. Chem.'', 2001, '''66''', 1938-1940.</ref>
<ref name="DAE1"> K. N. Houk, J. Gonzalez, Y. Li, ''Acc. Chem. Res.'', 1995, '''28''', 81-90.</ref>
<ref name="DAE2"> W. M. Bandaranayake, J. E. Banfield, D. St. C. Black, ''J. Chem. Soc., Chem. Commun.'', 1980, 902-903.</ref>
<ref name="DAE3"> K. C. Nicolaou, N. A. Petasis, in ''Strategies and Tactics in Organic Synthesis'', ed. T. Lindberg, Academic Press, 1984, ch. 6, pp. 153-170.</ref>
<ref name="DAE4"> W. R. Roush, K. Koyama, M. L. Curtin, K. J. Moriarty, ''J. Am. Chem. Soc.'', 1996, '''118''', 7502-7512.</ref>
<ref name="DAE5"> H. Oikawa, T. Kobayashi, K. Katayama, Y. Suzuki, A. Ichihara, ''J. Org. Chem.'', 1998, '''63''', 8748-8756.</ref>
<ref name="DAE6"> E. M. Stocking, J. F. Sanz-Cervera, R. M. Williams, ''J. Am. Chem. Soc.'', 2000, '''122''', 1675-1683.</ref>
<ref name="DAE7"> G. A. Wallace, C. H. Heathcock, ''J. Org. Chem.'', 2001, '''66''', 450-454.</ref>
<ref name="DAE8"> K. Auclair, A. Sutherland, J. Kennedy, D. J. Witter, J. P. Van den Heever, C. R. Hutchinson, J. C. Vederas, ''J. Am. Chem. Soc.'', 2000, '''122''', 11519-11520.</ref>
<ref name="IRC"> S. Maeda, Y. Harabuchi, Y. Ono, T. Taketsugu, K. Morokuma, ''International Journal of Quantum Chemistry'', 2015, '''115''', 258-269.</ref>
<ref name="Rate">D. A. McQuarrie, in ''Physical Chemistry : A Molecular Approach'', University Science Books, 1997.
</ref>
</references>

Rep:Kh1015TSEx3RD

2018-03-13T23:14:50Z

Kh1015: /* Part 3: Rationalizing the Reaction Profile Parameters. */

==Exercise 3 Results and Discussion.==

'''Note to Reader/Marker:'''
<br>The compartmentalization of the Results and Discussion into 5 parts was based on relevant discussion idea and for convenient navigation during the write-up. Also, the Jmol files in this page could display the relative energies of the MOs but they could not visualize the MOs. In response, the visualized HOMO of each TS was attached next to the Jmol files for viewing purposes.

===Part 1: Parameters from Reaction Profile.===

Referring to Table 5.3.2, calculations at PM6 level showed that only the Diels-Alder minor-regio-isomers were non-spontaneous. The Diels-Alder endo-major-regioisomer (referred to as endo product in Table 5.3.1) was calculated to be the kinetic product (based on lowest activation Gibbs-Free Energy equalled to 83.2 kJ mol<sup>-1</sup>) and an associated rate of reaction of 0.0165 s<sup>-1</sup> at 298.15K. The rate constant was calculated using the formula described under Introduction > Part D. The cheletropic product was calculated to be the thermodynamically favourable product (based on the most negative Δ Gibbs-Free Energy equalled to -155 kJ mol<sup>-1</sup>). This prediction could be verified experimentally by doing a kinetic study and analysis of ratio of Diels-Alder (including the regioisomers) and cheletropic products formed at rtp.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.3.1: Summary of Calculated Gibbs-Free Energy of Species in Diels-Alder and Cheletropic Reactions at 298.15 K and 1 atm (PM6 level).
|-
|rowspan="2"|''' '''
|colspan="12"|'''States'''
|-
|'''5,6-dimethylenecyclohexa-1,3-diene'''
|'''Sulfur Dioxide'''
|'''Endo TS'''
|'''Endo Product'''
|'''Exo TS'''
|'''Exo Product'''
|'''TS of Endo-Minor-Regioisomer'''
|'''Endo-Minor-Regioisomer'''
|'''TS of Exo-Minor-Regioisomer'''
|'''Exo-Minor-Regioisomer'''
|'''Cheletropic TS'''
|'''Cheletropic Product'''
|-
|'''Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
|468
| -313
|238
|57.0
|242
|56.3
|268
|172
|276
|177
|260
| -0.00263
|}

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.3.2: Summary of Calculated Reaction Profile Parameters for Diels-Alder and Cheletropic Reactions at 298.15 K and 1 atm (PM6 level).
|-
|''' '''
|'''Endo-Major-Regioisomer'''
|'''Exo-Major-Regioisomer'''
|'''Endo-Minor-Regioisomer'''
|'''Exo-Minor-Regioisomer'''
|'''Cheletropic'''
|-
|'''Activation Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
|83.2
|87.2
|113
|121
|106
|-
|'''Δ Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
| -97.6
| -98.2
|17.7
|22.2
| -155
|-
|'''Predicted Rate of Reaction (x10<sup>-6</sup> s<sup>-1</sup>)'''
|16,500
|3,280
|0.010
|0.004
|1.67
|}

===Part 2: Comparison of Reaction Profiles on a Standardized Reaction Coordinate.===

Figure 5.3.1 shows the comparison of the Diels-Alder and Cheletropic Reaction Profiles on a Standardized Reaction Coordinate at 298.15 K and 1 atm (PM6 level). In the Standardized Reaction Coordinate, the reactants' coordinates are set to -1, those of TS set to 0 and those of products set to 1. This was done to align the all the reaction states independent of the rate on a common scale such that the relative energetics could be compared between possible reaction paths.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Comparison.png|frame|Figure 5.3.1: Comparison of the Diels-Alder and Cheletropic Reaction Profiles on a Standardized Reaction Coordinate at 298.15 K and 1 atm (PM6 level).]]
|}

===Part 3: Rationalizing the Reaction Profile Parameters.===

Xylylene is an unstable compound because it is a system of 8 π electrons (4n anti-aromatic rule). From the IRC of all the reactions examined (excluding Diels-Alder minor-regio-isomers), it was observed that as xylelene reacted with sulfur dioxide, the 6 membered-ring would end up with a stable 6 π electrons system (4π+2 aromatic rule) in the product. This provided a strong thermodynamic driving force for the reaction with sulfur dioxide to proceed.

For all the reactions examined, there was no identifiable secondary orbital contribution from the Gaussview MO visualizations.

Referring to Figure 5.3.2-5.3.5, the calculated steric interactions were similar for Diels-Alder endo-exo products that react at the same regio-position. Because of similar steric interactions and electronic interactions within each set, the products that reacted at the same position would possess similar activation Gibbs-Free Energy (calculated) as shown in Table 5.3.2. However, when comparing '''between''' the two sets of Diels-Alder regio-isomers, it could be seen that the activation Gibbs-Free Energy for the minor-regio-isomer set was much higher than the other set ({113, 121} against {83.2, 87.2} where each element of the sets is in the form {endo, exo} and reported in kJ mol<sup>-1</sup>). For both sets, the TS formation involved severance of π interactions in the xylylene system. In the major-regio-isomer set, the activation Gibbs-Free Energy was reduced because there was a corresponding formation of favourable aromatic interaction in the 6-membered ring.

Referring to Figure 5.3.2-5.3.3 and 5.3.6, when comparing between the Diels-Alder major regio-isomer set and the cheletropic product, the steric clash (Red being not favourable and Blue being favourable) in the cheletropic TS was calculated to be higher than those in the Diels-Alder major regio-isomer set. This was due to the approach of two orthogonal lone pairs of S atom towards the 5,6-dimethylenecyclohexa-1,3-diene in the chelotropic TS (Orange colour) that was not present in the Diels-Alder reactions. This contributes to the observation that the calculated activation Gibbs-Free Energy of the cheletropic product, 106 kJ mol<sup>-1</sup>, was much higher than those of the endo and exo products, 83.2 and 87.2 <sup>-1</sup> respectively.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Endo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.2: Non Covalent Interactions in the Transition State During Diels-Alder Endo Product Formation.]]
|[[File:KH1015 Exo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.3: Non Covalent Interactions in the Transition State During Diels-Alder Exo Product Formation.]]
|[[File:KH1015 Var Endo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.4: Non Covalent Interactions in the Transition State During Diels-Alder Endo Minor-Regioisomer Formation.]]
| [[File:KH1015 Var Exo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.5: Non Covalent Interactions in the Transition State During Diels-Alder Exo Minor-Regioisomer Formation.]]
| [[File:KH1015 Isoindene-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.6: Non Covalent Interactions in the Transition State During Cheletropic Product Formation.]]
|-
|}

===Part 4: IRC.===
====1. Diels-Alder Products.====
=====1.A. Endo Major-Regio-Isomer.=====
Referring to Figure 5.3.7, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:Kh1015 Endo Diels Alder.gif|frame|left|Figure 5.3.7: IRC for Formation of Diels-Alder Endo Product at 298.15 K and 1 atm (PM6 Level).]]
|| [[File:KH1015 Endo Diels Alder IRC Graph.png|thumb|Figure 5.3.8: IRC Graph of Energy against Reaction Coordinate for the formation of Endo Product at 298.15 K and 1 atm (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_Diels_Alder_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.9: Jmol of TS of Endo Path.</title>
<color>white</color>
<size>400</size>
<script>frame 14; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 ENDO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Endo Diels Alder-TS HOMO Isovalue 0.02 Cube Grid Coarse.png|thumb|Figure 5.3.10: HOMO of the TS of Endo Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

=====1.B. Exo Major-Regio-Isomer.=====
Referring to Figure 5.3.11, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:Kh1015 Exo Diels Alder.gif|frame|left|Figure 5.3.11: IRC for Formation of Diels-Alder Exo Product (PM6 level).]]
|| [[File:KH1015 Exo Diels Alder IRC Graph.png|thumb|Figure 5.3.12: IRC Graph of Energy against Reaction Coordinate for the formation of Exo Product (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_Diels_Alder_IRC_Graph_Gradient.png here]for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.13: HOMO of TS of Exo Path.</title>
<color>white</color>
<size>400</size>
<script>frame 74; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 EXO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Exo Diels Alder-TS HOMO.png|thumb|Figure 5.3.14: HOMO of TS of Exo Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

=====2.A. Endo Minor-Regio-Isomer.=====
Referring to Figure 5.3.15, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Var Endo Diels Alder.gif|frame|left|Figure 5.3.15: IRC for Formation of Endo Minor-Regioisomer.]]
|| [[File:KH1015 Var Endo Diels Alder IRC Graph.png|thumb|Figure 5.3.16: IRC Graph of Energy against Reaction Coordinate for the formation of Endo Minor-Regioisomer (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Var_Endo_Diels_Alder_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.17: HOMO of Endo Minor-Regioisomer Path.</title>
<color>white</color>
<size>400</size>
<script>frame 24; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 VAR ENDO DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Var Endo Diels Alder-TS HOMO.png|thumb|Figure 5.3.18: HOMO of TS of Endo Minor-Regioisomer Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

=====2.B. Exo Minor-Regio-Isomer.=====
Referring to Figure 5.3.19, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Var Exo Diels Alder.gif|frame|left|Figure 5.3.19: IRC for Formation of Exo Minor-Regioisomer.]]
|| [[File:KH1015 Var Exo Diels Alder IRC Graph.png|thumb|Figure 5.3.20: IRC Graph of Energy against Reaction Coordinate for the formation of Exo Minor-Regioisomer (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Var_Exo_Diels_Alder_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.21: HOMO of TS of Exo Minor-Regioisomer Path.</title>
<color>white</color>
<size>400</size>
<script>frame 16; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 VAR DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Var Exo Diels Alder-TS HOMO.png|thumb|Figure 5.3.22: HOMO of TS of Exo Minor-Regioisomer Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

====2. Cheletropic Product.====
Referring to Figure 5.3.23, the IRC calculation at PM6 level showed that the two C-S sigma bonds were formed in a synchronous fashion in a concerted mechanism and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:Kh1015 Isoindene.gif|frame|left|Figure 5.3.23: IRC for Formation of Cheletropic Product.]]
|| [[File:KH1015 Isoindene IRC Graph.png|thumb|Figure 5.3.24: IRC Graph of Energy against Reaction Coordinate for the formation of Cheletropic Product (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Isoindene_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.25: HOMO of TS of Cheletropic Path.</title>
<color>white</color>
<size>400</size>
<script>frame 36; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 ISOINDENE ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Isoindene-TS HOMO.png|thumb|Figure 5.3.26: HOMO of TS of Cheletropic Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

===Part 5: Interactive Vibration Animations.===

Figures 5.3.27-5.3.31 show the interactive vibration animations.

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.27: Interactive Vibration Animation of the Endo TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 ENDO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Endo</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton>
<script>measure 14 18; measure 11 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>Endo</target>
</item>
<item>
<script>frame 15; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i334/cm</text>
<target>Endo</target>
</item>
<item>
<script>frame 16; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>63/cm</text>
<target>Endo</target>
</item>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.28: Interactive Vibration Animation of the Exo TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 EXO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Exo</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Exo</target>
</jmolbutton>
<jmolbutton>
<script>measure 14 18; measure 11 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>Exo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Exo</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Exo</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>Exo</target>
</item>
<item>
<script>frame 75; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i352/cm</text>
<target>Exo</target>
</item>
<item>
<script>frame 76; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>66/cm</text>
<target>Exo</target>
</item>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Exo</target>
</jmolbutton>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.29: Interactive Vibration Animation of the Endo Minor-Regioisomer TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 VAR ENDO DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>EndoVar</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>EndoVar</target>
</jmolbutton>
<jmolbutton>
<script>measure 5 17; measure 2 18</script>
<text>TS C-C Equilibrium Distance</text>
<target>EndoVar</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EndoVar</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>EndoVar</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>EndoVar</target>
</item>
<item>
<script>frame 25; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i453/cm</text>
<target>EndoVar</target>
</item>
<item>
<script>frame 26; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>57/cm</text>
<target>EndoVar</target>
</item>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.30: Interactive Vibration Animation of the Exo Minor-Regioisomer TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 VAR DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>ExoVar</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>ExoVar</target>
</jmolbutton>
<jmolbutton>
<script>measure 2 18; measure 5 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>ExoVar</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExoVar</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>ExoVar</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>ExoVar</target>
</item>
<item>
<script>frame 17; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i483/cm</text>
<target>ExoVar</target>
</item>
<item>
<script>frame 18; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>53/cm</text>
<target>ExoVar</target>
</item>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.31: Interactive Vibration Animation of the Cheletropic TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 ISOINDENE ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Cyclohexene</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton>
<script>measure 11 17; measure 14 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>Cyclohexene</target>
</item>
<item>
<script>frame 37; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i487/cm</text>
<target>Cyclohexene</target>
</item>
<item>
<script>frame 38; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>74/cm</text>
<target>Cyclohexene</target>
</item>
</jmolmenu>
</jmol>

Rep:Kh1015TSEx3RD

2018-03-13T23:14:13Z

Kh1015: /* Part 3: Rationalizing the Reaction Profile Parameters. */

==Exercise 3 Results and Discussion.==

'''Note to Reader/Marker:'''
<br>The compartmentalization of the Results and Discussion into 5 parts was based on relevant discussion idea and for convenient navigation during the write-up. Also, the Jmol files in this page could display the relative energies of the MOs but they could not visualize the MOs. In response, the visualized HOMO of each TS was attached next to the Jmol files for viewing purposes.

===Part 1: Parameters from Reaction Profile.===

Referring to Table 5.3.2, calculations at PM6 level showed that only the Diels-Alder minor-regio-isomers were non-spontaneous. The Diels-Alder endo-major-regioisomer (referred to as endo product in Table 5.3.1) was calculated to be the kinetic product (based on lowest activation Gibbs-Free Energy equalled to 83.2 kJ mol<sup>-1</sup>) and an associated rate of reaction of 0.0165 s<sup>-1</sup> at 298.15K. The rate constant was calculated using the formula described under Introduction > Part D. The cheletropic product was calculated to be the thermodynamically favourable product (based on the most negative Δ Gibbs-Free Energy equalled to -155 kJ mol<sup>-1</sup>). This prediction could be verified experimentally by doing a kinetic study and analysis of ratio of Diels-Alder (including the regioisomers) and cheletropic products formed at rtp.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.3.1: Summary of Calculated Gibbs-Free Energy of Species in Diels-Alder and Cheletropic Reactions at 298.15 K and 1 atm (PM6 level).
|-
|rowspan="2"|''' '''
|colspan="12"|'''States'''
|-
|'''5,6-dimethylenecyclohexa-1,3-diene'''
|'''Sulfur Dioxide'''
|'''Endo TS'''
|'''Endo Product'''
|'''Exo TS'''
|'''Exo Product'''
|'''TS of Endo-Minor-Regioisomer'''
|'''Endo-Minor-Regioisomer'''
|'''TS of Exo-Minor-Regioisomer'''
|'''Exo-Minor-Regioisomer'''
|'''Cheletropic TS'''
|'''Cheletropic Product'''
|-
|'''Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
|468
| -313
|238
|57.0
|242
|56.3
|268
|172
|276
|177
|260
| -0.00263
|}

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.3.2: Summary of Calculated Reaction Profile Parameters for Diels-Alder and Cheletropic Reactions at 298.15 K and 1 atm (PM6 level).
|-
|''' '''
|'''Endo-Major-Regioisomer'''
|'''Exo-Major-Regioisomer'''
|'''Endo-Minor-Regioisomer'''
|'''Exo-Minor-Regioisomer'''
|'''Cheletropic'''
|-
|'''Activation Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
|83.2
|87.2
|113
|121
|106
|-
|'''Δ Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
| -97.6
| -98.2
|17.7
|22.2
| -155
|-
|'''Predicted Rate of Reaction (x10<sup>-6</sup> s<sup>-1</sup>)'''
|16,500
|3,280
|0.010
|0.004
|1.67
|}

===Part 2: Comparison of Reaction Profiles on a Standardized Reaction Coordinate.===

Figure 5.3.1 shows the comparison of the Diels-Alder and Cheletropic Reaction Profiles on a Standardized Reaction Coordinate at 298.15 K and 1 atm (PM6 level). In the Standardized Reaction Coordinate, the reactants' coordinates are set to -1, those of TS set to 0 and those of products set to 1. This was done to align the all the reaction states independent of the rate on a common scale such that the relative energetics could be compared between possible reaction paths.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Comparison.png|frame|Figure 5.3.1: Comparison of the Diels-Alder and Cheletropic Reaction Profiles on a Standardized Reaction Coordinate at 298.15 K and 1 atm (PM6 level).]]
|}

===Part 3: Rationalizing the Reaction Profile Parameters.===

Xylylene is an unstable compound because it is a system of 8 π electrons (4n anti-aromatic rule). From the IRC of all the reactions examined (excluding Diels-Alder minor-regio-isomers), it was observed that as xylelene reacted with sulfur dioxide, the 6 membered-ring would end up with a stable 6 π electrons system (4π+2 aromatic rule) in the product. This provided a strong thermodynamic driving force for the reaction with sulfur dioxide to proceed.

For all the reactions examined, there was no identifiable secondary orbital contribution from the Gaussview MO visualizations.

Referring to Figure 5.3.2-5.3.5, the calculated steric interactions were similar for Diels-Alder endo-exo products that react at the same regio-position. Because of similar steric interactions and electronic interactions within each set, the products that reacted at the same position would possess similar activation Gibbs-Free Energy (calculated) as shown in Table 5.3.2. However, when comparing '''between''' the two sets of Diels-Alder regio-isomers, it could be seen that the activation Gibbs-Free Energy for the minor-regio-isomer set was much higher than the other set ({113, 121} against {83.2, 87.2} where each element of the sets is in the form {endo, exo} and reported in kJ mol<sup>-1</sup>). For both sets, the TS formation involved severance of π interactions in the xylylene system. In the major-regio-isomer set, the activation Gibbs-Free Energy was reduced because there was a corresponding formation of favourable aromatic interaction in the 6-membered ring.

Referring to Figure 5.3.2-5.3.3 and 5.3.6, when comparing between the Diels-Alder major regio-isomer set and the cheletropic product, the steric clash (Red being not favourable and Blue being favourable) in the cheletropic TS was calculated to be higher than those in the Diels-Alder major regio-isomer set. This is due to the approach of two lone pairs of S atom towards the 5,6-dimethylenecyclohexa-1,3-diene in the chelotropic TS (Orange colour) that was not present in the Diels-Alder reactions. This contributes to the observation that the calculated activation Gibbs-Free Energy of the cheletropic product, 106 kJ mol<sup>-1</sup>, was much higher than those of the endo and exo products, 83.2 and 87.2 <sup>-1</sup> respectively.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Endo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.2: Non Covalent Interactions in the Transition State During Diels-Alder Endo Product Formation.]]
|[[File:KH1015 Exo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.3: Non Covalent Interactions in the Transition State During Diels-Alder Exo Product Formation.]]
|[[File:KH1015 Var Endo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.4: Non Covalent Interactions in the Transition State During Diels-Alder Endo Minor-Regioisomer Formation.]]
| [[File:KH1015 Var Exo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.5: Non Covalent Interactions in the Transition State During Diels-Alder Exo Minor-Regioisomer Formation.]]
| [[File:KH1015 Isoindene-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.6: Non Covalent Interactions in the Transition State During Cheletropic Product Formation.]]
|-
|}

===Part 4: IRC.===
====1. Diels-Alder Products.====
=====1.A. Endo Major-Regio-Isomer.=====
Referring to Figure 5.3.7, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:Kh1015 Endo Diels Alder.gif|frame|left|Figure 5.3.7: IRC for Formation of Diels-Alder Endo Product at 298.15 K and 1 atm (PM6 Level).]]
|| [[File:KH1015 Endo Diels Alder IRC Graph.png|thumb|Figure 5.3.8: IRC Graph of Energy against Reaction Coordinate for the formation of Endo Product at 298.15 K and 1 atm (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_Diels_Alder_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.9: Jmol of TS of Endo Path.</title>
<color>white</color>
<size>400</size>
<script>frame 14; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 ENDO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Endo Diels Alder-TS HOMO Isovalue 0.02 Cube Grid Coarse.png|thumb|Figure 5.3.10: HOMO of the TS of Endo Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

=====1.B. Exo Major-Regio-Isomer.=====
Referring to Figure 5.3.11, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:Kh1015 Exo Diels Alder.gif|frame|left|Figure 5.3.11: IRC for Formation of Diels-Alder Exo Product (PM6 level).]]
|| [[File:KH1015 Exo Diels Alder IRC Graph.png|thumb|Figure 5.3.12: IRC Graph of Energy against Reaction Coordinate for the formation of Exo Product (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_Diels_Alder_IRC_Graph_Gradient.png here]for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.13: HOMO of TS of Exo Path.</title>
<color>white</color>
<size>400</size>
<script>frame 74; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 EXO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Exo Diels Alder-TS HOMO.png|thumb|Figure 5.3.14: HOMO of TS of Exo Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

=====2.A. Endo Minor-Regio-Isomer.=====
Referring to Figure 5.3.15, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Var Endo Diels Alder.gif|frame|left|Figure 5.3.15: IRC for Formation of Endo Minor-Regioisomer.]]
|| [[File:KH1015 Var Endo Diels Alder IRC Graph.png|thumb|Figure 5.3.16: IRC Graph of Energy against Reaction Coordinate for the formation of Endo Minor-Regioisomer (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Var_Endo_Diels_Alder_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.17: HOMO of Endo Minor-Regioisomer Path.</title>
<color>white</color>
<size>400</size>
<script>frame 24; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 VAR ENDO DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Var Endo Diels Alder-TS HOMO.png|thumb|Figure 5.3.18: HOMO of TS of Endo Minor-Regioisomer Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

=====2.B. Exo Minor-Regio-Isomer.=====
Referring to Figure 5.3.19, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Var Exo Diels Alder.gif|frame|left|Figure 5.3.19: IRC for Formation of Exo Minor-Regioisomer.]]
|| [[File:KH1015 Var Exo Diels Alder IRC Graph.png|thumb|Figure 5.3.20: IRC Graph of Energy against Reaction Coordinate for the formation of Exo Minor-Regioisomer (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Var_Exo_Diels_Alder_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.21: HOMO of TS of Exo Minor-Regioisomer Path.</title>
<color>white</color>
<size>400</size>
<script>frame 16; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 VAR DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Var Exo Diels Alder-TS HOMO.png|thumb|Figure 5.3.22: HOMO of TS of Exo Minor-Regioisomer Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

====2. Cheletropic Product.====
Referring to Figure 5.3.23, the IRC calculation at PM6 level showed that the two C-S sigma bonds were formed in a synchronous fashion in a concerted mechanism and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:Kh1015 Isoindene.gif|frame|left|Figure 5.3.23: IRC for Formation of Cheletropic Product.]]
|| [[File:KH1015 Isoindene IRC Graph.png|thumb|Figure 5.3.24: IRC Graph of Energy against Reaction Coordinate for the formation of Cheletropic Product (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Isoindene_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.25: HOMO of TS of Cheletropic Path.</title>
<color>white</color>
<size>400</size>
<script>frame 36; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 ISOINDENE ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Isoindene-TS HOMO.png|thumb|Figure 5.3.26: HOMO of TS of Cheletropic Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

===Part 5: Interactive Vibration Animations.===

Figures 5.3.27-5.3.31 show the interactive vibration animations.

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.27: Interactive Vibration Animation of the Endo TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 ENDO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Endo</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton>
<script>measure 14 18; measure 11 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>Endo</target>
</item>
<item>
<script>frame 15; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i334/cm</text>
<target>Endo</target>
</item>
<item>
<script>frame 16; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>63/cm</text>
<target>Endo</target>
</item>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.28: Interactive Vibration Animation of the Exo TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 EXO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Exo</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Exo</target>
</jmolbutton>
<jmolbutton>
<script>measure 14 18; measure 11 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>Exo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Exo</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Exo</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>Exo</target>
</item>
<item>
<script>frame 75; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i352/cm</text>
<target>Exo</target>
</item>
<item>
<script>frame 76; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>66/cm</text>
<target>Exo</target>
</item>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Exo</target>
</jmolbutton>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.29: Interactive Vibration Animation of the Endo Minor-Regioisomer TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 VAR ENDO DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>EndoVar</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>EndoVar</target>
</jmolbutton>
<jmolbutton>
<script>measure 5 17; measure 2 18</script>
<text>TS C-C Equilibrium Distance</text>
<target>EndoVar</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EndoVar</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>EndoVar</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>EndoVar</target>
</item>
<item>
<script>frame 25; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i453/cm</text>
<target>EndoVar</target>
</item>
<item>
<script>frame 26; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>57/cm</text>
<target>EndoVar</target>
</item>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.30: Interactive Vibration Animation of the Exo Minor-Regioisomer TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 VAR DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>ExoVar</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>ExoVar</target>
</jmolbutton>
<jmolbutton>
<script>measure 2 18; measure 5 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>ExoVar</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExoVar</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>ExoVar</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>ExoVar</target>
</item>
<item>
<script>frame 17; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i483/cm</text>
<target>ExoVar</target>
</item>
<item>
<script>frame 18; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>53/cm</text>
<target>ExoVar</target>
</item>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.31: Interactive Vibration Animation of the Cheletropic TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 ISOINDENE ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Cyclohexene</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton>
<script>measure 11 17; measure 14 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>Cyclohexene</target>
</item>
<item>
<script>frame 37; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i487/cm</text>
<target>Cyclohexene</target>
</item>
<item>
<script>frame 38; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>74/cm</text>
<target>Cyclohexene</target>
</item>
</jmolmenu>
</jmol>

Rep:Kh1015TSEx3RD

2018-03-13T23:10:59Z

Kh1015: /* Part 3: Rationalizing the Reaction Profile Parameters. */

==Exercise 3 Results and Discussion.==

'''Note to Reader/Marker:'''
<br>The compartmentalization of the Results and Discussion into 5 parts was based on relevant discussion idea and for convenient navigation during the write-up. Also, the Jmol files in this page could display the relative energies of the MOs but they could not visualize the MOs. In response, the visualized HOMO of each TS was attached next to the Jmol files for viewing purposes.

===Part 1: Parameters from Reaction Profile.===

Referring to Table 5.3.2, calculations at PM6 level showed that only the Diels-Alder minor-regio-isomers were non-spontaneous. The Diels-Alder endo-major-regioisomer (referred to as endo product in Table 5.3.1) was calculated to be the kinetic product (based on lowest activation Gibbs-Free Energy equalled to 83.2 kJ mol<sup>-1</sup>) and an associated rate of reaction of 0.0165 s<sup>-1</sup> at 298.15K. The rate constant was calculated using the formula described under Introduction > Part D. The cheletropic product was calculated to be the thermodynamically favourable product (based on the most negative Δ Gibbs-Free Energy equalled to -155 kJ mol<sup>-1</sup>). This prediction could be verified experimentally by doing a kinetic study and analysis of ratio of Diels-Alder (including the regioisomers) and cheletropic products formed at rtp.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.3.1: Summary of Calculated Gibbs-Free Energy of Species in Diels-Alder and Cheletropic Reactions at 298.15 K and 1 atm (PM6 level).
|-
|rowspan="2"|''' '''
|colspan="12"|'''States'''
|-
|'''5,6-dimethylenecyclohexa-1,3-diene'''
|'''Sulfur Dioxide'''
|'''Endo TS'''
|'''Endo Product'''
|'''Exo TS'''
|'''Exo Product'''
|'''TS of Endo-Minor-Regioisomer'''
|'''Endo-Minor-Regioisomer'''
|'''TS of Exo-Minor-Regioisomer'''
|'''Exo-Minor-Regioisomer'''
|'''Cheletropic TS'''
|'''Cheletropic Product'''
|-
|'''Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
|468
| -313
|238
|57.0
|242
|56.3
|268
|172
|276
|177
|260
| -0.00263
|}

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.3.2: Summary of Calculated Reaction Profile Parameters for Diels-Alder and Cheletropic Reactions at 298.15 K and 1 atm (PM6 level).
|-
|''' '''
|'''Endo-Major-Regioisomer'''
|'''Exo-Major-Regioisomer'''
|'''Endo-Minor-Regioisomer'''
|'''Exo-Minor-Regioisomer'''
|'''Cheletropic'''
|-
|'''Activation Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
|83.2
|87.2
|113
|121
|106
|-
|'''Δ Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
| -97.6
| -98.2
|17.7
|22.2
| -155
|-
|'''Predicted Rate of Reaction (x10<sup>-6</sup> s<sup>-1</sup>)'''
|16,500
|3,280
|0.010
|0.004
|1.67
|}

===Part 2: Comparison of Reaction Profiles on a Standardized Reaction Coordinate.===

Figure 5.3.1 shows the comparison of the Diels-Alder and Cheletropic Reaction Profiles on a Standardized Reaction Coordinate at 298.15 K and 1 atm (PM6 level). In the Standardized Reaction Coordinate, the reactants' coordinates are set to -1, those of TS set to 0 and those of products set to 1. This was done to align the all the reaction states independent of the rate on a common scale such that the relative energetics could be compared between possible reaction paths.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Comparison.png|frame|Figure 5.3.1: Comparison of the Diels-Alder and Cheletropic Reaction Profiles on a Standardized Reaction Coordinate at 298.15 K and 1 atm (PM6 level).]]
|}

===Part 3: Rationalizing the Reaction Profile Parameters.===

Xylylene is an unstable compound because it is a system of 8 π electrons (4n anti-aromatic rule). From the IRC of all the reactions examined (excluding Diels-Alder minor-regio-isomers), it was observed that as xylelene reacted with sulfur dioxide, the 6 membered-ring would end up with a stable 6 π electrons system (4π+2 aromatic rule) in the product. This provided a strong thermodynamic driving force for the reaction with sulfur dioxide to proceed.

For all the reactions examined, there was no identifiable secondary orbital contribution from the Gaussview MO visualizations.

Referring to Figure 5.3.2-5.3.5, the calculated steric interactions were similar for Diels-Alder endo-exo products that react at the same regio-position. Because of similar steric interactions and electronic interactions within each set, the products that reacted at the same position would possess similar activation Gibbs-Free Energy (calculated) as shown in Table 5.3.2. However, when comparing '''between''' the two sets of Diels-Alder regio-isomers, it could be seen that the activation Gibbs-Free Energy for the minor-regio-isomer set was much higher than the other set ({113, 121} against {83.2, 87.2} where each element of the sets is in the form {endo, exo} and reported in kJ mol<sup>-1</sup>). For both sets, the TS formation involved severance of π interactions in the xylylene system. In the major-regio-isomer set, the activation Gibbs-Free Energy was reduced because there was a corresponding formation of favourable aromatic interaction in the 6-membered ring.

Referring to Figure 5.3.2-5.3.3 and 5.3.6, when comparing between the Diels-Alder major regio-isomer set and the cheletropic product, the steric clash (Red being not favourable and Blue being favourable) in the cheletropic TS was calculated to be higher than those in the Diels-Alder major regio-isomer set. This partially explains the observation that the calculated activation Gibbs-Free Energy of the cheletropic product, 106 kJ mol<sup>-1</sup>, was much higher than those of the endo and exo products, 83.2 and 87.2 <sup>-1</sup> respectively.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Endo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.2: Non Covalent Interactions in the Transition State During Diels-Alder Endo Product Formation.]]
|[[File:KH1015 Exo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.3: Non Covalent Interactions in the Transition State During Diels-Alder Exo Product Formation.]]
|[[File:KH1015 Var Endo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.4: Non Covalent Interactions in the Transition State During Diels-Alder Endo Minor-Regioisomer Formation.]]
| [[File:KH1015 Var Exo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.5: Non Covalent Interactions in the Transition State During Diels-Alder Exo Minor-Regioisomer Formation.]]
| [[File:KH1015 Isoindene-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.6: Non Covalent Interactions in the Transition State During Cheletropic Product Formation.]]
|-
|}

===Part 4: IRC.===
====1. Diels-Alder Products.====
=====1.A. Endo Major-Regio-Isomer.=====
Referring to Figure 5.3.7, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:Kh1015 Endo Diels Alder.gif|frame|left|Figure 5.3.7: IRC for Formation of Diels-Alder Endo Product at 298.15 K and 1 atm (PM6 Level).]]
|| [[File:KH1015 Endo Diels Alder IRC Graph.png|thumb|Figure 5.3.8: IRC Graph of Energy against Reaction Coordinate for the formation of Endo Product at 298.15 K and 1 atm (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_Diels_Alder_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.9: Jmol of TS of Endo Path.</title>
<color>white</color>
<size>400</size>
<script>frame 14; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 ENDO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Endo Diels Alder-TS HOMO Isovalue 0.02 Cube Grid Coarse.png|thumb|Figure 5.3.10: HOMO of the TS of Endo Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

=====1.B. Exo Major-Regio-Isomer.=====
Referring to Figure 5.3.11, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:Kh1015 Exo Diels Alder.gif|frame|left|Figure 5.3.11: IRC for Formation of Diels-Alder Exo Product (PM6 level).]]
|| [[File:KH1015 Exo Diels Alder IRC Graph.png|thumb|Figure 5.3.12: IRC Graph of Energy against Reaction Coordinate for the formation of Exo Product (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_Diels_Alder_IRC_Graph_Gradient.png here]for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.13: HOMO of TS of Exo Path.</title>
<color>white</color>
<size>400</size>
<script>frame 74; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 EXO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Exo Diels Alder-TS HOMO.png|thumb|Figure 5.3.14: HOMO of TS of Exo Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

=====2.A. Endo Minor-Regio-Isomer.=====
Referring to Figure 5.3.15, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Var Endo Diels Alder.gif|frame|left|Figure 5.3.15: IRC for Formation of Endo Minor-Regioisomer.]]
|| [[File:KH1015 Var Endo Diels Alder IRC Graph.png|thumb|Figure 5.3.16: IRC Graph of Energy against Reaction Coordinate for the formation of Endo Minor-Regioisomer (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Var_Endo_Diels_Alder_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.17: HOMO of Endo Minor-Regioisomer Path.</title>
<color>white</color>
<size>400</size>
<script>frame 24; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 VAR ENDO DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Var Endo Diels Alder-TS HOMO.png|thumb|Figure 5.3.18: HOMO of TS of Endo Minor-Regioisomer Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

=====2.B. Exo Minor-Regio-Isomer.=====
Referring to Figure 5.3.19, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Var Exo Diels Alder.gif|frame|left|Figure 5.3.19: IRC for Formation of Exo Minor-Regioisomer.]]
|| [[File:KH1015 Var Exo Diels Alder IRC Graph.png|thumb|Figure 5.3.20: IRC Graph of Energy against Reaction Coordinate for the formation of Exo Minor-Regioisomer (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Var_Exo_Diels_Alder_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.21: HOMO of TS of Exo Minor-Regioisomer Path.</title>
<color>white</color>
<size>400</size>
<script>frame 16; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 VAR DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Var Exo Diels Alder-TS HOMO.png|thumb|Figure 5.3.22: HOMO of TS of Exo Minor-Regioisomer Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

====2. Cheletropic Product.====
Referring to Figure 5.3.23, the IRC calculation at PM6 level showed that the two C-S sigma bonds were formed in a synchronous fashion in a concerted mechanism and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:Kh1015 Isoindene.gif|frame|left|Figure 5.3.23: IRC for Formation of Cheletropic Product.]]
|| [[File:KH1015 Isoindene IRC Graph.png|thumb|Figure 5.3.24: IRC Graph of Energy against Reaction Coordinate for the formation of Cheletropic Product (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Isoindene_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.25: HOMO of TS of Cheletropic Path.</title>
<color>white</color>
<size>400</size>
<script>frame 36; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 ISOINDENE ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Isoindene-TS HOMO.png|thumb|Figure 5.3.26: HOMO of TS of Cheletropic Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

===Part 5: Interactive Vibration Animations.===

Figures 5.3.27-5.3.31 show the interactive vibration animations.

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.27: Interactive Vibration Animation of the Endo TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 ENDO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Endo</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton>
<script>measure 14 18; measure 11 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>Endo</target>
</item>
<item>
<script>frame 15; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i334/cm</text>
<target>Endo</target>
</item>
<item>
<script>frame 16; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>63/cm</text>
<target>Endo</target>
</item>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.28: Interactive Vibration Animation of the Exo TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 EXO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Exo</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Exo</target>
</jmolbutton>
<jmolbutton>
<script>measure 14 18; measure 11 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>Exo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Exo</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Exo</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>Exo</target>
</item>
<item>
<script>frame 75; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i352/cm</text>
<target>Exo</target>
</item>
<item>
<script>frame 76; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>66/cm</text>
<target>Exo</target>
</item>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Exo</target>
</jmolbutton>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.29: Interactive Vibration Animation of the Endo Minor-Regioisomer TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 VAR ENDO DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>EndoVar</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>EndoVar</target>
</jmolbutton>
<jmolbutton>
<script>measure 5 17; measure 2 18</script>
<text>TS C-C Equilibrium Distance</text>
<target>EndoVar</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EndoVar</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>EndoVar</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>EndoVar</target>
</item>
<item>
<script>frame 25; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i453/cm</text>
<target>EndoVar</target>
</item>
<item>
<script>frame 26; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>57/cm</text>
<target>EndoVar</target>
</item>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.30: Interactive Vibration Animation of the Exo Minor-Regioisomer TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 VAR DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>ExoVar</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>ExoVar</target>
</jmolbutton>
<jmolbutton>
<script>measure 2 18; measure 5 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>ExoVar</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExoVar</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>ExoVar</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>ExoVar</target>
</item>
<item>
<script>frame 17; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i483/cm</text>
<target>ExoVar</target>
</item>
<item>
<script>frame 18; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>53/cm</text>
<target>ExoVar</target>
</item>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.31: Interactive Vibration Animation of the Cheletropic TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 ISOINDENE ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Cyclohexene</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton>
<script>measure 11 17; measure 14 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>Cyclohexene</target>
</item>
<item>
<script>frame 37; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i487/cm</text>
<target>Cyclohexene</target>
</item>
<item>
<script>frame 38; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>74/cm</text>
<target>Cyclohexene</target>
</item>
</jmolmenu>
</jmol>

Rep:Kh1015TSEx3RD

2018-03-13T23:07:28Z

Kh1015: /* Part 3: Rationalizing the Reaction Profile Parameters. */

==Exercise 3 Results and Discussion.==

'''Note to Reader/Marker:'''
<br>The compartmentalization of the Results and Discussion into 5 parts was based on relevant discussion idea and for convenient navigation during the write-up. Also, the Jmol files in this page could display the relative energies of the MOs but they could not visualize the MOs. In response, the visualized HOMO of each TS was attached next to the Jmol files for viewing purposes.

===Part 1: Parameters from Reaction Profile.===

Referring to Table 5.3.2, calculations at PM6 level showed that only the Diels-Alder minor-regio-isomers were non-spontaneous. The Diels-Alder endo-major-regioisomer (referred to as endo product in Table 5.3.1) was calculated to be the kinetic product (based on lowest activation Gibbs-Free Energy equalled to 83.2 kJ mol<sup>-1</sup>) and an associated rate of reaction of 0.0165 s<sup>-1</sup> at 298.15K. The rate constant was calculated using the formula described under Introduction > Part D. The cheletropic product was calculated to be the thermodynamically favourable product (based on the most negative Δ Gibbs-Free Energy equalled to -155 kJ mol<sup>-1</sup>). This prediction could be verified experimentally by doing a kinetic study and analysis of ratio of Diels-Alder (including the regioisomers) and cheletropic products formed at rtp.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.3.1: Summary of Calculated Gibbs-Free Energy of Species in Diels-Alder and Cheletropic Reactions at 298.15 K and 1 atm (PM6 level).
|-
|rowspan="2"|''' '''
|colspan="12"|'''States'''
|-
|'''5,6-dimethylenecyclohexa-1,3-diene'''
|'''Sulfur Dioxide'''
|'''Endo TS'''
|'''Endo Product'''
|'''Exo TS'''
|'''Exo Product'''
|'''TS of Endo-Minor-Regioisomer'''
|'''Endo-Minor-Regioisomer'''
|'''TS of Exo-Minor-Regioisomer'''
|'''Exo-Minor-Regioisomer'''
|'''Cheletropic TS'''
|'''Cheletropic Product'''
|-
|'''Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
|468
| -313
|238
|57.0
|242
|56.3
|268
|172
|276
|177
|260
| -0.00263
|}

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.3.2: Summary of Calculated Reaction Profile Parameters for Diels-Alder and Cheletropic Reactions at 298.15 K and 1 atm (PM6 level).
|-
|''' '''
|'''Endo-Major-Regioisomer'''
|'''Exo-Major-Regioisomer'''
|'''Endo-Minor-Regioisomer'''
|'''Exo-Minor-Regioisomer'''
|'''Cheletropic'''
|-
|'''Activation Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
|83.2
|87.2
|113
|121
|106
|-
|'''Δ Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
| -97.6
| -98.2
|17.7
|22.2
| -155
|-
|'''Predicted Rate of Reaction (x10<sup>-6</sup> s<sup>-1</sup>)'''
|16,500
|3,280
|0.010
|0.004
|1.67
|}

===Part 2: Comparison of Reaction Profiles on a Standardized Reaction Coordinate.===

Figure 5.3.1 shows the comparison of the Diels-Alder and Cheletropic Reaction Profiles on a Standardized Reaction Coordinate at 298.15 K and 1 atm (PM6 level). In the Standardized Reaction Coordinate, the reactants' coordinates are set to -1, those of TS set to 0 and those of products set to 1. This was done to align the all the reaction states independent of the rate on a common scale such that the relative energetics could be compared between possible reaction paths.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Comparison.png|frame|Figure 5.3.1: Comparison of the Diels-Alder and Cheletropic Reaction Profiles on a Standardized Reaction Coordinate at 298.15 K and 1 atm (PM6 level).]]
|}

===Part 3: Rationalizing the Reaction Profile Parameters.===

Xylylene is an unstable compound because it is a system of 8 π electrons (4n anti-aromatic rule). From the IRC of all the reactions examined (excluding Diels-Alder minor-regio-isomers), it was observed that as xylelene reacted with sulfur dioxide, the 6 membered-ring would end up with a stable 6 π electrons system (4π+2 aromatic rule) in the product. This provided a strong thermodynamic driving force for the reaction with sulfur dioxide to proceed.

For all the reactions examined, there was no identifiable secondary orbital contribution from the Gaussview MO visualizations.

Referring to Figure 5.3.2-5.3.5, the calculated steric interactions were similar for Diels-Alder endo-exo products that react at the same regio-position. Because of similar steric interactions and electronic interactions within each set, the products that reacted at the same position would possess similar activation Gibbs-Free Energy (calculated) as shown in Table 5.3.2. However, when comparing '''between''' the two sets of Diels-Alder regio-isomers, it could be seen that the activation Gibbs-Free Energy for the minor-regio-isomer set was much higher than the other set ({113, 121} against {83.2, 87.2} where each element of the sets is in the form {endo, exo} and reported in kJ mol<sup>-1</sup>). For both sets, the TS formation involved severance of π interactions in the xylylene system. In the major-regio-isomer set, the activation Gibbs-Free Energy was reduced because there was a corresponding formation of favourable aromatic interaction in the 6-membered ring.

Referring to Figure 5.3.2-5.3.3 and 5.3.6, when comparing between the Diels-Alder major regio-isomer set and the cheletropic product, the steric clash (Red being not favourable and Blue being favourable) in the cheletropic TS was calculated to be higher than those in the Diels-Alder major regio-isomer set. This is reflected in the calculated activation Gibbs-Free Energy of the cheletropic product, 106 kJ mol<sup>-1</sup>, being much higher than those of the endo and exo products, 83.2 and 87.2 <sup>-1</sup> respectively.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Endo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.2: Non Covalent Interactions in the Transition State During Diels-Alder Endo Product Formation.]]
|[[File:KH1015 Exo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.3: Non Covalent Interactions in the Transition State During Diels-Alder Exo Product Formation.]]
|[[File:KH1015 Var Endo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.4: Non Covalent Interactions in the Transition State During Diels-Alder Endo Minor-Regioisomer Formation.]]
| [[File:KH1015 Var Exo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.5: Non Covalent Interactions in the Transition State During Diels-Alder Exo Minor-Regioisomer Formation.]]
| [[File:KH1015 Isoindene-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.6: Non Covalent Interactions in the Transition State During Cheletropic Product Formation.]]
|-
|}

===Part 4: IRC.===
====1. Diels-Alder Products.====
=====1.A. Endo Major-Regio-Isomer.=====
Referring to Figure 5.3.7, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:Kh1015 Endo Diels Alder.gif|frame|left|Figure 5.3.7: IRC for Formation of Diels-Alder Endo Product at 298.15 K and 1 atm (PM6 Level).]]
|| [[File:KH1015 Endo Diels Alder IRC Graph.png|thumb|Figure 5.3.8: IRC Graph of Energy against Reaction Coordinate for the formation of Endo Product at 298.15 K and 1 atm (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_Diels_Alder_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.9: Jmol of TS of Endo Path.</title>
<color>white</color>
<size>400</size>
<script>frame 14; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 ENDO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Endo Diels Alder-TS HOMO Isovalue 0.02 Cube Grid Coarse.png|thumb|Figure 5.3.10: HOMO of the TS of Endo Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

=====1.B. Exo Major-Regio-Isomer.=====
Referring to Figure 5.3.11, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:Kh1015 Exo Diels Alder.gif|frame|left|Figure 5.3.11: IRC for Formation of Diels-Alder Exo Product (PM6 level).]]
|| [[File:KH1015 Exo Diels Alder IRC Graph.png|thumb|Figure 5.3.12: IRC Graph of Energy against Reaction Coordinate for the formation of Exo Product (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_Diels_Alder_IRC_Graph_Gradient.png here]for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.13: HOMO of TS of Exo Path.</title>
<color>white</color>
<size>400</size>
<script>frame 74; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 EXO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Exo Diels Alder-TS HOMO.png|thumb|Figure 5.3.14: HOMO of TS of Exo Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

=====2.A. Endo Minor-Regio-Isomer.=====
Referring to Figure 5.3.15, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Var Endo Diels Alder.gif|frame|left|Figure 5.3.15: IRC for Formation of Endo Minor-Regioisomer.]]
|| [[File:KH1015 Var Endo Diels Alder IRC Graph.png|thumb|Figure 5.3.16: IRC Graph of Energy against Reaction Coordinate for the formation of Endo Minor-Regioisomer (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Var_Endo_Diels_Alder_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.17: HOMO of Endo Minor-Regioisomer Path.</title>
<color>white</color>
<size>400</size>
<script>frame 24; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 VAR ENDO DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Var Endo Diels Alder-TS HOMO.png|thumb|Figure 5.3.18: HOMO of TS of Endo Minor-Regioisomer Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

=====2.B. Exo Minor-Regio-Isomer.=====
Referring to Figure 5.3.19, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Var Exo Diels Alder.gif|frame|left|Figure 5.3.19: IRC for Formation of Exo Minor-Regioisomer.]]
|| [[File:KH1015 Var Exo Diels Alder IRC Graph.png|thumb|Figure 5.3.20: IRC Graph of Energy against Reaction Coordinate for the formation of Exo Minor-Regioisomer (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Var_Exo_Diels_Alder_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.21: HOMO of TS of Exo Minor-Regioisomer Path.</title>
<color>white</color>
<size>400</size>
<script>frame 16; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 VAR DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Var Exo Diels Alder-TS HOMO.png|thumb|Figure 5.3.22: HOMO of TS of Exo Minor-Regioisomer Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

====2. Cheletropic Product.====
Referring to Figure 5.3.23, the IRC calculation at PM6 level showed that the two C-S sigma bonds were formed in a synchronous fashion in a concerted mechanism and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:Kh1015 Isoindene.gif|frame|left|Figure 5.3.23: IRC for Formation of Cheletropic Product.]]
|| [[File:KH1015 Isoindene IRC Graph.png|thumb|Figure 5.3.24: IRC Graph of Energy against Reaction Coordinate for the formation of Cheletropic Product (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Isoindene_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.25: HOMO of TS of Cheletropic Path.</title>
<color>white</color>
<size>400</size>
<script>frame 36; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 ISOINDENE ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Isoindene-TS HOMO.png|thumb|Figure 5.3.26: HOMO of TS of Cheletropic Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

===Part 5: Interactive Vibration Animations.===

Figures 5.3.27-5.3.31 show the interactive vibration animations.

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.27: Interactive Vibration Animation of the Endo TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 ENDO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Endo</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton>
<script>measure 14 18; measure 11 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>Endo</target>
</item>
<item>
<script>frame 15; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i334/cm</text>
<target>Endo</target>
</item>
<item>
<script>frame 16; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>63/cm</text>
<target>Endo</target>
</item>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.28: Interactive Vibration Animation of the Exo TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 EXO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Exo</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Exo</target>
</jmolbutton>
<jmolbutton>
<script>measure 14 18; measure 11 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>Exo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Exo</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Exo</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>Exo</target>
</item>
<item>
<script>frame 75; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i352/cm</text>
<target>Exo</target>
</item>
<item>
<script>frame 76; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>66/cm</text>
<target>Exo</target>
</item>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Exo</target>
</jmolbutton>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.29: Interactive Vibration Animation of the Endo Minor-Regioisomer TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 VAR ENDO DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>EndoVar</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>EndoVar</target>
</jmolbutton>
<jmolbutton>
<script>measure 5 17; measure 2 18</script>
<text>TS C-C Equilibrium Distance</text>
<target>EndoVar</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EndoVar</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>EndoVar</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>EndoVar</target>
</item>
<item>
<script>frame 25; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i453/cm</text>
<target>EndoVar</target>
</item>
<item>
<script>frame 26; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>57/cm</text>
<target>EndoVar</target>
</item>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.30: Interactive Vibration Animation of the Exo Minor-Regioisomer TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 VAR DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>ExoVar</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>ExoVar</target>
</jmolbutton>
<jmolbutton>
<script>measure 2 18; measure 5 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>ExoVar</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExoVar</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>ExoVar</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>ExoVar</target>
</item>
<item>
<script>frame 17; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i483/cm</text>
<target>ExoVar</target>
</item>
<item>
<script>frame 18; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>53/cm</text>
<target>ExoVar</target>
</item>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.31: Interactive Vibration Animation of the Cheletropic TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 ISOINDENE ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Cyclohexene</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton>
<script>measure 11 17; measure 14 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>Cyclohexene</target>
</item>
<item>
<script>frame 37; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i487/cm</text>
<target>Cyclohexene</target>
</item>
<item>
<script>frame 38; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>74/cm</text>
<target>Cyclohexene</target>
</item>
</jmolmenu>
</jmol>

Rep:Kh1015TSEx3RD

2018-03-13T23:05:31Z

Kh1015: /* Part 3: Rationalizing the Reaction Profile Parameters. */

==Exercise 3 Results and Discussion.==

'''Note to Reader/Marker:'''
<br>The compartmentalization of the Results and Discussion into 5 parts was based on relevant discussion idea and for convenient navigation during the write-up. Also, the Jmol files in this page could display the relative energies of the MOs but they could not visualize the MOs. In response, the visualized HOMO of each TS was attached next to the Jmol files for viewing purposes.

===Part 1: Parameters from Reaction Profile.===

Referring to Table 5.3.2, calculations at PM6 level showed that only the Diels-Alder minor-regio-isomers were non-spontaneous. The Diels-Alder endo-major-regioisomer (referred to as endo product in Table 5.3.1) was calculated to be the kinetic product (based on lowest activation Gibbs-Free Energy equalled to 83.2 kJ mol<sup>-1</sup>) and an associated rate of reaction of 0.0165 s<sup>-1</sup> at 298.15K. The rate constant was calculated using the formula described under Introduction > Part D. The cheletropic product was calculated to be the thermodynamically favourable product (based on the most negative Δ Gibbs-Free Energy equalled to -155 kJ mol<sup>-1</sup>). This prediction could be verified experimentally by doing a kinetic study and analysis of ratio of Diels-Alder (including the regioisomers) and cheletropic products formed at rtp.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.3.1: Summary of Calculated Gibbs-Free Energy of Species in Diels-Alder and Cheletropic Reactions at 298.15 K and 1 atm (PM6 level).
|-
|rowspan="2"|''' '''
|colspan="12"|'''States'''
|-
|'''5,6-dimethylenecyclohexa-1,3-diene'''
|'''Sulfur Dioxide'''
|'''Endo TS'''
|'''Endo Product'''
|'''Exo TS'''
|'''Exo Product'''
|'''TS of Endo-Minor-Regioisomer'''
|'''Endo-Minor-Regioisomer'''
|'''TS of Exo-Minor-Regioisomer'''
|'''Exo-Minor-Regioisomer'''
|'''Cheletropic TS'''
|'''Cheletropic Product'''
|-
|'''Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
|468
| -313
|238
|57.0
|242
|56.3
|268
|172
|276
|177
|260
| -0.00263
|}

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.3.2: Summary of Calculated Reaction Profile Parameters for Diels-Alder and Cheletropic Reactions at 298.15 K and 1 atm (PM6 level).
|-
|''' '''
|'''Endo-Major-Regioisomer'''
|'''Exo-Major-Regioisomer'''
|'''Endo-Minor-Regioisomer'''
|'''Exo-Minor-Regioisomer'''
|'''Cheletropic'''
|-
|'''Activation Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
|83.2
|87.2
|113
|121
|106
|-
|'''Δ Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
| -97.6
| -98.2
|17.7
|22.2
| -155
|-
|'''Predicted Rate of Reaction (x10<sup>-6</sup> s<sup>-1</sup>)'''
|16,500
|3,280
|0.010
|0.004
|1.67
|}

===Part 2: Comparison of Reaction Profiles on a Standardized Reaction Coordinate.===

Figure 5.3.1 shows the comparison of the Diels-Alder and Cheletropic Reaction Profiles on a Standardized Reaction Coordinate at 298.15 K and 1 atm (PM6 level). In the Standardized Reaction Coordinate, the reactants' coordinates are set to -1, those of TS set to 0 and those of products set to 1. This was done to align the all the reaction states independent of the rate on a common scale such that the relative energetics could be compared between possible reaction paths.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Comparison.png|frame|Figure 5.3.1: Comparison of the Diels-Alder and Cheletropic Reaction Profiles on a Standardized Reaction Coordinate at 298.15 K and 1 atm (PM6 level).]]
|}

===Part 3: Rationalizing the Reaction Profile Parameters.===

Xylylene is an unstable compound because it is a system of 8 π electrons (4n anti-aromatic rule). From the IRC of all the reactions examined (excluding Diels-Alder minor-regio-isomers), it was observed that as xylelene reacted with sulfur dioxide, the 6 membered-ring would end up with a stable 6 π electrons system (4π+2 aromatic rule) in the product. This provided a strong thermodynamic driving force for the reaction with sulfur dioxide to proceed.

For all the reactions examined, there was no identifiable secondary orbital contribution from the Gaussview MO visualizations.

Referring to Figure 5.3.2-5.3.5, the calculated steric interactions were similar for Diels-Alder endo-exo products that react at the same regio-position. Because of similar steric interactions and electronic interactions within each set, the products that reacted at the same position would possess similar activation Gibbs-Free Energy (calculated) as shown in Table 5.3.2. However, when comparing '''between''' the two sets of Diels-Alder regio-isomers, it could be seen that the activation Gibbs-Free Energy for the minor-regio-isomer set was much higher than the other set ({113, 121} against {83.2, 87.2} where each element of the sets is in the form {endo, exo} and reported in kJ mol<sup>-1</sup>). For both sets, the TS formation involved severance of π interactions in the xylylene system. In the major-regio-isomer set, the activation Gibbs-Free Energy was reduced because there was a corresponding formation of favourable aromatic interaction in the 6-membered ring.

Referring to Figure 5.3.2-5.3.3 and 5.3.6, when comparing between the Diels-Alder major regio-isomer set and the cheletropic product, the steric clash in the cheletropic TS was calculated to be higher than those in the Diels-Alder major regio-isomer set. This is reflected in the calculated activation Gibbs-Free Energy of the cheletropic product, 106 kJ mol<sup>-1</sup>, being much higher than those of the endo and exo products, 83.2 and 87.2 <sup>-1</sup> respectively.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Endo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.2: Non Covalent Interactions in the Transition State During Diels-Alder Endo Product Formation.]]
|[[File:KH1015 Exo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.3: Non Covalent Interactions in the Transition State During Diels-Alder Exo Product Formation.]]
|[[File:KH1015 Var Endo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.4: Non Covalent Interactions in the Transition State During Diels-Alder Endo Minor-Regioisomer Formation.]]
| [[File:KH1015 Var Exo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.5: Non Covalent Interactions in the Transition State During Diels-Alder Exo Minor-Regioisomer Formation.]]
| [[File:KH1015 Isoindene-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.6: Non Covalent Interactions in the Transition State During Cheletropic Product Formation.]]
|-
|}

===Part 4: IRC.===
====1. Diels-Alder Products.====
=====1.A. Endo Major-Regio-Isomer.=====
Referring to Figure 5.3.7, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:Kh1015 Endo Diels Alder.gif|frame|left|Figure 5.3.7: IRC for Formation of Diels-Alder Endo Product at 298.15 K and 1 atm (PM6 Level).]]
|| [[File:KH1015 Endo Diels Alder IRC Graph.png|thumb|Figure 5.3.8: IRC Graph of Energy against Reaction Coordinate for the formation of Endo Product at 298.15 K and 1 atm (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_Diels_Alder_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.9: Jmol of TS of Endo Path.</title>
<color>white</color>
<size>400</size>
<script>frame 14; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 ENDO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Endo Diels Alder-TS HOMO Isovalue 0.02 Cube Grid Coarse.png|thumb|Figure 5.3.10: HOMO of the TS of Endo Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

=====1.B. Exo Major-Regio-Isomer.=====
Referring to Figure 5.3.11, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:Kh1015 Exo Diels Alder.gif|frame|left|Figure 5.3.11: IRC for Formation of Diels-Alder Exo Product (PM6 level).]]
|| [[File:KH1015 Exo Diels Alder IRC Graph.png|thumb|Figure 5.3.12: IRC Graph of Energy against Reaction Coordinate for the formation of Exo Product (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_Diels_Alder_IRC_Graph_Gradient.png here]for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.13: HOMO of TS of Exo Path.</title>
<color>white</color>
<size>400</size>
<script>frame 74; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 EXO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Exo Diels Alder-TS HOMO.png|thumb|Figure 5.3.14: HOMO of TS of Exo Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

=====2.A. Endo Minor-Regio-Isomer.=====
Referring to Figure 5.3.15, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Var Endo Diels Alder.gif|frame|left|Figure 5.3.15: IRC for Formation of Endo Minor-Regioisomer.]]
|| [[File:KH1015 Var Endo Diels Alder IRC Graph.png|thumb|Figure 5.3.16: IRC Graph of Energy against Reaction Coordinate for the formation of Endo Minor-Regioisomer (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Var_Endo_Diels_Alder_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.17: HOMO of Endo Minor-Regioisomer Path.</title>
<color>white</color>
<size>400</size>
<script>frame 24; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 VAR ENDO DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Var Endo Diels Alder-TS HOMO.png|thumb|Figure 5.3.18: HOMO of TS of Endo Minor-Regioisomer Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

=====2.B. Exo Minor-Regio-Isomer.=====
Referring to Figure 5.3.19, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Var Exo Diels Alder.gif|frame|left|Figure 5.3.19: IRC for Formation of Exo Minor-Regioisomer.]]
|| [[File:KH1015 Var Exo Diels Alder IRC Graph.png|thumb|Figure 5.3.20: IRC Graph of Energy against Reaction Coordinate for the formation of Exo Minor-Regioisomer (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Var_Exo_Diels_Alder_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.21: HOMO of TS of Exo Minor-Regioisomer Path.</title>
<color>white</color>
<size>400</size>
<script>frame 16; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 VAR DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Var Exo Diels Alder-TS HOMO.png|thumb|Figure 5.3.22: HOMO of TS of Exo Minor-Regioisomer Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

====2. Cheletropic Product.====
Referring to Figure 5.3.23, the IRC calculation at PM6 level showed that the two C-S sigma bonds were formed in a synchronous fashion in a concerted mechanism and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:Kh1015 Isoindene.gif|frame|left|Figure 5.3.23: IRC for Formation of Cheletropic Product.]]
|| [[File:KH1015 Isoindene IRC Graph.png|thumb|Figure 5.3.24: IRC Graph of Energy against Reaction Coordinate for the formation of Cheletropic Product (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Isoindene_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.25: HOMO of TS of Cheletropic Path.</title>
<color>white</color>
<size>400</size>
<script>frame 36; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 ISOINDENE ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Isoindene-TS HOMO.png|thumb|Figure 5.3.26: HOMO of TS of Cheletropic Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

===Part 5: Interactive Vibration Animations.===

Figures 5.3.27-5.3.31 show the interactive vibration animations.

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.27: Interactive Vibration Animation of the Endo TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 ENDO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Endo</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton>
<script>measure 14 18; measure 11 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>Endo</target>
</item>
<item>
<script>frame 15; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i334/cm</text>
<target>Endo</target>
</item>
<item>
<script>frame 16; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>63/cm</text>
<target>Endo</target>
</item>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.28: Interactive Vibration Animation of the Exo TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 EXO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Exo</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Exo</target>
</jmolbutton>
<jmolbutton>
<script>measure 14 18; measure 11 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>Exo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Exo</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Exo</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>Exo</target>
</item>
<item>
<script>frame 75; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i352/cm</text>
<target>Exo</target>
</item>
<item>
<script>frame 76; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>66/cm</text>
<target>Exo</target>
</item>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Exo</target>
</jmolbutton>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.29: Interactive Vibration Animation of the Endo Minor-Regioisomer TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 VAR ENDO DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>EndoVar</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>EndoVar</target>
</jmolbutton>
<jmolbutton>
<script>measure 5 17; measure 2 18</script>
<text>TS C-C Equilibrium Distance</text>
<target>EndoVar</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EndoVar</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>EndoVar</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>EndoVar</target>
</item>
<item>
<script>frame 25; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i453/cm</text>
<target>EndoVar</target>
</item>
<item>
<script>frame 26; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>57/cm</text>
<target>EndoVar</target>
</item>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.30: Interactive Vibration Animation of the Exo Minor-Regioisomer TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 VAR DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>ExoVar</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>ExoVar</target>
</jmolbutton>
<jmolbutton>
<script>measure 2 18; measure 5 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>ExoVar</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExoVar</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>ExoVar</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>ExoVar</target>
</item>
<item>
<script>frame 17; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i483/cm</text>
<target>ExoVar</target>
</item>
<item>
<script>frame 18; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>53/cm</text>
<target>ExoVar</target>
</item>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.31: Interactive Vibration Animation of the Cheletropic TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 ISOINDENE ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Cyclohexene</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton>
<script>measure 11 17; measure 14 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>Cyclohexene</target>
</item>
<item>
<script>frame 37; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i487/cm</text>
<target>Cyclohexene</target>
</item>
<item>
<script>frame 38; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>74/cm</text>
<target>Cyclohexene</target>
</item>
</jmolmenu>
</jmol>

Rep:Kh1015TSEx3RD

2018-03-13T22:58:34Z

Kh1015: /* Part 3: Rationalizing the Reaction Profile Parameters. */

==Exercise 3 Results and Discussion.==

'''Note to Reader/Marker:'''
<br>The compartmentalization of the Results and Discussion into 5 parts was based on relevant discussion idea and for convenient navigation during the write-up. Also, the Jmol files in this page could display the relative energies of the MOs but they could not visualize the MOs. In response, the visualized HOMO of each TS was attached next to the Jmol files for viewing purposes.

===Part 1: Parameters from Reaction Profile.===

Referring to Table 5.3.2, calculations at PM6 level showed that only the Diels-Alder minor-regio-isomers were non-spontaneous. The Diels-Alder endo-major-regioisomer (referred to as endo product in Table 5.3.1) was calculated to be the kinetic product (based on lowest activation Gibbs-Free Energy equalled to 83.2 kJ mol<sup>-1</sup>) and an associated rate of reaction of 0.0165 s<sup>-1</sup> at 298.15K. The rate constant was calculated using the formula described under Introduction > Part D. The cheletropic product was calculated to be the thermodynamically favourable product (based on the most negative Δ Gibbs-Free Energy equalled to -155 kJ mol<sup>-1</sup>). This prediction could be verified experimentally by doing a kinetic study and analysis of ratio of Diels-Alder (including the regioisomers) and cheletropic products formed at rtp.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.3.1: Summary of Calculated Gibbs-Free Energy of Species in Diels-Alder and Cheletropic Reactions at 298.15 K and 1 atm (PM6 level).
|-
|rowspan="2"|''' '''
|colspan="12"|'''States'''
|-
|'''5,6-dimethylenecyclohexa-1,3-diene'''
|'''Sulfur Dioxide'''
|'''Endo TS'''
|'''Endo Product'''
|'''Exo TS'''
|'''Exo Product'''
|'''TS of Endo-Minor-Regioisomer'''
|'''Endo-Minor-Regioisomer'''
|'''TS of Exo-Minor-Regioisomer'''
|'''Exo-Minor-Regioisomer'''
|'''Cheletropic TS'''
|'''Cheletropic Product'''
|-
|'''Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
|468
| -313
|238
|57.0
|242
|56.3
|268
|172
|276
|177
|260
| -0.00263
|}

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.3.2: Summary of Calculated Reaction Profile Parameters for Diels-Alder and Cheletropic Reactions at 298.15 K and 1 atm (PM6 level).
|-
|''' '''
|'''Endo-Major-Regioisomer'''
|'''Exo-Major-Regioisomer'''
|'''Endo-Minor-Regioisomer'''
|'''Exo-Minor-Regioisomer'''
|'''Cheletropic'''
|-
|'''Activation Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
|83.2
|87.2
|113
|121
|106
|-
|'''Δ Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
| -97.6
| -98.2
|17.7
|22.2
| -155
|-
|'''Predicted Rate of Reaction (x10<sup>-6</sup> s<sup>-1</sup>)'''
|16,500
|3,280
|0.010
|0.004
|1.67
|}

===Part 2: Comparison of Reaction Profiles on a Standardized Reaction Coordinate.===

Figure 5.3.1 shows the comparison of the Diels-Alder and Cheletropic Reaction Profiles on a Standardized Reaction Coordinate at 298.15 K and 1 atm (PM6 level). In the Standardized Reaction Coordinate, the reactants' coordinates are set to -1, those of TS set to 0 and those of products set to 1. This was done to align the all the reaction states independent of the rate on a common scale such that the relative energetics could be compared between possible reaction paths.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Comparison.png|frame|Figure 5.3.1: Comparison of the Diels-Alder and Cheletropic Reaction Profiles on a Standardized Reaction Coordinate at 298.15 K and 1 atm (PM6 level).]]
|}

===Part 3: Rationalizing the Reaction Profile Parameters.===

Xylylene is an unstable compound because it is a system of 8 π electrons (4n anti-aromatic rule). From the IRC of all the reactions examined (excluding Diels-Alder minor-regio-isomers), it was observed that as xylelene reacted with sulfur dioxide, the 6 membered-ring became ended up with 6 π electrons (4π+2 aromatic rule) in the product. This provided a strong thermodynamic driving force for the reaction with sulfur dioxide to proceed.

For all the reactions examined, there was no identifiable secondary orbital contribution from the Gaussview MO visualizations.

Referring to Figure 5.3.2-5.3.5, the calculated steric interactions were similar for Diels-Alder endo-exo products that react at the same regio-position. Because of similar steric interactions and electronic interactions within each set, the products that reacted at the same position would possess similar activation Gibbs-Free Energy (calculated) as shown in Table 5.3.2. However, when comparing '''between''' the two sets of Diels-Alder regio-isomers, it could be seen that the activation Gibbs-Free Energy for the minor-regio-isomer set was much higher than the other set ({113, 121} against {83.2, 87.2} where each element of the sets is in the form {endo, exo} and reported in kJ mol<sup>-1</sup>). For both sets, the TS formation involved severance of π interactions in the xylylene system. In the major-regio-isomer set, the activation Gibbs-Free Energy was reduced because there was a corresponding formation of favourable aromatic interaction in the 6-membered ring.

Referring to Figure 5.3.2-5.3.3 and 5.3.6, when comparing between the Diels-Alder major regio-isomer set and the cheletropic product, the steric clash in the cheletropic TS was calculated to be higher than those in the Diels-Alder major regio-isomer set. This is reflected in the calculated activation Gibbs-Free Energy of the cheletropic product, 106 kJ mol<sup>-1</sup>, being much higher than those of the endo and exo products, 83.2 and 87.2 <sup>-1</sup> respectively.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Endo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.2: Non Covalent Interactions in the Transition State During Diels-Alder Endo Product Formation.]]
|[[File:KH1015 Exo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.3: Non Covalent Interactions in the Transition State During Diels-Alder Exo Product Formation.]]
|[[File:KH1015 Var Endo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.4: Non Covalent Interactions in the Transition State During Diels-Alder Endo Minor-Regioisomer Formation.]]
| [[File:KH1015 Var Exo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.5: Non Covalent Interactions in the Transition State During Diels-Alder Exo Minor-Regioisomer Formation.]]
| [[File:KH1015 Isoindene-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.6: Non Covalent Interactions in the Transition State During Cheletropic Product Formation.]]
|-
|}

===Part 4: IRC.===
====1. Diels-Alder Products.====
=====1.A. Endo Major-Regio-Isomer.=====
Referring to Figure 5.3.7, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:Kh1015 Endo Diels Alder.gif|frame|left|Figure 5.3.7: IRC for Formation of Diels-Alder Endo Product at 298.15 K and 1 atm (PM6 Level).]]
|| [[File:KH1015 Endo Diels Alder IRC Graph.png|thumb|Figure 5.3.8: IRC Graph of Energy against Reaction Coordinate for the formation of Endo Product at 298.15 K and 1 atm (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_Diels_Alder_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.9: Jmol of TS of Endo Path.</title>
<color>white</color>
<size>400</size>
<script>frame 14; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 ENDO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Endo Diels Alder-TS HOMO Isovalue 0.02 Cube Grid Coarse.png|thumb|Figure 5.3.10: HOMO of the TS of Endo Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

=====1.B. Exo Major-Regio-Isomer.=====
Referring to Figure 5.3.11, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:Kh1015 Exo Diels Alder.gif|frame|left|Figure 5.3.11: IRC for Formation of Diels-Alder Exo Product (PM6 level).]]
|| [[File:KH1015 Exo Diels Alder IRC Graph.png|thumb|Figure 5.3.12: IRC Graph of Energy against Reaction Coordinate for the formation of Exo Product (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_Diels_Alder_IRC_Graph_Gradient.png here]for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.13: HOMO of TS of Exo Path.</title>
<color>white</color>
<size>400</size>
<script>frame 74; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 EXO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Exo Diels Alder-TS HOMO.png|thumb|Figure 5.3.14: HOMO of TS of Exo Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

=====2.A. Endo Minor-Regio-Isomer.=====
Referring to Figure 5.3.15, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Var Endo Diels Alder.gif|frame|left|Figure 5.3.15: IRC for Formation of Endo Minor-Regioisomer.]]
|| [[File:KH1015 Var Endo Diels Alder IRC Graph.png|thumb|Figure 5.3.16: IRC Graph of Energy against Reaction Coordinate for the formation of Endo Minor-Regioisomer (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Var_Endo_Diels_Alder_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.17: HOMO of Endo Minor-Regioisomer Path.</title>
<color>white</color>
<size>400</size>
<script>frame 24; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 VAR ENDO DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Var Endo Diels Alder-TS HOMO.png|thumb|Figure 5.3.18: HOMO of TS of Endo Minor-Regioisomer Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

=====2.B. Exo Minor-Regio-Isomer.=====
Referring to Figure 5.3.19, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Var Exo Diels Alder.gif|frame|left|Figure 5.3.19: IRC for Formation of Exo Minor-Regioisomer.]]
|| [[File:KH1015 Var Exo Diels Alder IRC Graph.png|thumb|Figure 5.3.20: IRC Graph of Energy against Reaction Coordinate for the formation of Exo Minor-Regioisomer (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Var_Exo_Diels_Alder_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.21: HOMO of TS of Exo Minor-Regioisomer Path.</title>
<color>white</color>
<size>400</size>
<script>frame 16; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 VAR DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Var Exo Diels Alder-TS HOMO.png|thumb|Figure 5.3.22: HOMO of TS of Exo Minor-Regioisomer Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

====2. Cheletropic Product.====
Referring to Figure 5.3.23, the IRC calculation at PM6 level showed that the two C-S sigma bonds were formed in a synchronous fashion in a concerted mechanism and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:Kh1015 Isoindene.gif|frame|left|Figure 5.3.23: IRC for Formation of Cheletropic Product.]]
|| [[File:KH1015 Isoindene IRC Graph.png|thumb|Figure 5.3.24: IRC Graph of Energy against Reaction Coordinate for the formation of Cheletropic Product (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Isoindene_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.25: HOMO of TS of Cheletropic Path.</title>
<color>white</color>
<size>400</size>
<script>frame 36; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 ISOINDENE ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Isoindene-TS HOMO.png|thumb|Figure 5.3.26: HOMO of TS of Cheletropic Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

===Part 5: Interactive Vibration Animations.===

Figures 5.3.27-5.3.31 show the interactive vibration animations.

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.27: Interactive Vibration Animation of the Endo TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 ENDO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Endo</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton>
<script>measure 14 18; measure 11 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>Endo</target>
</item>
<item>
<script>frame 15; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i334/cm</text>
<target>Endo</target>
</item>
<item>
<script>frame 16; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>63/cm</text>
<target>Endo</target>
</item>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.28: Interactive Vibration Animation of the Exo TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 EXO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Exo</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Exo</target>
</jmolbutton>
<jmolbutton>
<script>measure 14 18; measure 11 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>Exo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Exo</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Exo</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>Exo</target>
</item>
<item>
<script>frame 75; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i352/cm</text>
<target>Exo</target>
</item>
<item>
<script>frame 76; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>66/cm</text>
<target>Exo</target>
</item>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Exo</target>
</jmolbutton>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.29: Interactive Vibration Animation of the Endo Minor-Regioisomer TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 VAR ENDO DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>EndoVar</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>EndoVar</target>
</jmolbutton>
<jmolbutton>
<script>measure 5 17; measure 2 18</script>
<text>TS C-C Equilibrium Distance</text>
<target>EndoVar</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EndoVar</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>EndoVar</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>EndoVar</target>
</item>
<item>
<script>frame 25; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i453/cm</text>
<target>EndoVar</target>
</item>
<item>
<script>frame 26; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>57/cm</text>
<target>EndoVar</target>
</item>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.30: Interactive Vibration Animation of the Exo Minor-Regioisomer TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 VAR DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>ExoVar</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>ExoVar</target>
</jmolbutton>
<jmolbutton>
<script>measure 2 18; measure 5 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>ExoVar</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExoVar</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>ExoVar</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>ExoVar</target>
</item>
<item>
<script>frame 17; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i483/cm</text>
<target>ExoVar</target>
</item>
<item>
<script>frame 18; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>53/cm</text>
<target>ExoVar</target>
</item>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.31: Interactive Vibration Animation of the Cheletropic TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 ISOINDENE ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Cyclohexene</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton>
<script>measure 11 17; measure 14 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>Cyclohexene</target>
</item>
<item>
<script>frame 37; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i487/cm</text>
<target>Cyclohexene</target>
</item>
<item>
<script>frame 38; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>74/cm</text>
<target>Cyclohexene</target>
</item>
</jmolmenu>
</jmol>

Rep:Kh1015TSEx3RD

2018-03-13T22:56:05Z

Kh1015: /* Part 1: Parameters from Reaction Profile. */

==Exercise 3 Results and Discussion.==

'''Note to Reader/Marker:'''
<br>The compartmentalization of the Results and Discussion into 5 parts was based on relevant discussion idea and for convenient navigation during the write-up. Also, the Jmol files in this page could display the relative energies of the MOs but they could not visualize the MOs. In response, the visualized HOMO of each TS was attached next to the Jmol files for viewing purposes.

===Part 1: Parameters from Reaction Profile.===

Referring to Table 5.3.2, calculations at PM6 level showed that only the Diels-Alder minor-regio-isomers were non-spontaneous. The Diels-Alder endo-major-regioisomer (referred to as endo product in Table 5.3.1) was calculated to be the kinetic product (based on lowest activation Gibbs-Free Energy equalled to 83.2 kJ mol<sup>-1</sup>) and an associated rate of reaction of 0.0165 s<sup>-1</sup> at 298.15K. The rate constant was calculated using the formula described under Introduction > Part D. The cheletropic product was calculated to be the thermodynamically favourable product (based on the most negative Δ Gibbs-Free Energy equalled to -155 kJ mol<sup>-1</sup>). This prediction could be verified experimentally by doing a kinetic study and analysis of ratio of Diels-Alder (including the regioisomers) and cheletropic products formed at rtp.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.3.1: Summary of Calculated Gibbs-Free Energy of Species in Diels-Alder and Cheletropic Reactions at 298.15 K and 1 atm (PM6 level).
|-
|rowspan="2"|''' '''
|colspan="12"|'''States'''
|-
|'''5,6-dimethylenecyclohexa-1,3-diene'''
|'''Sulfur Dioxide'''
|'''Endo TS'''
|'''Endo Product'''
|'''Exo TS'''
|'''Exo Product'''
|'''TS of Endo-Minor-Regioisomer'''
|'''Endo-Minor-Regioisomer'''
|'''TS of Exo-Minor-Regioisomer'''
|'''Exo-Minor-Regioisomer'''
|'''Cheletropic TS'''
|'''Cheletropic Product'''
|-
|'''Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
|468
| -313
|238
|57.0
|242
|56.3
|268
|172
|276
|177
|260
| -0.00263
|}

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.3.2: Summary of Calculated Reaction Profile Parameters for Diels-Alder and Cheletropic Reactions at 298.15 K and 1 atm (PM6 level).
|-
|''' '''
|'''Endo-Major-Regioisomer'''
|'''Exo-Major-Regioisomer'''
|'''Endo-Minor-Regioisomer'''
|'''Exo-Minor-Regioisomer'''
|'''Cheletropic'''
|-
|'''Activation Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
|83.2
|87.2
|113
|121
|106
|-
|'''Δ Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
| -97.6
| -98.2
|17.7
|22.2
| -155
|-
|'''Predicted Rate of Reaction (x10<sup>-6</sup> s<sup>-1</sup>)'''
|16,500
|3,280
|0.010
|0.004
|1.67
|}

===Part 2: Comparison of Reaction Profiles on a Standardized Reaction Coordinate.===

Figure 5.3.1 shows the comparison of the Diels-Alder and Cheletropic Reaction Profiles on a Standardized Reaction Coordinate at 298.15 K and 1 atm (PM6 level). In the Standardized Reaction Coordinate, the reactants' coordinates are set to -1, those of TS set to 0 and those of products set to 1. This was done to align the all the reaction states independent of the rate on a common scale such that the relative energetics could be compared between possible reaction paths.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Comparison.png|frame|Figure 5.3.1: Comparison of the Diels-Alder and Cheletropic Reaction Profiles on a Standardized Reaction Coordinate at 298.15 K and 1 atm (PM6 level).]]
|}

===Part 3: Rationalizing the Reaction Profile Parameters.===

Xylylene is an unstable compound because it is a system of 8 π electrons (4n anti-aromatic rule). From the IRC of all the reactions examined (excluding Diels-Alder minor-regio-isomer, it was observed that as xylelene reacted with sulfur dioxide, the 6 membered-ring became ended up with 6 π electrons (4π+2 aromatic rule) in the product. This provided a strong thermodynamic driving force for the reaction with sulfur dioxide to proceed.

For all the reactions examined, there was no identifiable secondary orbital contribution from the Gaussview MO visualizations.

Referring to Figure 5.3.2-5.3.5, the calculated steric interactions were similar for Diels-Alder endo-exo products that react at the same regio-position. Because of similar steric interactions and electronic interactions within each set, the products that reacted at the same position would possess similar activation Gibbs-Free Energy (calculated) as shown in Table 5.3.2. However, when comparing '''between''' the two sets of Diels-Alder regio-isomers, it could be seen that the activation Gibbs-Free Energy for the minor-regio-isomer set was much higher than the other set ({113, 121} against {83.2, 87.2} where each element of the sets is in the form {endo, exo} and reported in kJ mol<sup>-1</sup>). For both sets, the TS formation involved severance of π interactions in the xylylene system. In the major-regio-isomer set, the activation Gibbs-Free Energy was reduced because there was a corresponding formation of favourable aromatic interaction in the 6-membered ring.

Referring to Figure 5.3.2-5.3.3 and 5.3.6, when comparing between the Diels-Alder major regio-isomer set and the cheletropic product, the steric clash in the cheletropic TS was calculated to be higher than those in the Diels-Alder major regio-isomer set. This is reflected in the calculated activation Gibbs-Free Energy of the cheletropic product, 106 kJ mol<sup>-1</sup>, being much higher than those of the endo and exo products, 83.2 and 87.2 <sup>-1</sup> respectively.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Endo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.2: Non Covalent Interactions in the Transition State During Diels-Alder Endo Product Formation.]]
|[[File:KH1015 Exo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.3: Non Covalent Interactions in the Transition State During Diels-Alder Exo Product Formation.]]
|[[File:KH1015 Var Endo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.4: Non Covalent Interactions in the Transition State During Diels-Alder Endo Minor-Regioisomer Formation.]]
| [[File:KH1015 Var Exo Diels Alder-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.5: Non Covalent Interactions in the Transition State During Diels-Alder Exo Minor-Regioisomer Formation.]]
| [[File:KH1015 Isoindene-Ultrafinegrid Fragment TS den.png|thumb|Figure 5.3.6: Non Covalent Interactions in the Transition State During Cheletropic Product Formation.]]
|-
|}

===Part 4: IRC.===
====1. Diels-Alder Products.====
=====1.A. Endo Major-Regio-Isomer.=====
Referring to Figure 5.3.7, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:Kh1015 Endo Diels Alder.gif|frame|left|Figure 5.3.7: IRC for Formation of Diels-Alder Endo Product at 298.15 K and 1 atm (PM6 Level).]]
|| [[File:KH1015 Endo Diels Alder IRC Graph.png|thumb|Figure 5.3.8: IRC Graph of Energy against Reaction Coordinate for the formation of Endo Product at 298.15 K and 1 atm (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_Diels_Alder_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.9: Jmol of TS of Endo Path.</title>
<color>white</color>
<size>400</size>
<script>frame 14; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 ENDO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Endo Diels Alder-TS HOMO Isovalue 0.02 Cube Grid Coarse.png|thumb|Figure 5.3.10: HOMO of the TS of Endo Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

=====1.B. Exo Major-Regio-Isomer.=====
Referring to Figure 5.3.11, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:Kh1015 Exo Diels Alder.gif|frame|left|Figure 5.3.11: IRC for Formation of Diels-Alder Exo Product (PM6 level).]]
|| [[File:KH1015 Exo Diels Alder IRC Graph.png|thumb|Figure 5.3.12: IRC Graph of Energy against Reaction Coordinate for the formation of Exo Product (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_Diels_Alder_IRC_Graph_Gradient.png here]for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.13: HOMO of TS of Exo Path.</title>
<color>white</color>
<size>400</size>
<script>frame 74; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 EXO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Exo Diels Alder-TS HOMO.png|thumb|Figure 5.3.14: HOMO of TS of Exo Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

=====2.A. Endo Minor-Regio-Isomer.=====
Referring to Figure 5.3.15, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Var Endo Diels Alder.gif|frame|left|Figure 5.3.15: IRC for Formation of Endo Minor-Regioisomer.]]
|| [[File:KH1015 Var Endo Diels Alder IRC Graph.png|thumb|Figure 5.3.16: IRC Graph of Energy against Reaction Coordinate for the formation of Endo Minor-Regioisomer (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Var_Endo_Diels_Alder_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.17: HOMO of Endo Minor-Regioisomer Path.</title>
<color>white</color>
<size>400</size>
<script>frame 24; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 VAR ENDO DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Var Endo Diels Alder-TS HOMO.png|thumb|Figure 5.3.18: HOMO of TS of Endo Minor-Regioisomer Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

=====2.B. Exo Minor-Regio-Isomer.=====
Referring to Figure 5.3.19, the IRC calculation at PM6 level showed that the C-O and C-S sigma bonds were formed in an asynchronous fashion in a concerted mechanism, with C-O bond forming earlier than C-S bond, and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Var Exo Diels Alder.gif|frame|left|Figure 5.3.19: IRC for Formation of Exo Minor-Regioisomer.]]
|| [[File:KH1015 Var Exo Diels Alder IRC Graph.png|thumb|Figure 5.3.20: IRC Graph of Energy against Reaction Coordinate for the formation of Exo Minor-Regioisomer (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Var_Exo_Diels_Alder_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.21: HOMO of TS of Exo Minor-Regioisomer Path.</title>
<color>white</color>
<size>400</size>
<script>frame 16; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 VAR DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Var Exo Diels Alder-TS HOMO.png|thumb|Figure 5.3.22: HOMO of TS of Exo Minor-Regioisomer Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

====2. Cheletropic Product.====
Referring to Figure 5.3.23, the IRC calculation at PM6 level showed that the two C-S sigma bonds were formed in a synchronous fashion in a concerted mechanism and that the TS had been optimized.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:Kh1015 Isoindene.gif|frame|left|Figure 5.3.23: IRC for Formation of Cheletropic Product.]]
|| [[File:KH1015 Isoindene IRC Graph.png|thumb|Figure 5.3.24: IRC Graph of Energy against Reaction Coordinate for the formation of Cheletropic Product (PM6 Method). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Isoindene_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|<jmol>
<jmolApplet>
<title>Figure 5.3.25: HOMO of TS of Cheletropic Path.</title>
<color>white</color>
<size>400</size>
<script>frame 36; mo 29; mo nodots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>KH1015 ISOINDENE ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Isoindene-TS HOMO.png|thumb|Figure 5.3.26: HOMO of TS of Cheletropic Path (Isovalue=0.02; Cube Grid=Coarse; MO 29).]]
|-
|}

===Part 5: Interactive Vibration Animations.===

Figures 5.3.27-5.3.31 show the interactive vibration animations.

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.27: Interactive Vibration Animation of the Endo TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 ENDO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Endo</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton>
<script>measure 14 18; measure 11 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>Endo</target>
</item>
<item>
<script>frame 15; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i334/cm</text>
<target>Endo</target>
</item>
<item>
<script>frame 16; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>63/cm</text>
<target>Endo</target>
</item>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.28: Interactive Vibration Animation of the Exo TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 EXO DIELS ALDER-ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Exo</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Exo</target>
</jmolbutton>
<jmolbutton>
<script>measure 14 18; measure 11 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>Exo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Exo</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Exo</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>Exo</target>
</item>
<item>
<script>frame 75; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i352/cm</text>
<target>Exo</target>
</item>
<item>
<script>frame 76; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>66/cm</text>
<target>Exo</target>
</item>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Exo</target>
</jmolbutton>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.29: Interactive Vibration Animation of the Endo Minor-Regioisomer TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 VAR ENDO DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>EndoVar</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>EndoVar</target>
</jmolbutton>
<jmolbutton>
<script>measure 5 17; measure 2 18</script>
<text>TS C-C Equilibrium Distance</text>
<target>EndoVar</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>EndoVar</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>EndoVar</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>EndoVar</target>
</item>
<item>
<script>frame 25; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i453/cm</text>
<target>EndoVar</target>
</item>
<item>
<script>frame 26; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>57/cm</text>
<target>EndoVar</target>
</item>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.30: Interactive Vibration Animation of the Exo Minor-Regioisomer TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 VAR DIELS ALDER PM6 FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>ExoVar</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>ExoVar</target>
</jmolbutton>
<jmolbutton>
<script>measure 2 18; measure 5 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>ExoVar</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>ExoVar</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>ExoVar</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>ExoVar</target>
</item>
<item>
<script>frame 17; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i483/cm</text>
<target>ExoVar</target>
</item>
<item>
<script>frame 18; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>53/cm</text>
<target>ExoVar</target>
</item>
</jmolmenu>
</jmol>

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.3.31: Interactive Vibration Animation of the Cheletropic TS (PM6 Method).</title> //Initialise the applet
<uploadedFileContents>KH1015 ISOINDENE ULTRAFINEGRID FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Cyclohexene</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton>
<script>measure 11 17; measure 14 17</script>
<text>TS C-C Equilibrium Distance</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>Cyclohexene</target>
</item>
<item>
<script>frame 37; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i487/cm</text>
<target>Cyclohexene</target>
</item>
<item>
<script>frame 38; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>74/cm</text>
<target>Cyclohexene</target>
</item>
</jmolmenu>
</jmol>

Rep:Kh1015TSEx2RD

2018-03-13T22:50:53Z

Kh1015: /* Part 3: Secondary Orbital Interactions and Sterics. */

==Exercise 2 Results and Discussion.==

'''Note to Reader/Marker:'''
<br>The compartmentalization of the Results and Discussion into 4 parts was based on relevant discussion idea and for convenient navigation during the write-up.

===Part 1: Determining the Type of Diels-Alder Reaction.===
Referring to Figure 5.2.5 and 5.2.10, both of the endo and exo reactions were calculated to be inverse-electron-demand Diels Alder reactions at B3YLP-6-31 G(D) level, whereby the electron-poor dienophile (cyclohexadiene) interacted with the electron-rich diene (1,3-dioxole).

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.2.1: Summary of MO Interactions To Form the TS for Both Endo and Exo Reactions (Same Set of Orbitals for Both, Difference is only in the Relative Approach Orientation).
|-
|'''TS Symmetry Label (in Increasing Energy Level)'''
|'''Constituent Fragment Orbital Interactions (Cyclohexadiene - 1,3 Dioxole)'''
|-
|Anti-Symmetrical
|MO22-MO20 (Bonding)
|-
|Symmetrical
|MO23-MO19 (Bonding)
|-
|Symmetrical*
|MO23-MO19 (Anti-Bonding)
|-
|Anti-Symmetrical*
|MO22-MO20 (Anti-Bonding)
|}

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 HOMO of Cyclohexadiene (MO22).png|thumb|150px|Figure 5.2.1: HOMO of Cyclohexadiene (MO 22, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_CYCLOHEXADIENE_B3LYP-6-31G(D).LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Cyclohexadiene_B3LYP-6-31G(d).chk *.chk] output.]]
|[[File:KH1015 LUMO of Cyclohexadiene (MO23).png|thumb|150px|Figure 5.2.2: LUMO of Cyclohexadiene (MO 23, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_1-4-BUTADIENE_S-CIS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_1-4-Butadiene_S-cis.chk *.chk] output.]]
|[[File:KH1015 HOMO of 1,3 Dioxole (MO19).png|thumb|150px|Figure 5.2.3: HOMO of 1,3-Dioxole(MO 19, B3YLP-6-31 G(D) Calculation. Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_DIOXANE_B3LYP-6-31G(D).LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Dioxane_B3LYP-6-31G(d).chk *.chk] output.]]
|[[File:KH1015 LUMO of 1,3 Dioxole (MO20).png|thumb|150px|Figure 5.2.4: LUMO of 1,3-Dioxole(MO 20, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_DIOXANE_B3LYP-6-31G(D).LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Dioxane_B3LYP-6-31G(d).chk *.chk] output.]]
|}

=====Endo Product ((3aR,4S,7R,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====
{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
| colspan="4"|[[File:KH1015 Chemdraw TS Molecular Orbital Endo.png|thumb|center|400px|Figure 5.2.5: Frontier MO diagram for the formation of the Endo TS.]]
|-
|[[File:KH1015 HOMO-1 MO 40.png|thumb|150px|Figure 5.2.6: HOMO-1 of Endo TS (MO 40, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:ENDO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 HOMO MO 41.png|thumb|150px|Figure 5.2.7: HOMO of Endo TS (MO 41, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:ENDO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 LUMO MO 42.png|thumb|150px|Figure 5.2.8: LUMO of Endo TS (MO 42, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:ENDO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 LUMO+1 MO 43.png|thumb|150px|Figure 5.2.9: LUMO+1 of Endo TS (MO 43, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:ENDO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|}

=====Exo Product ((3aS,4R,7S,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
| colspan="4"|[[File:KH1015 Chemdraw TS Molecular Orbital Exo.png|thumb|center|400px|Figure 5.2.10: Frontier MO diagram for the formation of the Exo TS.]]
|-
|[[File:KH1015 HOMO-1 Exo MO40.png|thumb|150px|Figure 5.2.11: HOMO-1 of Exo TS (MO 40, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_EXO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 HOMO Exo MO41.png|thumb|150px|Figure 5.2.12: HOMO of Exo TS (MO 41, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_EXO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 LUMO Exo MO42.png|thumb|150px|Figure 5.2.13: LUMO of Exo TS (MO 42, B3YLP-6-31 G(D) Calculation).Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_EXO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 LUMO+1 Exo MO43.png|thumb|150px|Figure 5.2.14: LUMO+1 of Exo TS (MO 43, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_EXO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|}

===Part 2: Parameters from the Reaction Profile.===

Referring to Table 5.2.2, it can be seen that the Gibbs-Free Energies of the different species are much larger than the Δ Gibbs-Free Energy in Table 5.2.3. From the calculation of this reaction, it can be observed that the activation Gibbs-Free Energy and energy released/absorbed were only a small fraction relative to the total energy of the system (less than 0.01%).

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.2.2: Summary of Calculated Gibbs-Free Energy of Species in Both Endo and Exo Reactions at 298.15 K and 1 atm (B3YLP-6-31 G(D) level).
|-
|rowspan="2"|''' '''
|colspan="6"|'''States'''
|-
|'''Cyclohexadiene'''
|'''1,3-Dioxole'''
|'''Endo TS'''
|'''Endo Product'''
|'''Exo TS'''
|'''Exo Product'''
|-
|'''Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
| -612,593
| -701,189
| -1,313,622
| -1,313,849
| -1,313,614
| -1,313,846
|}

Referring to Table 5.2.3, calculations showed that both reactions were spontaneous and that the endo product was the kinetically (based on activation Gibbs-Free Energy) and thermodynamically favourable product (based on Δ Gibbs-Free Energy). The endo path had a lower activation Gibbs-Free Energy (160 against 168 kJ mol<sup>-1</sup>) with higher rate constant at 298.15 K (5.77 against 0.23 x 10<sup>-16</sup>), and had a more negative Δ Gibbs-Free Energy (-67.4 against -63.8 kJ mol<sup>-1</sup>), which meant that it was more stable than the exo form. The rate constant was calculated using the formula described under Introduction > Part D. This prediction could be verified experimentally by doing a kinetic study and analysis of ratio of endo to exo products formed at rtp.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.2.3: Summary of Calculated Reaction Profile Parameters for Both Endo and Exo Reactions at 298.15 K and 1 atm (B3YLP-6-31 G(D) level).
|-
|''' '''
|'''Activation Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
|'''Δ Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
|'''Predicted Rate of Reaction (x10<sup>-16</sup> s<sup>-1</sup>)'''
|-
|'''Endo-Path'''
|160
| -67.4
|5.77
|-
|'''Exo-Path'''
|168
| -63.8
|0.23
|}

===Part 3: Secondary Orbital Interactions and Sterics.===
Referring to MO 41 for both endo and exo TS in Figure 5.2.15 and 5.2.17, the calculation showed favourable secondary orbital interaction in the endo TS that was not present in the exo TS due to the relative orientation of the two reacting fragments, which would lower the activation energy. Referring to Figure 5.2.16 and 5.2.18, there are significant non-favourable steric interactions (Red being not favourable and Blue being favourable) in the exo TS between the methyl-group and the 6-membered-ring (Green) that was not present in the exo TS due to the relative orientation of the two reacting fragments, which would raise the activation energy. Conversely, both secondary orbital interaction and steric clash accounted for the lower calculated activation energy of the endo path relative to exo path, 160 kJ mol<sup>-1</sup> against 168 kJ mol<sup>-1</sup>.

=====Endo Product ((3aR,4S,7R,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====
{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol>
<jmolApplet>
<title>Figure 5.2.15: HOMO of Endo TS (Default view is MO 41, B3YLP-6-31 G(D) Calculation).</title>
<color>white</color>
<size>400</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>KH1015 ENDO B3YLP-6-31 G(D) FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:Kh1015 Endo B3LYP 631Gd Steric Clash surface.png|thumb|Figure 5.2.16: Non Covalent Interactions in the Endo TS (B3YLP-6-31 G(D) Calculation).]]
|-
|}

=====Exo Product ((3aS,4R,7S,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====
{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol>
<jmolApplet>
<title>Figure 5.2.17: HOMO of Exo TS (Default view is MO 41, B3YLP-6-31 G(D) Calculation).</title>
<color>white</color>
<size>400</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>KH1015 EXO B3YLP-6-31 G(D) FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Exo B3LYP 631Gd Steric Clash surface.png|thumb|Figure 5.2.18: Non Covalent Interactions in the Exo TS (B3YLP-6-31 G(D) Calculation).]]
|-
|}

===Part 4: Interactive Vibration Animation of TS for Both Endo and Exo Path.===
Both Figure 5.2.19 and 5.2.20 contained interactive vibration animation of the Endo and Exo TS (B3YLP-6-31 G(D) level).

=====Endo Product ((3aR,4S,7R,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.2.19: Interactive Vibration Animation of the Endo TS (B3YLP-6-31 G(D) level).</title> //Initialise the applet
<uploadedFileContents>KH1015 ENDO B3YLP-6-31 G(D) FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Endo</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton>
<script>measure 1 2; measure 5 6</script>
<text>TS C-C Equilibrium Distance</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>Endo</target>
</item>
<item>
<script>frame 17; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i521/cm</text>
<target>Endo</target>
</item>
<item>
<script>frame 18; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>66/cm</text>
<target>Endo</target>
</item>
</jmolmenu>
</jmol>

=====Exo Product ((3aS,4R,7S,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.2.20: Interactive Vibration Animation of the Exo TS (B3YLP-6-31 G(D) level).</title> //Initialise the applet
<uploadedFileContents>KH1015 EXO B3YLP-6-31 G(D) FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Cyclohexene</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton>
<script>measure 1 17; measure 4 15</script>
<text>TS C-C Equilibrium Distance</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>===Select Vibration===</text>
<target>Cyclohexene</target>
</item>
<item>
<script>frame 21; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i529/cm</text>
<target>Cyclohexene</target>
</item>
<item>
<script>frame 22; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>99/cm</text>
<target>Cyclohexene</target>
</item>
</jmolmenu>
</jmol>

===Part 5: Interactive Vibration Animations (PM6 Level).===
The IRC calculations at PM6 level showed that the two C-C sigma bonds were formed in a synchronous fashion in a concerted mechanism for both paths and that the TS for both reactions had been optimized.

====Endo Product ((3aR,4S,7R,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).====

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex2 Endo PM6 IRC.gif|frame|left|Figure 5.2.21: IRC for Formation of Diels-Alder Endo Product ((3aR,4S,7R,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole) (PM6 Calculation).]]
|| [[File:KH1015 Endo PM6 IRC Graph.png|thumb|Figure 5.2.22: IRC Graph of Energy against Reaction Coordinate for the formation of Endo Product (PM6 Calculation). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_PM6_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|}

====Exo Product ((3aS,4R,7S,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).====

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:Kh1015 Exo Crosscheck PM6 IRC.gif|frame|left|Figure 5.2.23: IRC for Formation of Diels-Alder Exo Product ((3aS,4R,7S,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole)) (PM6 Calculation).]]
|| [[File:KH1015 Exo PM6 IRC Graph.png|thumb|Figure 5.2.24: IRC Graph of Energy against Reaction Coordinate for the formation of Exo-Product (PM6 Calculation). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_PM6_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|}

Rep:Kh1015TSEx2RD

2018-03-13T22:48:47Z

Kh1015: /* Part 3: Secondary Orbital Interactions and Sterics. */

==Exercise 2 Results and Discussion.==

'''Note to Reader/Marker:'''
<br>The compartmentalization of the Results and Discussion into 4 parts was based on relevant discussion idea and for convenient navigation during the write-up.

===Part 1: Determining the Type of Diels-Alder Reaction.===
Referring to Figure 5.2.5 and 5.2.10, both of the endo and exo reactions were calculated to be inverse-electron-demand Diels Alder reactions at B3YLP-6-31 G(D) level, whereby the electron-poor dienophile (cyclohexadiene) interacted with the electron-rich diene (1,3-dioxole).

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.2.1: Summary of MO Interactions To Form the TS for Both Endo and Exo Reactions (Same Set of Orbitals for Both, Difference is only in the Relative Approach Orientation).
|-
|'''TS Symmetry Label (in Increasing Energy Level)'''
|'''Constituent Fragment Orbital Interactions (Cyclohexadiene - 1,3 Dioxole)'''
|-
|Anti-Symmetrical
|MO22-MO20 (Bonding)
|-
|Symmetrical
|MO23-MO19 (Bonding)
|-
|Symmetrical*
|MO23-MO19 (Anti-Bonding)
|-
|Anti-Symmetrical*
|MO22-MO20 (Anti-Bonding)
|}

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 HOMO of Cyclohexadiene (MO22).png|thumb|150px|Figure 5.2.1: HOMO of Cyclohexadiene (MO 22, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_CYCLOHEXADIENE_B3LYP-6-31G(D).LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Cyclohexadiene_B3LYP-6-31G(d).chk *.chk] output.]]
|[[File:KH1015 LUMO of Cyclohexadiene (MO23).png|thumb|150px|Figure 5.2.2: LUMO of Cyclohexadiene (MO 23, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_1-4-BUTADIENE_S-CIS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_1-4-Butadiene_S-cis.chk *.chk] output.]]
|[[File:KH1015 HOMO of 1,3 Dioxole (MO19).png|thumb|150px|Figure 5.2.3: HOMO of 1,3-Dioxole(MO 19, B3YLP-6-31 G(D) Calculation. Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_DIOXANE_B3LYP-6-31G(D).LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Dioxane_B3LYP-6-31G(d).chk *.chk] output.]]
|[[File:KH1015 LUMO of 1,3 Dioxole (MO20).png|thumb|150px|Figure 5.2.4: LUMO of 1,3-Dioxole(MO 20, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_DIOXANE_B3LYP-6-31G(D).LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Dioxane_B3LYP-6-31G(d).chk *.chk] output.]]
|}

=====Endo Product ((3aR,4S,7R,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====
{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
| colspan="4"|[[File:KH1015 Chemdraw TS Molecular Orbital Endo.png|thumb|center|400px|Figure 5.2.5: Frontier MO diagram for the formation of the Endo TS.]]
|-
|[[File:KH1015 HOMO-1 MO 40.png|thumb|150px|Figure 5.2.6: HOMO-1 of Endo TS (MO 40, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:ENDO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 HOMO MO 41.png|thumb|150px|Figure 5.2.7: HOMO of Endo TS (MO 41, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:ENDO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 LUMO MO 42.png|thumb|150px|Figure 5.2.8: LUMO of Endo TS (MO 42, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:ENDO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 LUMO+1 MO 43.png|thumb|150px|Figure 5.2.9: LUMO+1 of Endo TS (MO 43, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:ENDO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|}

=====Exo Product ((3aS,4R,7S,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
| colspan="4"|[[File:KH1015 Chemdraw TS Molecular Orbital Exo.png|thumb|center|400px|Figure 5.2.10: Frontier MO diagram for the formation of the Exo TS.]]
|-
|[[File:KH1015 HOMO-1 Exo MO40.png|thumb|150px|Figure 5.2.11: HOMO-1 of Exo TS (MO 40, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_EXO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 HOMO Exo MO41.png|thumb|150px|Figure 5.2.12: HOMO of Exo TS (MO 41, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_EXO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 LUMO Exo MO42.png|thumb|150px|Figure 5.2.13: LUMO of Exo TS (MO 42, B3YLP-6-31 G(D) Calculation).Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_EXO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 LUMO+1 Exo MO43.png|thumb|150px|Figure 5.2.14: LUMO+1 of Exo TS (MO 43, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_EXO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|}

===Part 2: Parameters from the Reaction Profile.===

Referring to Table 5.2.2, it can be seen that the Gibbs-Free Energies of the different species are much larger than the Δ Gibbs-Free Energy in Table 5.2.3. From the calculation of this reaction, it can be observed that the activation Gibbs-Free Energy and energy released/absorbed were only a small fraction relative to the total energy of the system (less than 0.01%).

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.2.2: Summary of Calculated Gibbs-Free Energy of Species in Both Endo and Exo Reactions at 298.15 K and 1 atm (B3YLP-6-31 G(D) level).
|-
|rowspan="2"|''' '''
|colspan="6"|'''States'''
|-
|'''Cyclohexadiene'''
|'''1,3-Dioxole'''
|'''Endo TS'''
|'''Endo Product'''
|'''Exo TS'''
|'''Exo Product'''
|-
|'''Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
| -612,593
| -701,189
| -1,313,622
| -1,313,849
| -1,313,614
| -1,313,846
|}

Referring to Table 5.2.3, calculations showed that both reactions were spontaneous and that the endo product was the kinetically (based on activation Gibbs-Free Energy) and thermodynamically favourable product (based on Δ Gibbs-Free Energy). The endo path had a lower activation Gibbs-Free Energy (160 against 168 kJ mol<sup>-1</sup>) with higher rate constant at 298.15 K (5.77 against 0.23 x 10<sup>-16</sup>), and had a more negative Δ Gibbs-Free Energy (-67.4 against -63.8 kJ mol<sup>-1</sup>), which meant that it was more stable than the exo form. The rate constant was calculated using the formula described under Introduction > Part D. This prediction could be verified experimentally by doing a kinetic study and analysis of ratio of endo to exo products formed at rtp.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.2.3: Summary of Calculated Reaction Profile Parameters for Both Endo and Exo Reactions at 298.15 K and 1 atm (B3YLP-6-31 G(D) level).
|-
|''' '''
|'''Activation Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
|'''Δ Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
|'''Predicted Rate of Reaction (x10<sup>-16</sup> s<sup>-1</sup>)'''
|-
|'''Endo-Path'''
|160
| -67.4
|5.77
|-
|'''Exo-Path'''
|168
| -63.8
|0.23
|}

===Part 3: Secondary Orbital Interactions and Sterics.===
Referring to MO 41 for both endo and exo TS in Figure 5.2.15 and 5.2.17, the calculation showed favourable secondary orbital interaction in the endo TS that was not present in the exo TS due to the relative orientation of the two reacting fragments, which would lower the activation energy. Referring to Figure 5.2.16 and 5.2.18, there are significant non-favourable steric interactions (Red being not favourable and Blue being favourable) in the exo TS that was not present in the exo TS due to the relative orientation of the two reacting fragments, which would raise the activation energy. Conversely, both secondary orbital interaction and steric clash accounted for the lower calculated activation energy of the endo path relative to exo path, 160 kJ mol<sup>-1</sup> against 168 kJ mol<sup>-1</sup>.

=====Endo Product ((3aR,4S,7R,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====
{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol>
<jmolApplet>
<title>Figure 5.2.15: HOMO of Endo TS (Default view is MO 41, B3YLP-6-31 G(D) Calculation).</title>
<color>white</color>
<size>400</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>KH1015 ENDO B3YLP-6-31 G(D) FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:Kh1015 Endo B3LYP 631Gd Steric Clash surface.png|thumb|Figure 5.2.16: Non Covalent Interactions in the Endo TS (B3YLP-6-31 G(D) Calculation).]]
|-
|}

=====Exo Product ((3aS,4R,7S,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====
{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol>
<jmolApplet>
<title>Figure 5.2.17: HOMO of Exo TS (Default view is MO 41, B3YLP-6-31 G(D) Calculation).</title>
<color>white</color>
<size>400</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>KH1015 EXO B3YLP-6-31 G(D) FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Exo B3LYP 631Gd Steric Clash surface.png|thumb|Figure 5.2.18: Non Covalent Interactions in the Exo TS (B3YLP-6-31 G(D) Calculation).]]
|-
|}

===Part 4: Interactive Vibration Animation of TS for Both Endo and Exo Path.===
Both Figure 5.2.19 and 5.2.20 contained interactive vibration animation of the Endo and Exo TS (B3YLP-6-31 G(D) level).

=====Endo Product ((3aR,4S,7R,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.2.19: Interactive Vibration Animation of the Endo TS (B3YLP-6-31 G(D) level).</title> //Initialise the applet
<uploadedFileContents>KH1015 ENDO B3YLP-6-31 G(D) FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Endo</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton>
<script>measure 1 2; measure 5 6</script>
<text>TS C-C Equilibrium Distance</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>Endo</target>
</item>
<item>
<script>frame 17; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i521/cm</text>
<target>Endo</target>
</item>
<item>
<script>frame 18; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>66/cm</text>
<target>Endo</target>
</item>
</jmolmenu>
</jmol>

=====Exo Product ((3aS,4R,7S,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.2.20: Interactive Vibration Animation of the Exo TS (B3YLP-6-31 G(D) level).</title> //Initialise the applet
<uploadedFileContents>KH1015 EXO B3YLP-6-31 G(D) FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Cyclohexene</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton>
<script>measure 1 17; measure 4 15</script>
<text>TS C-C Equilibrium Distance</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>===Select Vibration===</text>
<target>Cyclohexene</target>
</item>
<item>
<script>frame 21; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i529/cm</text>
<target>Cyclohexene</target>
</item>
<item>
<script>frame 22; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>99/cm</text>
<target>Cyclohexene</target>
</item>
</jmolmenu>
</jmol>

===Part 5: Interactive Vibration Animations (PM6 Level).===
The IRC calculations at PM6 level showed that the two C-C sigma bonds were formed in a synchronous fashion in a concerted mechanism for both paths and that the TS for both reactions had been optimized.

====Endo Product ((3aR,4S,7R,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).====

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex2 Endo PM6 IRC.gif|frame|left|Figure 5.2.21: IRC for Formation of Diels-Alder Endo Product ((3aR,4S,7R,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole) (PM6 Calculation).]]
|| [[File:KH1015 Endo PM6 IRC Graph.png|thumb|Figure 5.2.22: IRC Graph of Energy against Reaction Coordinate for the formation of Endo Product (PM6 Calculation). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_PM6_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|}

====Exo Product ((3aS,4R,7S,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).====

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:Kh1015 Exo Crosscheck PM6 IRC.gif|frame|left|Figure 5.2.23: IRC for Formation of Diels-Alder Exo Product ((3aS,4R,7S,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole)) (PM6 Calculation).]]
|| [[File:KH1015 Exo PM6 IRC Graph.png|thumb|Figure 5.2.24: IRC Graph of Energy against Reaction Coordinate for the formation of Exo-Product (PM6 Calculation). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_PM6_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|}

Rep:Kh1015TSEx2RD

2018-03-13T22:47:29Z

Kh1015: /* Part 2: Parameters from the Reaction Profile. */

==Exercise 2 Results and Discussion.==

'''Note to Reader/Marker:'''
<br>The compartmentalization of the Results and Discussion into 4 parts was based on relevant discussion idea and for convenient navigation during the write-up.

===Part 1: Determining the Type of Diels-Alder Reaction.===
Referring to Figure 5.2.5 and 5.2.10, both of the endo and exo reactions were calculated to be inverse-electron-demand Diels Alder reactions at B3YLP-6-31 G(D) level, whereby the electron-poor dienophile (cyclohexadiene) interacted with the electron-rich diene (1,3-dioxole).

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.2.1: Summary of MO Interactions To Form the TS for Both Endo and Exo Reactions (Same Set of Orbitals for Both, Difference is only in the Relative Approach Orientation).
|-
|'''TS Symmetry Label (in Increasing Energy Level)'''
|'''Constituent Fragment Orbital Interactions (Cyclohexadiene - 1,3 Dioxole)'''
|-
|Anti-Symmetrical
|MO22-MO20 (Bonding)
|-
|Symmetrical
|MO23-MO19 (Bonding)
|-
|Symmetrical*
|MO23-MO19 (Anti-Bonding)
|-
|Anti-Symmetrical*
|MO22-MO20 (Anti-Bonding)
|}

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 HOMO of Cyclohexadiene (MO22).png|thumb|150px|Figure 5.2.1: HOMO of Cyclohexadiene (MO 22, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_CYCLOHEXADIENE_B3LYP-6-31G(D).LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Cyclohexadiene_B3LYP-6-31G(d).chk *.chk] output.]]
|[[File:KH1015 LUMO of Cyclohexadiene (MO23).png|thumb|150px|Figure 5.2.2: LUMO of Cyclohexadiene (MO 23, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_1-4-BUTADIENE_S-CIS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_1-4-Butadiene_S-cis.chk *.chk] output.]]
|[[File:KH1015 HOMO of 1,3 Dioxole (MO19).png|thumb|150px|Figure 5.2.3: HOMO of 1,3-Dioxole(MO 19, B3YLP-6-31 G(D) Calculation. Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_DIOXANE_B3LYP-6-31G(D).LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Dioxane_B3LYP-6-31G(d).chk *.chk] output.]]
|[[File:KH1015 LUMO of 1,3 Dioxole (MO20).png|thumb|150px|Figure 5.2.4: LUMO of 1,3-Dioxole(MO 20, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_DIOXANE_B3LYP-6-31G(D).LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Dioxane_B3LYP-6-31G(d).chk *.chk] output.]]
|}

=====Endo Product ((3aR,4S,7R,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====
{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
| colspan="4"|[[File:KH1015 Chemdraw TS Molecular Orbital Endo.png|thumb|center|400px|Figure 5.2.5: Frontier MO diagram for the formation of the Endo TS.]]
|-
|[[File:KH1015 HOMO-1 MO 40.png|thumb|150px|Figure 5.2.6: HOMO-1 of Endo TS (MO 40, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:ENDO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 HOMO MO 41.png|thumb|150px|Figure 5.2.7: HOMO of Endo TS (MO 41, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:ENDO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 LUMO MO 42.png|thumb|150px|Figure 5.2.8: LUMO of Endo TS (MO 42, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:ENDO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 LUMO+1 MO 43.png|thumb|150px|Figure 5.2.9: LUMO+1 of Endo TS (MO 43, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:ENDO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|}

=====Exo Product ((3aS,4R,7S,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
| colspan="4"|[[File:KH1015 Chemdraw TS Molecular Orbital Exo.png|thumb|center|400px|Figure 5.2.10: Frontier MO diagram for the formation of the Exo TS.]]
|-
|[[File:KH1015 HOMO-1 Exo MO40.png|thumb|150px|Figure 5.2.11: HOMO-1 of Exo TS (MO 40, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_EXO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 HOMO Exo MO41.png|thumb|150px|Figure 5.2.12: HOMO of Exo TS (MO 41, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_EXO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 LUMO Exo MO42.png|thumb|150px|Figure 5.2.13: LUMO of Exo TS (MO 42, B3YLP-6-31 G(D) Calculation).Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_EXO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 LUMO+1 Exo MO43.png|thumb|150px|Figure 5.2.14: LUMO+1 of Exo TS (MO 43, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_EXO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|}

===Part 2: Parameters from the Reaction Profile.===

Referring to Table 5.2.2, it can be seen that the Gibbs-Free Energies of the different species are much larger than the Δ Gibbs-Free Energy in Table 5.2.3. From the calculation of this reaction, it can be observed that the activation Gibbs-Free Energy and energy released/absorbed were only a small fraction relative to the total energy of the system (less than 0.01%).

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.2.2: Summary of Calculated Gibbs-Free Energy of Species in Both Endo and Exo Reactions at 298.15 K and 1 atm (B3YLP-6-31 G(D) level).
|-
|rowspan="2"|''' '''
|colspan="6"|'''States'''
|-
|'''Cyclohexadiene'''
|'''1,3-Dioxole'''
|'''Endo TS'''
|'''Endo Product'''
|'''Exo TS'''
|'''Exo Product'''
|-
|'''Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
| -612,593
| -701,189
| -1,313,622
| -1,313,849
| -1,313,614
| -1,313,846
|}

Referring to Table 5.2.3, calculations showed that both reactions were spontaneous and that the endo product was the kinetically (based on activation Gibbs-Free Energy) and thermodynamically favourable product (based on Δ Gibbs-Free Energy). The endo path had a lower activation Gibbs-Free Energy (160 against 168 kJ mol<sup>-1</sup>) with higher rate constant at 298.15 K (5.77 against 0.23 x 10<sup>-16</sup>), and had a more negative Δ Gibbs-Free Energy (-67.4 against -63.8 kJ mol<sup>-1</sup>), which meant that it was more stable than the exo form. The rate constant was calculated using the formula described under Introduction > Part D. This prediction could be verified experimentally by doing a kinetic study and analysis of ratio of endo to exo products formed at rtp.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.2.3: Summary of Calculated Reaction Profile Parameters for Both Endo and Exo Reactions at 298.15 K and 1 atm (B3YLP-6-31 G(D) level).
|-
|''' '''
|'''Activation Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
|'''Δ Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
|'''Predicted Rate of Reaction (x10<sup>-16</sup> s<sup>-1</sup>)'''
|-
|'''Endo-Path'''
|160
| -67.4
|5.77
|-
|'''Exo-Path'''
|168
| -63.8
|0.23
|}

===Part 3: Secondary Orbital Interactions and Sterics.===
Referring to MO 41 for both endo and exo TS in Figure 5.2.15 and 5.2.17, the calculation showed favourable secondary orbital interaction in the endo TS that was not present in the exo TS due to the relative orientation of the two reacting fragments, which would lower the activation energy. Referring to Figure 5.2.16 and 5.2.18, there are significant non-favourable steric interactions in the exo TS that was not present in the exo TS due to the relative orientation of the two reacting fragments, which would raise the activation energy. Conversely, both secondary orbital interaction and steric clash accounted for the lower calculated activation energy of the endo path relative to exo path, 160 kJ mol<sup>-1</sup> against 168 kJ mol<sup>-1</sup>.

=====Endo Product ((3aR,4S,7R,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====
{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol>
<jmolApplet>
<title>Figure 5.2.15: HOMO of Endo TS (Default view is MO 41, B3YLP-6-31 G(D) Calculation).</title>
<color>white</color>
<size>400</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>KH1015 ENDO B3YLP-6-31 G(D) FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:Kh1015 Endo B3LYP 631Gd Steric Clash surface.png|thumb|Figure 5.2.16: Non Covalent Interactions in the Endo TS (B3YLP-6-31 G(D) Calculation).]]
|-
|}

=====Exo Product ((3aS,4R,7S,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====
{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol>
<jmolApplet>
<title>Figure 5.2.17: HOMO of Exo TS (Default view is MO 41, B3YLP-6-31 G(D) Calculation).</title>
<color>white</color>
<size>400</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>KH1015 EXO B3YLP-6-31 G(D) FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Exo B3LYP 631Gd Steric Clash surface.png|thumb|Figure 5.2.18: Non Covalent Interactions in the Exo TS (B3YLP-6-31 G(D) Calculation).]]
|-
|}

===Part 4: Interactive Vibration Animation of TS for Both Endo and Exo Path.===
Both Figure 5.2.19 and 5.2.20 contained interactive vibration animation of the Endo and Exo TS (B3YLP-6-31 G(D) level).

=====Endo Product ((3aR,4S,7R,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.2.19: Interactive Vibration Animation of the Endo TS (B3YLP-6-31 G(D) level).</title> //Initialise the applet
<uploadedFileContents>KH1015 ENDO B3YLP-6-31 G(D) FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Endo</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton>
<script>measure 1 2; measure 5 6</script>
<text>TS C-C Equilibrium Distance</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>Endo</target>
</item>
<item>
<script>frame 17; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i521/cm</text>
<target>Endo</target>
</item>
<item>
<script>frame 18; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>66/cm</text>
<target>Endo</target>
</item>
</jmolmenu>
</jmol>

=====Exo Product ((3aS,4R,7S,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.2.20: Interactive Vibration Animation of the Exo TS (B3YLP-6-31 G(D) level).</title> //Initialise the applet
<uploadedFileContents>KH1015 EXO B3YLP-6-31 G(D) FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Cyclohexene</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton>
<script>measure 1 17; measure 4 15</script>
<text>TS C-C Equilibrium Distance</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>===Select Vibration===</text>
<target>Cyclohexene</target>
</item>
<item>
<script>frame 21; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i529/cm</text>
<target>Cyclohexene</target>
</item>
<item>
<script>frame 22; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>99/cm</text>
<target>Cyclohexene</target>
</item>
</jmolmenu>
</jmol>

===Part 5: Interactive Vibration Animations (PM6 Level).===
The IRC calculations at PM6 level showed that the two C-C sigma bonds were formed in a synchronous fashion in a concerted mechanism for both paths and that the TS for both reactions had been optimized.

====Endo Product ((3aR,4S,7R,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).====

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex2 Endo PM6 IRC.gif|frame|left|Figure 5.2.21: IRC for Formation of Diels-Alder Endo Product ((3aR,4S,7R,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole) (PM6 Calculation).]]
|| [[File:KH1015 Endo PM6 IRC Graph.png|thumb|Figure 5.2.22: IRC Graph of Energy against Reaction Coordinate for the formation of Endo Product (PM6 Calculation). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_PM6_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|}

====Exo Product ((3aS,4R,7S,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).====

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:Kh1015 Exo Crosscheck PM6 IRC.gif|frame|left|Figure 5.2.23: IRC for Formation of Diels-Alder Exo Product ((3aS,4R,7S,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole)) (PM6 Calculation).]]
|| [[File:KH1015 Exo PM6 IRC Graph.png|thumb|Figure 5.2.24: IRC Graph of Energy against Reaction Coordinate for the formation of Exo-Product (PM6 Calculation). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_PM6_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|}

Rep:Kh1015TSEx2RD

2018-03-13T22:45:10Z

Kh1015: /* Part 1: Determining the Type of Diels-Alder Reaction. */

==Exercise 2 Results and Discussion.==

'''Note to Reader/Marker:'''
<br>The compartmentalization of the Results and Discussion into 4 parts was based on relevant discussion idea and for convenient navigation during the write-up.

===Part 1: Determining the Type of Diels-Alder Reaction.===
Referring to Figure 5.2.5 and 5.2.10, both of the endo and exo reactions were calculated to be inverse-electron-demand Diels Alder reactions at B3YLP-6-31 G(D) level, whereby the electron-poor dienophile (cyclohexadiene) interacted with the electron-rich diene (1,3-dioxole).

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.2.1: Summary of MO Interactions To Form the TS for Both Endo and Exo Reactions (Same Set of Orbitals for Both, Difference is only in the Relative Approach Orientation).
|-
|'''TS Symmetry Label (in Increasing Energy Level)'''
|'''Constituent Fragment Orbital Interactions (Cyclohexadiene - 1,3 Dioxole)'''
|-
|Anti-Symmetrical
|MO22-MO20 (Bonding)
|-
|Symmetrical
|MO23-MO19 (Bonding)
|-
|Symmetrical*
|MO23-MO19 (Anti-Bonding)
|-
|Anti-Symmetrical*
|MO22-MO20 (Anti-Bonding)
|}

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 HOMO of Cyclohexadiene (MO22).png|thumb|150px|Figure 5.2.1: HOMO of Cyclohexadiene (MO 22, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_CYCLOHEXADIENE_B3LYP-6-31G(D).LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Cyclohexadiene_B3LYP-6-31G(d).chk *.chk] output.]]
|[[File:KH1015 LUMO of Cyclohexadiene (MO23).png|thumb|150px|Figure 5.2.2: LUMO of Cyclohexadiene (MO 23, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_1-4-BUTADIENE_S-CIS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_1-4-Butadiene_S-cis.chk *.chk] output.]]
|[[File:KH1015 HOMO of 1,3 Dioxole (MO19).png|thumb|150px|Figure 5.2.3: HOMO of 1,3-Dioxole(MO 19, B3YLP-6-31 G(D) Calculation. Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_DIOXANE_B3LYP-6-31G(D).LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Dioxane_B3LYP-6-31G(d).chk *.chk] output.]]
|[[File:KH1015 LUMO of 1,3 Dioxole (MO20).png|thumb|150px|Figure 5.2.4: LUMO of 1,3-Dioxole(MO 20, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_DIOXANE_B3LYP-6-31G(D).LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Dioxane_B3LYP-6-31G(d).chk *.chk] output.]]
|}

=====Endo Product ((3aR,4S,7R,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====
{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
| colspan="4"|[[File:KH1015 Chemdraw TS Molecular Orbital Endo.png|thumb|center|400px|Figure 5.2.5: Frontier MO diagram for the formation of the Endo TS.]]
|-
|[[File:KH1015 HOMO-1 MO 40.png|thumb|150px|Figure 5.2.6: HOMO-1 of Endo TS (MO 40, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:ENDO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 HOMO MO 41.png|thumb|150px|Figure 5.2.7: HOMO of Endo TS (MO 41, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:ENDO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 LUMO MO 42.png|thumb|150px|Figure 5.2.8: LUMO of Endo TS (MO 42, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:ENDO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 LUMO+1 MO 43.png|thumb|150px|Figure 5.2.9: LUMO+1 of Endo TS (MO 43, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:ENDO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|}

=====Exo Product ((3aS,4R,7S,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
| colspan="4"|[[File:KH1015 Chemdraw TS Molecular Orbital Exo.png|thumb|center|400px|Figure 5.2.10: Frontier MO diagram for the formation of the Exo TS.]]
|-
|[[File:KH1015 HOMO-1 Exo MO40.png|thumb|150px|Figure 5.2.11: HOMO-1 of Exo TS (MO 40, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_EXO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 HOMO Exo MO41.png|thumb|150px|Figure 5.2.12: HOMO of Exo TS (MO 41, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_EXO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 LUMO Exo MO42.png|thumb|150px|Figure 5.2.13: LUMO of Exo TS (MO 42, B3YLP-6-31 G(D) Calculation).Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_EXO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|[[File:KH1015 LUMO+1 Exo MO43.png|thumb|150px|Figure 5.2.14: LUMO+1 of Exo TS (MO 43, B3YLP-6-31 G(D) Calculation). Click for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_EXO_B3YLP-6-31_G(D)_FRAGMENT_TS.LOG *.log] output and for [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_B3YLP-6-31_G(d)_Fragment_TS.chk *.chk] output.]]
|}

===Part 2: Parameters from the Reaction Profile.===

Referring to Table 5.2.2, it can be seen that the Gibbs-Free Energies of the different species are much larger than the Δ Gibbs-Free Energy in Table 5.2.3. From the calculation of this reaction, it can be observed that the activation Gibbs-Free Energy and energy released/absorbed were only a small fraction relative to the total energy of the system (less than 0.01%).

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.2.2: Summary of Calculated Gibbs-Free Energy of Species in Both Endo and Exo Reactions at 298.15 K and 1 atm (B3YLP-6-31 G(D) level).
|-
|rowspan="2"|''' '''
|colspan="6"|'''States'''
|-
|'''Cyclohexadiene'''
|'''1,3-Dioxole'''
|'''Endo TS'''
|'''Endo Product'''
|'''Exo TS'''
|'''Exo Product'''
|-
|'''Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
| -612,593
| -701,189
| -1,313,622
| -1,313,849
| -1,313,614
| -1,313,846
|}

Referring to Table 5.2.3, calculations showed that both reactions were spontaneous and that the endo product was the kinetically (based on activation Gibbs-Free Energy) and thermodynamically favourable product (based on Δ Gibbs-Free Energy). The endo path had a lower activation Gibbs-Free Energy (160 against 168 kJ mol<sup>-1</sup>) with higher rate constant at 298.15 K (5.77 against 0.23 x 10<sup>-16</sup>), and had a more negative Δ Gibbs-Free Energy (-67.4 against -63.8 kJ mol<sup>-1</sup>), which meant that it was more stable. The rate constant was calculated using the formula described under Introduction > Part D. This prediction could be verified experimentally by doing a kinetic study and analysis of ratio of endo to exo products formed at rtp.

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5.2.3: Summary of Calculated Reaction Profile Parameters for Both Endo and Exo Reactions at 298.15 K and 1 atm (B3YLP-6-31 G(D) level).
|-
|''' '''
|'''Activation Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
|'''Δ Gibbs-Free Energy (kJ mol<sup>-1</sup>)'''
|'''Predicted Rate of Reaction (x10<sup>-16</sup> s<sup>-1</sup>)'''
|-
|'''Endo-Path'''
|160
| -67.4
|5.77
|-
|'''Exo-Path'''
|168
| -63.8
|0.23
|}

===Part 3: Secondary Orbital Interactions and Sterics.===
Referring to MO 41 for both endo and exo TS in Figure 5.2.15 and 5.2.17, the calculation showed favourable secondary orbital interaction in the endo TS that was not present in the exo TS due to the relative orientation of the two reacting fragments, which would lower the activation energy. Referring to Figure 5.2.16 and 5.2.18, there are significant non-favourable steric interactions in the exo TS that was not present in the exo TS due to the relative orientation of the two reacting fragments, which would raise the activation energy. Conversely, both secondary orbital interaction and steric clash accounted for the lower calculated activation energy of the endo path relative to exo path, 160 kJ mol<sup>-1</sup> against 168 kJ mol<sup>-1</sup>.

=====Endo Product ((3aR,4S,7R,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====
{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol>
<jmolApplet>
<title>Figure 5.2.15: HOMO of Endo TS (Default view is MO 41, B3YLP-6-31 G(D) Calculation).</title>
<color>white</color>
<size>400</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>KH1015 ENDO B3YLP-6-31 G(D) FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:Kh1015 Endo B3LYP 631Gd Steric Clash surface.png|thumb|Figure 5.2.16: Non Covalent Interactions in the Endo TS (B3YLP-6-31 G(D) Calculation).]]
|-
|}

=====Exo Product ((3aS,4R,7S,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====
{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol>
<jmolApplet>
<title>Figure 5.2.17: HOMO of Exo TS (Default view is MO 41, B3YLP-6-31 G(D) Calculation).</title>
<color>white</color>
<size>400</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>KH1015 EXO B3YLP-6-31 G(D) FRAGMENT TS MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|| [[File:KH1015 Exo B3LYP 631Gd Steric Clash surface.png|thumb|Figure 5.2.18: Non Covalent Interactions in the Exo TS (B3YLP-6-31 G(D) Calculation).]]
|-
|}

===Part 4: Interactive Vibration Animation of TS for Both Endo and Exo Path.===
Both Figure 5.2.19 and 5.2.20 contained interactive vibration animation of the Endo and Exo TS (B3YLP-6-31 G(D) level).

=====Endo Product ((3aR,4S,7R,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.2.19: Interactive Vibration Animation of the Endo TS (B3YLP-6-31 G(D) level).</title> //Initialise the applet
<uploadedFileContents>KH1015 ENDO B3YLP-6-31 G(D) FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Endo</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton>
<script>measure 1 2; measure 5 6</script>
<text>TS C-C Equilibrium Distance</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Endo</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>=Select Vibration=</text>
<target>Endo</target>
</item>
<item>
<script>frame 17; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i521/cm</text>
<target>Endo</target>
</item>
<item>
<script>frame 18; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>66/cm</text>
<target>Endo</target>
</item>
</jmolmenu>
</jmol>

=====Exo Product ((3aS,4R,7S,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).=====

<jmol> //Group all the HTML within "jmol"
<jmolApplet>
<title>Figure 5.2.20: Interactive Vibration Animation of the Exo TS (B3YLP-6-31 G(D) level).</title> //Initialise the applet
<uploadedFileContents>KH1015 EXO B3YLP-6-31 G(D) FRAGMENT TS MO.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 15; rotate x -20; frank off</script> //Set the variables (vibrating and spinning) as the applet initialises. Also switched off the frank (JSmol that normally appears on the bottom right)
<name>Cyclohexene</name> //The name of the applet must be set. This is the name that the controls refer to (the target)
</jmolApplet>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton>
<script>measure 1 17; measure 4 15</script>
<text>TS C-C Equilibrium Distance</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>Cyclohexene</target>
</jmolbutton>
<jmolbutton> //Adding a jmol button, which executes code on the target
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script> //Using IF functions to make a toggle. If it's not vibrating, set vibration period to 2 and change "vibrating" variable to 1, else switch off vibration and change "vibrating" to 0
<text>Vibrate</text>
<target>Endo</target>
</jmolbutton>
<jmolmenu> //The dropdown menu. Each item has to be declared individually and can execute script
<item>
<script>vibrating=0; vibration off</script>
<text>===Select Vibration===</text>
<target>Cyclohexene</target>
</item>
<item>
<script>frame 21; if(vibrating==0) vibration off; else; vibration 2; endif</script> //Adding vibration code as a safety net. It might not be necessary but it ensures the applet behaves properly
<text>i529/cm</text>
<target>Cyclohexene</target>
</item>
<item>
<script>frame 22; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>99/cm</text>
<target>Cyclohexene</target>
</item>
</jmolmenu>
</jmol>

===Part 5: Interactive Vibration Animations (PM6 Level).===
The IRC calculations at PM6 level showed that the two C-C sigma bonds were formed in a synchronous fashion in a concerted mechanism for both paths and that the TS for both reactions had been optimized.

====Endo Product ((3aR,4S,7R,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).====

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:KH1015 Ex2 Endo PM6 IRC.gif|frame|left|Figure 5.2.21: IRC for Formation of Diels-Alder Endo Product ((3aR,4S,7R,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole) (PM6 Calculation).]]
|| [[File:KH1015 Endo PM6 IRC Graph.png|thumb|Figure 5.2.22: IRC Graph of Energy against Reaction Coordinate for the formation of Endo Product (PM6 Calculation). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Endo_PM6_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
|-
|}

====Exo Product ((3aS,4R,7S,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole).====

{| class="wikitable" border="0" style='text-align: center style="margin-left: auto; margin-right: auto; border: none;"
|-
|[[File:Kh1015 Exo Crosscheck PM6 IRC.gif|frame|left|Figure 5.2.23: IRC for Formation of Diels-Alder Exo Product ((3aS,4R,7S,7aS)-3a,4,7,7a-tetrahydro-4,7-ethanobenzo[d][1,3]dioxole)) (PM6 Calculation).]]
|| [[File:KH1015 Exo PM6 IRC Graph.png|thumb|Figure 5.2.24: IRC Graph of Energy against Reaction Coordinate for the formation of Exo-Product (PM6 Calculation). Click [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:KH1015_Exo_PM6_IRC_Graph_Gradient.png here] for the concurrent RMS Gradient Norm analysis.]]
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