ChemWiki - User contributions [en]

Rep:Mod:yhw14cts

2017-02-10T04:59:29Z

Yhw14: /* Instability of Xylylene */

''' Transition States and Reactivity '''

'' Yi Hang Cherie WONG (yhw14) ''
'' CID: 00933828 ''

== Introduction ==
A potential energy surface is a mathematical or graphical function that gives relationship between the energy of a molecule and its geometry with the relative positions of the atoms participating in the reaction. The stationary points may be classified according to the first and second derivatives of the energy with respect to position. At the minimum of a reaction profile, the gradient is represented by the first derivative of the reaction coordinate, which is zero, while curvature is represented by the second derivative, is positive in this case; hence energy rises in all directions. Energy minima correspond to physically stable chemical species, which could be reactants and products. The transition state is defined as the maximum in a reaction profile, where the gradient is again, zero, while curvature is negative; hence energy decreases in one direction, which indicates the reaction pathway of the chemical reaction. The potential energy surface can be computed using GaussView, which is a graphical interface for Gaussian, where structure and energy of reactants or products can be modelled to illustrate the transition states, which can rarely be obtained experimentally. The intrinsic reaction coordinate can then be calculated and compared to predict the reaction path at a transition state and follow it to the correct minima.

In this computational lab, all of the reactants and products were optimised to their minima, and the transition states were also optimised. The calculations were done by GaussView, using mainly semi-empirical method PM6 and Density Functional Theory-B3LYP-631G. The latter is a more detailed and accurate optimisation, which is more time consuming as it involves a higher number of basis set. Frequency calculations were performed to show molecular vibrations to confirm the position on the potential energy surface. If all the vibrational frequencies are real, this confirms the structure is a minimum, and vice versa, the presence of imaginary frequency may suggest that the structure is at its transition state. Intrinsic reaction coordinate method was carried out using calculated force constants to predict which conformer a reaction path from the transition state would lead to.

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

The reaction between butadiene and ethene is a typical pericyclic [4+2] Diels-Alder reaction that proceeds via a concerted mechanism through a cyclic transition state. The reaction scheme is shown below.

[[File:Ex1 reactionscheme revised yhw14.png|550px|center|thumb|Diagram 1: Reaction Scheme of Butadiene and Ethene]]

=== Molecular Orbital Analysis ===

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of butadiene and ethene.

[[File:Ex1 mo diagram yhw14 revised v3.png|550px|center|thumb|Diagram 2: MO diagram of Reaction of Butadiene and Ethene]]

Butadiene and ethene were optimised to their minima at semi-empirical method PM6 level. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #06DCFB; color: #ffffff;" |'''Molecule'''
! '''Butadiene'''
! '''Ethene'''
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Butadiene lumo yhw14.png|center|150px]]
|[[File:Ethene lumo yhw14.png|center|150px]]
|-
|Corresponding to the s orbital (symmetric)
|Corresponding to the a orbital (asymmetric)
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Butadiene homo yhw14.png|center|150px]]
|[[File:Ethene homo yhw14.png|center|150px]]
|-
|Corresponding to the a orbital (antisymmetric)
|Corresponding to the s orbital (symmetric)
|}

The transition state was first optimised to its minimum, followed by a transition state calculation at semi-empirical method PM6 level. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #01FCEF; color: #ffffff;" |'''Molecule'''
! '''Transition State'''
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Ts lumo+1 yhw14.png|center|150px]]
|-
|Corresponding to the 5 orbital (asymmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Ts lumo 1 yhw14.png|center|150px]]
|-
|Corresponding to the 4 orbital (symmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Ts homo yhw14.png|center|150px]]
|-
|Corresponding to the 3 orbital (symmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Ts homo-1 yhw14.png|center|150px]]
|-
|Corresponding to the 2 orbital (asymmetrical)
|}

Based on the MO diagram and the computed MOs shown above, a reaction is only allowed when the MOs with the same symmetry interact with each other, i.e. symmetric-symmetric and asymmetric-asymmetric interactions; and a reaction is forbidden when the MOs with different symmetry interact with each other, i.e. symmetric-asymmetric interactions. The MOs have to be close in energy in order to overlap effectively.

In the reaction between butadiene and ethene, the butadiene asymmetric MO interacts with the ethene asymmetric MO to give the MOs 2 and 5 of the transition state, and the butadiene symmetric MO interacts with the ethene symmetric MO to give the MOs 3 and 4 of the transition state. Therefore, a reaction is allowed when the symmetry labels of the MOs of the reactants are the same; and forbidden when the symmetry labels are different.

The orbital overlap integral is zero in a symmetric-asymmetric interaction and non-zero in symmetric-symmetric and asymmetric-asymmetric interactions.

=== Bond Length Analysis ===

The changes in bond lengths between carbons in reactant, transition state and product as the reaction progresses were studied by comparing the bond lengths between carbons before and after the reaction. The summary of bond lengths is shown below.
[[File:Ex1 bondlength yhw14.png|470px|center|thumb|Diagram 3: Labelled carbons]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #0000FF; color: #ffffff" | State
! style="background: #0000FF; color: #ffffff" | C1-C2
! style="background: #0000FF; color: #ffffff" | C2-C3
! style="background: #0000FF; color: #ffffff" | C3-C4
! style="background: #0000FF; color: #ffffff" | C4-C5
! style="background: #0000FF; color: #ffffff" | C5-C6
! style="background: #0000FF; color: #ffffff" | C6-C1
|-
|Reactants
|1.335
|1.468
|1.335
|/
|1.327
|/
|-
|Transition State
|1.380
|1.411
|1.380
|2.115
|1.382
|2.114
|-
|Product
|1.500
|1.338
|1.500
|1.540
|1.540
|1.540
|+Table 1: Measurements of the C-C bond lengths of the reactants, transition state and products (Å)
|}

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #97A7ED; color: #ffffff" |
! style="background: #97A7ED; color: #ffffff" | sp3-sp3 (C-C single bond) <ref name="C-C bond lengths"/>
! style="background: #97A7ED; color: #ffffff" | sp2-sp2 (C-C double bond) <ref name="C-C bond lengths"/>
! style="background: #97A7ED; color: #ffffff" | Van der Waals radius of the C atom <ref name="Van der Waals radius of C"/>
|-
|Bond Lengths (Å)
|1.54
|1.33
|1.7
|+Table 2: Literature Values of C-C bond lengths and Van der Waals radius of the C atom (Å)
|}
As the reaction progresses, the bond lengths between C1-C2, C3-C4 and C5-C6 lengthen from ~1.3 Å to ~1.5 Å as the bond order decrease to one, whereas bond length of C2-C3 shortens from ~1.5 Å to ~1.3 Å as the bond order increases from one to two.
This could be explained as the increase in bond length suggest a change from sp2-sp2 (C-C double bond) with typical bond length of 1.33 Å <ref name="C-C bond lengths"/> to sp3-sp3 (C-C single bond) with typical bond length of 1.54 Å <ref name="C-C bond lengths"/>, and vice versa for the decrease in bond length. Based on the calculated bond lengths above in Table 1, it is clear that bond lengths and bond orders of the reactants changed during the reaction and the new bonds formed at C4-C5 and C6-C1 are single bonds as they have bond lengths of 1.54 Å.
The typical Van der Waals radius of the C atom is 1.7 Å <ref name="Van der Waals radius of C"/>. As the bond lengths between C4-C5 and C6-C1 of the transition state are shorter than 2 x Van der Waals radii of C, this reflects that C-C bonds are forming at the transition state.

=== Vibration Analysis ===

The imaginary frequency at -948.32 cm-1 corresponds to the reaction path at the transition state, which shows a synchronous bond formation, which agrees with the concerted mechanism of [4+2] cycloaddition, where both reaction centres converge at the same time to form two new bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 15;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Reaction Path at the Transition State
|}

The lowest positive frequency at 145.14 cm-1 is asynchronous as shown below, where one of the C from the ethene moves towards the butadiene reaction centre and the other C moves away. This suggests that bonds are formed one at a time.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 16;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Lowest positive frequency
|}

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

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via two different pathways, endo and exo, which are shown in the reaction scheme below. GaussView calculations could be carried out to compare the reaction barriers and reaction energies of the two pathways to determine the kinetic and thermodynamic products.

[[File:Ex2 reactionscheme.png|550px|center|thumb|Diagram 4: Reaction Scheme of Cyclohexadiene and 1,3-Dioxole]]

=== Frequency Analysis ===

Frequency calculations were run to confirm that reactants (cyclohexadiene and 1,3-dioxole), and both endo and exo products did not have imaginary vibrations, suggesting they are structures at relative minima to the transition state; whereas both endo and exo transition states each had one imaginary vibration.

=== Molecular Orbital Analysis ===

Cyclohexadiene and 1,3-dioxole were optimised to their minima at DFT-B3LYP 631-G level. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #9A03FE; color: #ffffff;" |'''Molecule'''
! '''Cyclohexadiene'''
! '''1,3-Dioxole'''
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Cyclo lumo 631g yhw14.png|center|150px]]
|[[File:Dioxole lumo 631g yhw14.png|center|150px]]
|-
|Corresponding to the s orbital
|Corresponding to the a orbital
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Cyclo homo 631g yhw14.png|center|150px]]
|[[File:Dioxole homo 631g yhw14.png|center|150px]]
|-
|Corresponding to the a orbital
|Corresponding to the s orbital
|}

The transition state was first optimised to its minimum, followed by a transition state calculation at DFT-B3LYP 631-G level. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #BD5CFE; color: #ffffff;" |'''Molecule'''
! '''Endo Transition State'''
! '''Exo Transition State'''
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Endo ts lumo+1 yhw14.png|center|150px]]
|[[File:Exo ts lumo+1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 5 orbital (asymmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Endo ts lumo yhw14.png|center|150px]]
|[[File:Exo ts lumo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 4 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Endo ts homo yhw14.png|center|150px]]
|[[File:Exo ts homo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 3 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Endo ts homo-1 yhw14.png|center|150px]]
|[[File:Exo ts homo-1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 2 orbital (asymmetric)
|}

The diagram below illustrates the π molecular orbitals of cyclohexadiene and 1,3-dioxole involved in the formation of the transition state.

[[File:Ex2 mo diagram yhw14.png|550px|center|thumb|Diagram 5: MO diagram of Reaction of Cyclohexadiene and 1,3-dioxole]]

=== Normal Demand vs Inverse Demand Diels-Alder Reaction ===

A normal electron demand Diels-Alder reaction can be defined as a reaction between electron rich diene and electron poor dienophile. An inverse electron demand is the reaction between electron poor diene and electron rich dienophile.

The LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are very close in energy, which results in strong bonding interaction between the two to form the HOMO and LUMO of both endo and exo TS. Since the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole have the correct symmetry (symmetric) to interact, they interact to form the symmetric HOMO and LUMO of both TS.

The presence of the two electron donating oxygen atoms on 1,3-dioxole raise the energy of both its HOMO and LUMO, making the overlap between the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole much better than the HOMO of cyclohexadiene and the LUMO of 1,3-dioxole. Thus, the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are now the frontier orbitals that interact the most, hence this is an inverse demand Diels-Alder reaction.

=== Reaction Energies and Secondary Orbital Interaction ===

The reaction paths at the endo and exo transition states are shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="text-align: center;"|Reaction Path at the Endo Transition State
! style="text-align: center;"|Reaction Path at the Exo Transition State
|-
|<jmol><jmolApplet>
<uploadedFileContents>ENDO TS OPT TS 631G yhw14.LOG</uploadedFileContents>
<color>white</color>
<size>300</size>
<script>frame 33;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|<jmol><jmolApplet>
<uploadedFileContents>EXO TS OPT TS 631G yhw14.LOG</uploadedFileContents>
<color>white</color>
<size>300</size>
<script>frame 17;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|}

The energies of reactants were taken using the sum of the energies of cyclohexadiene and 1,3-dioxole optimised to their minima at DFT-B3LYP 631-G. The calculations were done using DFT-B3LYP 631-G.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FF4AFF; color: #ffffff" |
! style="background: #FF4AFF; color: #ffffff" | Reactants
! style="background: #FF4AFF; color: #ffffff" | Transition State
! style="background: #FF4AFF; color: #ffffff" | Product
! style="background: #FF4AFF; color: #ffffff" | Activation Energy
! style="background: #FF4AFF; color: #ffffff" | Gibbs Free Energy
|-
|Endo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313622</nowiki>
|<nowiki>-1313849</nowiki>
|160
|<nowiki>-67</nowiki>
|-
|Exo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313614</nowiki>
|<nowiki>-1313846</nowiki>
|168
|<nowiki>-64</nowiki>
|+Table 3: Energies of Reactants, Transition States and Products of both Endo and Exo Pathways in Diels-Alder Reaction of Cyclohexadiene and 1,3-Dioxole (kJ mol-1)
|}

Kinetically favourable product of a reaction is the one that has the lowest activation energy; Thermodynamically favourable product is the product with lowest energy conformer, hence the more stabilised product.

The endo transition state is the kinetic product of this reaction as it has lower activation energy. This could be explained using the secondary orbital interaction between the lone pair orbital on the oxygen atom and the empty π* orbital of diene. This favourable effect stabilises the endo transition state.

As the oxygen atom lone pair is oriented away from the diene π system in the exo transition state, the secondary orbital effect is not present, hence the activation energy of exo reaction is higher.

However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, i.e. increasing temperature, formation of the exo product would be more favourable.

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

Xylylene can react with sulfur dioxide through Diels-Alder reaction via either endo or exo pathways to form a 6-membered ring, or through cheletropic reaction to form a 5-membered ring. The reaction scheme is shown below. Reaction barriers and reaction energies for each pathway were compared to determine the reaction that is most favourable.

[[File:Ex3 reactionscheme yhw14.png|550px|center|thumb|Diagram 6: Reaction Scheme of Xylylene and Sulfur Dioxide]]

=== Intrinsic Reaction Coordinate ===
The following files show the intrinsic reaction coordinates of the three different reaction pathways of xylylene and SO2. Please click to see animation.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Endo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Exo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Cheletropic TS
|-
|[[File:DA endo irc animation yhw14.gif|center]]
|[[File:DA exo irc animation yhw14.gif|center]]
|[[File:Cheletropic irc animation yhw14.gif|center]]
|-
|[[File:DA endo irc plot yhw14.png|center|500px]]
|[[File:DA exo irc plot yhw14.png|center|500px]]
|[[File:Cheletropic irc plot yhw14.png|center|650px]]
|}

=== Reaction Energies and Reaction Barriers ===

[[File:Ex3 reactionprofile yhw14.png|550px|center|thumb|Diagram 7: Reaction Profile of Xylylene and Sulfur Dioxide]]

The energies of reactants were taken using the sum of the energies of xylylene and SO2 optimised to their minima. All calculations were done using semi-empirical PM6 method.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FFD1C3; color: #ffffff" |
! style="background: #FFD1C3; color: #ffffff" | Reactants
! style="background: #FFD1C3; color: #ffffff" | Transition State
! style="background: #FFD1C3; color: #ffffff" | Product
! style="background: #FFD1C3; color: #ffffff" | Activation Energy
! style="background: #FFD1C3; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|237.767824
|56.9576013
|83.391038
|<nowiki>-97.4191847</nowiki>
|-
|Exo
|154.376786
|241.753433
|56.3196048
|87.406647
|<nowiki>-98.0571812</nowiki>
|-
|Cheletropic
|154.376786
|260.08205
|0.013127501
|105.705264
|<nowiki>-154.3636585</nowiki>
|+Table 4: Energies of Reactants, Transition States and Products of Reactions between Xylylene and Sulfur Dioxide (kJ mol-1)
|}

With reference to the reaction profile and Table 4, the Diels-Alder reaction via the endo pathway has the lowest activation energy, making it a more kinetically favourable product, i.e. the kinetic product; the Diels-Alder exo product has a lower energy than endo, however with a higher activation energy hence it will not form under low temperature condition; the cheletropic product is the most stabilised product out of the three and it has the lowest reaction energy, therefore is the thermodynamic product.

=== Instability of Xylylene ===

Xylylene does not follow the Hückel rule (4n+2 electrons) hence it is not aromatic. In addition, it is rich in double bonds, all these factors make xylylene a very unstable molecule.

[[File:Ex3 xylylene instability yhw14.png|550px|center|thumb|Diagram 8: Electrocyclic Reaction Xylylene]]

Electrocyclic reaction to form benzocyclobutane could also be another possible reaction pathway apart from Diels-Alder reaction and cheletropic reaction. During all the reactions including the Diels-Alder and cheletropic reactions, as well as the electrocyclic reaction, they aromatise the 6-membered ring and the driving force of these reactions is the formation of the aromatic benzene ring, which stabilise the reaction to become more thermodynamically favourable.

=== Side Reaction between cis-diene in Xylylene 6-membered ring and SO2===

o-Xylylene contains another cis-butadiene fragment located in the 6-membered ring that can undergo a Diels-Alder reaction with SO2. The reaction energies and reaction barriers between endo and exo pathways are compared in the table below.

The energies of reactants were taken using the sum of the energies of xylylene and SO2 optimised to their minima. All calculations were done using semi-empirical PM6 method.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #4EBEBA; color: #ffffff" |
! style="background: #4EBEBA; color: #ffffff" | Reactants
! style="background: #4EBEBA; color: #ffffff" | Transition State
! style="background: #4EBEBA; color: #ffffff" | Product
! style="background: #4EBEBA; color: #ffffff" | Activation Energy
! style="background: #4EBEBA; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|267.984805
|172.272196
|113.608019
|17.89541
|-
|Exo
|154.376786
|275.821924
|176.711916
|121.445138
|22.33513
|+Table 5: Energies of Reactants, Transition States and Products of the Side Reaction in Xylylene 6-membered ring and Sulfur Dioxide (kJ mol-1)
|}

It is clear that both endo and exo Diels-Alder side reactions are kinetically and thermodynamically unfavourable at this site as the activation energies are much higher than the previous reactions mentioned above in Table 4 and the reaction energies show that the reactions are endothermic.

== Conclusion ==

The transition states of three pericyclic reactions were investigated in this computational lab, using GaussView to optimise the reactants, transition states and products respectively, and the vibrational frequencies and intrinsic reaction coordinates were computed.

In the reaction between butadiene and ethene, the importance of molecular orbital symmetry in the interaction of molecular orbitals was illustrated, such that a reaction is only allowed when the molecular orbitals with the same symmetry interact with each other and forbidden when symmetric molecular orbital interact with asymmetric orbitals. Furthermore, the vibration frequency calculation proved that this [4+2] Diels-Alder reaction proceeds via a concerted mechanism as synchronous bond formation was demonstrated. Bonding interaction can be further confirmed as the bond distance between the two termini carbon atoms in the transition state is shorter than the sum of two Van der Waals radii of carbon.

In the reaction of cyclohexadiene and 1,3-dioxole, both the endo and exo transition states were investigated. In general, the endo transition state is kinetically more favourable as it has lower activation barrier, possibly due to the secondary orbital interaction between the lone pair in p orbital on the oxygen atom and the empty π* orbital in the diene, which stabilises the transition state. However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, formation of the exo product could be possible.

The final reaction between xylylene and SO2 again proved that the endo Diels-Alder transition state has the lowest activation energy, making it kinetically favourable at low temperature. However, the cheletropic product is the most stabilised and thermodynamically favourable product. Therefore the reaction would yield the cheletropic product under thermodynamic control instead of the exo Diels-Alder product.

==References==
<references>
<ref name="C-C bond lengths">L. Pauling and L. O. Brockway, ''Journal of the American Chemical Society'', '''1937''', Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref>
<ref name="Van der Waals radius of C">S. S. Batsanov, ''Inorganic Materials'', '''2001''', Volume 37, Number 9, pp. 871-885, https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf.</ref>
</references>

Rep:Mod:yhw14cts

2017-02-10T04:21:45Z

Yhw14:

''' Transition States and Reactivity '''

'' Yi Hang Cherie WONG (yhw14) ''
'' CID: 00933828 ''

== Introduction ==
A potential energy surface is a mathematical or graphical function that gives relationship between the energy of a molecule and its geometry with the relative positions of the atoms participating in the reaction. The stationary points may be classified according to the first and second derivatives of the energy with respect to position. At the minimum of a reaction profile, the gradient is represented by the first derivative of the reaction coordinate, which is zero, while curvature is represented by the second derivative, is positive in this case; hence energy rises in all directions. Energy minima correspond to physically stable chemical species, which could be reactants and products. The transition state is defined as the maximum in a reaction profile, where the gradient is again, zero, while curvature is negative; hence energy decreases in one direction, which indicates the reaction pathway of the chemical reaction. The potential energy surface can be computed using GaussView, which is a graphical interface for Gaussian, where structure and energy of reactants or products can be modelled to illustrate the transition states, which can rarely be obtained experimentally. The intrinsic reaction coordinate can then be calculated and compared to predict the reaction path at a transition state and follow it to the correct minima.

In this computational lab, all of the reactants and products were optimised to their minima, and the transition states were also optimised. The calculations were done by GaussView, using mainly semi-empirical method PM6 and Density Functional Theory-B3LYP-631G. The latter is a more detailed and accurate optimisation, which is more time consuming as it involves a higher number of basis set. Frequency calculations were performed to show molecular vibrations to confirm the position on the potential energy surface. If all the vibrational frequencies are real, this confirms the structure is a minimum, and vice versa, the presence of imaginary frequency may suggest that the structure is at its transition state. Intrinsic reaction coordinate method was carried out using calculated force constants to predict which conformer a reaction path from the transition state would lead to.

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

The reaction between butadiene and ethene is a typical pericyclic [4+2] Diels-Alder reaction that proceeds via a concerted mechanism through a cyclic transition state. The reaction scheme is shown below.

[[File:Ex1 reactionscheme revised yhw14.png|550px|center|thumb|Diagram 1: Reaction Scheme of Butadiene and Ethene]]

=== Molecular Orbital Analysis ===

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of butadiene and ethene.

[[File:Ex1 mo diagram yhw14 revised v3.png|550px|center|thumb|Diagram 2: MO diagram of Reaction of Butadiene and Ethene]]

Butadiene and ethene were optimised to their minima at semi-empirical method PM6 level. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #06DCFB; color: #ffffff;" |'''Molecule'''
! '''Butadiene'''
! '''Ethene'''
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Butadiene lumo yhw14.png|center|150px]]
|[[File:Ethene lumo yhw14.png|center|150px]]
|-
|Corresponding to the s orbital (symmetric)
|Corresponding to the a orbital (asymmetric)
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Butadiene homo yhw14.png|center|150px]]
|[[File:Ethene homo yhw14.png|center|150px]]
|-
|Corresponding to the a orbital (antisymmetric)
|Corresponding to the s orbital (symmetric)
|}

The transition state was first optimised to its minimum, followed by a transition state calculation at semi-empirical method PM6 level. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #01FCEF; color: #ffffff;" |'''Molecule'''
! '''Transition State'''
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Ts lumo+1 yhw14.png|center|150px]]
|-
|Corresponding to the 5 orbital (asymmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Ts lumo 1 yhw14.png|center|150px]]
|-
|Corresponding to the 4 orbital (symmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Ts homo yhw14.png|center|150px]]
|-
|Corresponding to the 3 orbital (symmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Ts homo-1 yhw14.png|center|150px]]
|-
|Corresponding to the 2 orbital (asymmetrical)
|}

Based on the MO diagram and the computed MOs shown above, a reaction is only allowed when the MOs with the same symmetry interact with each other, i.e. symmetric-symmetric and asymmetric-asymmetric interactions; and a reaction is forbidden when the MOs with different symmetry interact with each other, i.e. symmetric-asymmetric interactions. The MOs have to be close in energy in order to overlap effectively.

In the reaction between butadiene and ethene, the butadiene asymmetric MO interacts with the ethene asymmetric MO to give the MOs 2 and 5 of the transition state, and the butadiene symmetric MO interacts with the ethene symmetric MO to give the MOs 3 and 4 of the transition state. Therefore, a reaction is allowed when the symmetry labels of the MOs of the reactants are the same; and forbidden when the symmetry labels are different.

The orbital overlap integral is zero in a symmetric-asymmetric interaction and non-zero in symmetric-symmetric and asymmetric-asymmetric interactions.

=== Bond Length Analysis ===

The changes in bond lengths between carbons in reactant, transition state and product as the reaction progresses were studied by comparing the bond lengths between carbons before and after the reaction. The summary of bond lengths is shown below.
[[File:Ex1 bondlength yhw14.png|470px|center|thumb|Diagram 3: Labelled carbons]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #0000FF; color: #ffffff" | State
! style="background: #0000FF; color: #ffffff" | C1-C2
! style="background: #0000FF; color: #ffffff" | C2-C3
! style="background: #0000FF; color: #ffffff" | C3-C4
! style="background: #0000FF; color: #ffffff" | C4-C5
! style="background: #0000FF; color: #ffffff" | C5-C6
! style="background: #0000FF; color: #ffffff" | C6-C1
|-
|Reactants
|1.335
|1.468
|1.335
|/
|1.327
|/
|-
|Transition State
|1.380
|1.411
|1.380
|2.115
|1.382
|2.114
|-
|Product
|1.500
|1.338
|1.500
|1.540
|1.540
|1.540
|+Table 1: Measurements of the C-C bond lengths of the reactants, transition state and products (Å)
|}

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #97A7ED; color: #ffffff" |
! style="background: #97A7ED; color: #ffffff" | sp3-sp3 (C-C single bond) <ref name="C-C bond lengths"/>
! style="background: #97A7ED; color: #ffffff" | sp2-sp2 (C-C double bond) <ref name="C-C bond lengths"/>
! style="background: #97A7ED; color: #ffffff" | Van der Waals radius of the C atom <ref name="Van der Waals radius of C"/>
|-
|Bond Lengths (Å)
|1.54
|1.33
|1.7
|+Table 2: Literature Values of C-C bond lengths and Van der Waals radius of the C atom (Å)
|}
As the reaction progresses, the bond lengths between C1-C2, C3-C4 and C5-C6 lengthen from ~1.3 Å to ~1.5 Å as the bond order decrease to one, whereas bond length of C2-C3 shortens from ~1.5 Å to ~1.3 Å as the bond order increases from one to two.
This could be explained as the increase in bond length suggest a change from sp2-sp2 (C-C double bond) with typical bond length of 1.33 Å <ref name="C-C bond lengths"/> to sp3-sp3 (C-C single bond) with typical bond length of 1.54 Å <ref name="C-C bond lengths"/>, and vice versa for the decrease in bond length. Based on the calculated bond lengths above in Table 1, it is clear that bond lengths and bond orders of the reactants changed during the reaction and the new bonds formed at C4-C5 and C6-C1 are single bonds as they have bond lengths of 1.54 Å.
The typical Van der Waals radius of the C atom is 1.7 Å <ref name="Van der Waals radius of C"/>. As the bond lengths between C4-C5 and C6-C1 of the transition state are shorter than 2 x Van der Waals radii of C, this reflects that C-C bonds are forming at the transition state.

=== Vibration Analysis ===

The imaginary frequency at -948.32 cm-1 corresponds to the reaction path at the transition state, which shows a synchronous bond formation, which agrees with the concerted mechanism of [4+2] cycloaddition, where both reaction centres converge at the same time to form two new bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 15;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Reaction Path at the Transition State
|}

The lowest positive frequency at 145.14 cm-1 is asynchronous as shown below, where one of the C from the ethene moves towards the butadiene reaction centre and the other C moves away. This suggests that bonds are formed one at a time.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 16;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Lowest positive frequency
|}

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

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via two different pathways, endo and exo, which are shown in the reaction scheme below. GaussView calculations could be carried out to compare the reaction barriers and reaction energies of the two pathways to determine the kinetic and thermodynamic products.

[[File:Ex2 reactionscheme.png|550px|center|thumb|Diagram 4: Reaction Scheme of Cyclohexadiene and 1,3-Dioxole]]

=== Frequency Analysis ===

Frequency calculations were run to confirm that reactants (cyclohexadiene and 1,3-dioxole), and both endo and exo products did not have imaginary vibrations, suggesting they are structures at relative minima to the transition state; whereas both endo and exo transition states each had one imaginary vibration.

=== Molecular Orbital Analysis ===

Cyclohexadiene and 1,3-dioxole were optimised to their minima at DFT-B3LYP 631-G level. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #9A03FE; color: #ffffff;" |'''Molecule'''
! '''Cyclohexadiene'''
! '''1,3-Dioxole'''
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Cyclo lumo 631g yhw14.png|center|150px]]
|[[File:Dioxole lumo 631g yhw14.png|center|150px]]
|-
|Corresponding to the s orbital
|Corresponding to the a orbital
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Cyclo homo 631g yhw14.png|center|150px]]
|[[File:Dioxole homo 631g yhw14.png|center|150px]]
|-
|Corresponding to the a orbital
|Corresponding to the s orbital
|}

The transition state was first optimised to its minimum, followed by a transition state calculation at DFT-B3LYP 631-G level. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #BD5CFE; color: #ffffff;" |'''Molecule'''
! '''Endo Transition State'''
! '''Exo Transition State'''
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Endo ts lumo+1 yhw14.png|center|150px]]
|[[File:Exo ts lumo+1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 5 orbital (asymmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Endo ts lumo yhw14.png|center|150px]]
|[[File:Exo ts lumo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 4 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Endo ts homo yhw14.png|center|150px]]
|[[File:Exo ts homo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 3 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Endo ts homo-1 yhw14.png|center|150px]]
|[[File:Exo ts homo-1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 2 orbital (asymmetric)
|}

The diagram below illustrates the π molecular orbitals of cyclohexadiene and 1,3-dioxole involved in the formation of the transition state.

[[File:Ex2 mo diagram yhw14.png|550px|center|thumb|Diagram 5: MO diagram of Reaction of Cyclohexadiene and 1,3-dioxole]]

=== Normal Demand vs Inverse Demand Diels-Alder Reaction ===

A normal electron demand Diels-Alder reaction can be defined as a reaction between electron rich diene and electron poor dienophile. An inverse electron demand is the reaction between electron poor diene and electron rich dienophile.

The LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are very close in energy, which results in strong bonding interaction between the two to form the HOMO and LUMO of both endo and exo TS. Since the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole have the correct symmetry (symmetric) to interact, they interact to form the symmetric HOMO and LUMO of both TS.

The presence of the two electron donating oxygen atoms on 1,3-dioxole raise the energy of both its HOMO and LUMO, making the overlap between the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole much better than the HOMO of cyclohexadiene and the LUMO of 1,3-dioxole. Thus, the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are now the frontier orbitals that interact the most, hence this is an inverse demand Diels-Alder reaction.

=== Reaction Energies and Secondary Orbital Interaction ===

The reaction paths at the endo and exo transition states are shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="text-align: center;"|Reaction Path at the Endo Transition State
! style="text-align: center;"|Reaction Path at the Exo Transition State
|-
|<jmol><jmolApplet>
<uploadedFileContents>ENDO TS OPT TS 631G yhw14.LOG</uploadedFileContents>
<color>white</color>
<size>300</size>
<script>frame 33;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|<jmol><jmolApplet>
<uploadedFileContents>EXO TS OPT TS 631G yhw14.LOG</uploadedFileContents>
<color>white</color>
<size>300</size>
<script>frame 17;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|}

The energies of reactants were taken using the sum of the energies of cyclohexadiene and 1,3-dioxole optimised to their minima at DFT-B3LYP 631-G. The calculations were done using DFT-B3LYP 631-G.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FF4AFF; color: #ffffff" |
! style="background: #FF4AFF; color: #ffffff" | Reactants
! style="background: #FF4AFF; color: #ffffff" | Transition State
! style="background: #FF4AFF; color: #ffffff" | Product
! style="background: #FF4AFF; color: #ffffff" | Activation Energy
! style="background: #FF4AFF; color: #ffffff" | Gibbs Free Energy
|-
|Endo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313622</nowiki>
|<nowiki>-1313849</nowiki>
|160
|<nowiki>-67</nowiki>
|-
|Exo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313614</nowiki>
|<nowiki>-1313846</nowiki>
|168
|<nowiki>-64</nowiki>
|+Table 3: Energies of Reactants, Transition States and Products of both Endo and Exo Pathways in Diels-Alder Reaction of Cyclohexadiene and 1,3-Dioxole (kJ mol-1)
|}

Kinetically favourable product of a reaction is the one that has the lowest activation energy; Thermodynamically favourable product is the product with lowest energy conformer, hence the more stabilised product.

The endo transition state is the kinetic product of this reaction as it has lower activation energy. This could be explained using the secondary orbital interaction between the lone pair orbital on the oxygen atom and the empty π* orbital of diene. This favourable effect stabilises the endo transition state.

As the oxygen atom lone pair is oriented away from the diene π system in the exo transition state, the secondary orbital effect is not present, hence the activation energy of exo reaction is higher.

However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, i.e. increasing temperature, formation of the exo product would be more favourable.

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

Xylylene can react with sulfur dioxide through Diels-Alder reaction via either endo or exo pathways to form a 6-membered ring, or through cheletropic reaction to form a 5-membered ring. The reaction scheme is shown below. Reaction barriers and reaction energies for each pathway were compared to determine the reaction that is most favourable.

[[File:Ex3 reactionscheme yhw14.png|550px|center|thumb|Diagram 6: Reaction Scheme of Xylylene and Sulfur Dioxide]]

=== Intrinsic Reaction Coordinate ===
The following files show the intrinsic reaction coordinates of the three different reaction pathways of xylylene and SO2. Please click to see animation.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Endo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Exo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Cheletropic TS
|-
|[[File:DA endo irc animation yhw14.gif|center]]
|[[File:DA exo irc animation yhw14.gif|center]]
|[[File:Cheletropic irc animation yhw14.gif|center]]
|-
|[[File:DA endo irc plot yhw14.png|center|500px]]
|[[File:DA exo irc plot yhw14.png|center|500px]]
|[[File:Cheletropic irc plot yhw14.png|center|650px]]
|}

=== Reaction Energies and Reaction Barriers ===

[[File:Ex3 reactionprofile yhw14.png|550px|center|thumb|Diagram 7: Reaction Profile of Xylylene and Sulfur Dioxide]]

The energies of reactants were taken using the sum of the energies of xylylene and SO2 optimised to their minima. All calculations were done using semi-empirical PM6 method.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FFD1C3; color: #ffffff" |
! style="background: #FFD1C3; color: #ffffff" | Reactants
! style="background: #FFD1C3; color: #ffffff" | Transition State
! style="background: #FFD1C3; color: #ffffff" | Product
! style="background: #FFD1C3; color: #ffffff" | Activation Energy
! style="background: #FFD1C3; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|237.767824
|56.9576013
|83.391038
|<nowiki>-97.4191847</nowiki>
|-
|Exo
|154.376786
|241.753433
|56.3196048
|87.406647
|<nowiki>-98.0571812</nowiki>
|-
|Cheletropic
|154.376786
|260.08205
|0.013127501
|105.705264
|<nowiki>-154.3636585</nowiki>
|+Table 4: Energies of Reactants, Transition States and Products of Reactions between Xylylene and Sulfur Dioxide (kJ mol-1)
|}

With reference to the reaction profile and Table 4, the Diels-Alder reaction via the endo pathway has the lowest activation energy, making it a more kinetically favourable product, i.e. the kinetic product; the Diels-Alder exo product has a lower energy than endo, however with a higher activation energy hence it will not form under low temperature condition; the cheletropic product is the most stabilised product out of the three and it has the lowest reaction energy, therefore is the thermodynamic product.

=== Instability of Xylylene ===

Xylylene does not follow the Hückel rule (4n+2 electrons) hence it is not aromatic. In addition, it is rich in double bonds, all these factors make xylylene a very unstable molecule.

[[File:Ex3 xylylene instability yhw14.png|550px|center|thumb|Diagram 8: Electrocyclic Reaction Xylylene]]

The driving force of this electrocyclic reaction is the formation of an aromatic 6-membered benzene ring in the benzocyclobutane, which could also be another possible reaction pathway apart from Diels-Alder reaction and cheletropic reaction.

=== Side Reaction between cis-diene in Xylylene 6-membered ring and SO2===

o-Xylylene contains another cis-butadiene fragment located in the 6-membered ring that can undergo a Diels-Alder reaction with SO2. The reaction energies and reaction barriers between endo and exo pathways are compared in the table below.

The energies of reactants were taken using the sum of the energies of xylylene and SO2 optimised to their minima. All calculations were done using semi-empirical PM6 method.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #4EBEBA; color: #ffffff" |
! style="background: #4EBEBA; color: #ffffff" | Reactants
! style="background: #4EBEBA; color: #ffffff" | Transition State
! style="background: #4EBEBA; color: #ffffff" | Product
! style="background: #4EBEBA; color: #ffffff" | Activation Energy
! style="background: #4EBEBA; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|267.984805
|172.272196
|113.608019
|17.89541
|-
|Exo
|154.376786
|275.821924
|176.711916
|121.445138
|22.33513
|+Table 5: Energies of Reactants, Transition States and Products of the Side Reaction in Xylylene 6-membered ring and Sulfur Dioxide (kJ mol-1)
|}

It is clear that both endo and exo Diels-Alder side reactions are kinetically and thermodynamically unfavourable at this site as the activation energies are much higher than the previous reactions mentioned above in Table 4 and the reaction energies show that the reactions are endothermic.

== Conclusion ==

The transition states of three pericyclic reactions were investigated in this computational lab, using GaussView to optimise the reactants, transition states and products respectively, and the vibrational frequencies and intrinsic reaction coordinates were computed.

In the reaction between butadiene and ethene, the importance of molecular orbital symmetry in the interaction of molecular orbitals was illustrated, such that a reaction is only allowed when the molecular orbitals with the same symmetry interact with each other and forbidden when symmetric molecular orbital interact with asymmetric orbitals. Furthermore, the vibration frequency calculation proved that this [4+2] Diels-Alder reaction proceeds via a concerted mechanism as synchronous bond formation was demonstrated. Bonding interaction can be further confirmed as the bond distance between the two termini carbon atoms in the transition state is shorter than the sum of two Van der Waals radii of carbon.

In the reaction of cyclohexadiene and 1,3-dioxole, both the endo and exo transition states were investigated. In general, the endo transition state is kinetically more favourable as it has lower activation barrier, possibly due to the secondary orbital interaction between the lone pair in p orbital on the oxygen atom and the empty π* orbital in the diene, which stabilises the transition state. However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, formation of the exo product could be possible.

The final reaction between xylylene and SO2 again proved that the endo Diels-Alder transition state has the lowest activation energy, making it kinetically favourable at low temperature. However, the cheletropic product is the most stabilised and thermodynamically favourable product. Therefore the reaction would yield the cheletropic product under thermodynamic control instead of the exo Diels-Alder product.

==References==
<references>
<ref name="C-C bond lengths">L. Pauling and L. O. Brockway, ''Journal of the American Chemical Society'', '''1937''', Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref>
<ref name="Van der Waals radius of C">S. S. Batsanov, ''Inorganic Materials'', '''2001''', Volume 37, Number 9, pp. 871-885, https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf.</ref>
</references>

Rep:Mod:yhw14cts

2017-02-10T03:56:38Z

Yhw14: /* Introduction */

''' Transition States and Reactivity '''

'' Yi Hang Cherie WONG (yhw14) ''
'' CID: 00933828 ''

== Introduction ==
A potential energy surface is a mathematical or graphical function that gives relationship between the energy of a molecule and its geometry with the relative positions of the atoms participating in the reaction. The stationary points may be classified according to the first and second derivatives of the energy with respect to position. At the minimum of a reaction profile, the gradient is represented by the first derivative of the reaction coordinate, which is zero, while curvature is represented by the second derivative, is positive in this case; hence energy rises in all directions. Energy minima correspond to physically stable chemical species, which could be reactants and products. The transition state is defined as the maximum in a reaction profile, where the gradient is again, zero, while curvature is negative; hence energy decreases in one direction, which indicates the reaction pathway of the chemical reaction. The potential energy surface can be computed using GaussView, which is a graphical interface for Gaussian, where structure and energy of reactants or products can be modelled to illustrate the transition states, which can rarely be obtained experimentally. The intrinsic reaction coordinate can then be calculated and compared to predict the reaction path at a transition state and follow it to the correct minima.

In this computational lab, all of the reactants and products were optimised to their minima, and the transition states were also optimised. The calculations were done by GaussView, using mainly semi-empirical method PM6 and Density Functional Theory-B3LYP-631G. The latter is a more detailed and accurate optimisation, which is more time consuming method as it involves a higher number of basis set. Frequency calculations were performed to show molecular vibrations to confirm the position on the potential energy surface. If all the vibrational frequencies are real, this confirms the structure is a minimum, and vice versa, the presence of imaginary frequency may suggest that the structure is at its transition state. Intrinsic reaction coordinate method was carried out using calculated force constants to predict which conformer a reaction path from the transition state would lead to.

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

The reaction between butadiene and ethene is a typical pericyclic [4+2] Diels-Alder reaction that proceeds via a concerted mechanism through a cyclic transition state. The reaction scheme is shown below.

[[File:Ex1 reactionscheme revised yhw14.png|550px|center|thumb|Diagram 1: Reaction Scheme of Butadiene and Ethene]]

=== Molecular Orbital Analysis ===

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of butadiene and ethene.

[[File:Ex1 mo diagram yhw14 revised v3.png|550px|center|thumb|Diagram 2: MO diagram of Reaction of Butadiene and Ethene]]

Butadiene and ethene were optimised to their minima at semi-empirical method PM6 level. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #06DCFB; color: #ffffff;" |'''Molecule'''
! '''Butadiene'''
! '''Ethene'''
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Butadiene lumo yhw14.png|center|150px]]
|[[File:Ethene lumo yhw14.png|center|150px]]
|-
|Corresponding to the s orbital (symmetric)
|Corresponding to the a orbital (asymmetric)
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Butadiene homo yhw14.png|center|150px]]
|[[File:Ethene homo yhw14.png|center|150px]]
|-
|Corresponding to the a orbital (antisymmetric)
|Corresponding to the s orbital (symmetric)
|}

The transition state was first optimised to its minimum, followed by a transition state calculation at semi-empirical method PM6 level. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #01FCEF; color: #ffffff;" |'''Molecule'''
! '''Transition State'''
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Ts lumo+1 yhw14.png|center|150px]]
|-
|Corresponding to the 5 orbital (asymmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Ts lumo 1 yhw14.png|center|150px]]
|-
|Corresponding to the 4 orbital (symmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Ts homo yhw14.png|center|150px]]
|-
|Corresponding to the 3 orbital (symmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Ts homo-1 yhw14.png|center|150px]]
|-
|Corresponding to the 2 orbital (asymmetrical)
|}

Based on the MO diagram and the computed MOs shown above, a reaction is only allowed when the MOs with the same symmetry interact with each other, i.e. symmetric-symmetric and asymmetric-asymmetric interactions; and a reaction is forbidden when the MOs with different symmetry interact with each other, i.e. symmetric-asymmetric interactions. The MOs have to be close in energy in order to overlap effectively.

In the reaction between butadiene and ethene, the butadiene asymmetric MO interacts with the ethene asymmetric MO to give the MOs 2 and 5 of the transition state, and the butadiene symmetric MO interacts with the ethene symmetric MO to give the MOs 3 and 4 of the transition state. Therefore, a reaction is allowed when the symmetry labels of the MOs of the reactants are the same; and forbidden when the symmetry labels are different.

The orbital overlap integral is zero in a symmetric-asymmetric interaction and non-zero in symmetric-symmetric and asymmetric-asymmetric interactions.

=== Bond Length Analysis ===

The changes in bond lengths between carbons in reactant, transition state and product as the reaction progresses were studied by comparing the bond lengths between carbons before and after the reaction. The summary of bond lengths is shown below.
[[File:Ex1 bondlength yhw14.png|470px|center|thumb|Diagram 3: Labelled carbons]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #0000FF; color: #ffffff" | State
! style="background: #0000FF; color: #ffffff" | C1-C2
! style="background: #0000FF; color: #ffffff" | C2-C3
! style="background: #0000FF; color: #ffffff" | C3-C4
! style="background: #0000FF; color: #ffffff" | C4-C5
! style="background: #0000FF; color: #ffffff" | C5-C6
! style="background: #0000FF; color: #ffffff" | C6-C1
|-
|Reactants
|1.335
|1.468
|1.335
|/
|1.327
|/
|-
|Transition State
|1.380
|1.411
|1.380
|2.115
|1.382
|2.114
|-
|Product
|1.500
|1.338
|1.500
|1.540
|1.540
|1.540
|+Table 1: Measurements of the C-C bond lengths of the reactants, transition state and products (Å)
|}

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #97A7ED; color: #ffffff" |
! style="background: #97A7ED; color: #ffffff" | sp3-sp3 (C-C single bond) <ref name="C-C bond lengths"/>
! style="background: #97A7ED; color: #ffffff" | sp2-sp2 (C-C double bond) <ref name="C-C bond lengths"/>
! style="background: #97A7ED; color: #ffffff" | Van der Waals radius of the C atom <ref name="Van der Waals radius of C"/>
|-
|Bond Lengths (Å)
|1.54
|1.33
|1.7
|+Table 2: Literature Values of C-C bond lengths and Van der Waals radius of the C atom (Å)
|}
As the reaction progresses, the bond lengths between C1-C2, C3-C4 and C5-C6 lengthen from ~1.3 Å to ~1.5 Å as the bond order decrease to one, whereas bond length of C2-C3 shortens from ~1.5 Å to ~1.3 Å as the bond order increases from one to two.
This could be explained as the increase in bond length suggest a change from sp2-sp2 (C-C double bond) with typical bond length of 1.33 Å <ref name="C-C bond lengths"/> to sp3-sp3 (C-C single bond) with typical bond length of 1.54 Å <ref name="C-C bond lengths"/>, and vice versa for the decrease in bond length. Based on the calculated bond lengths above in Table 1, it is clear that bond lengths and bond orders of the reactants changed during the reaction and the new bonds formed at C4-C5 and C6-C1 are single bonds as they have bond lengths of 1.54 Å.
The typical Van der Waals radius of the C atom is 1.7 Å <ref name="Van der Waals radius of C"/>. As the bond lengths between C4-C5 and C6-C1 of the transition state are shorter than 2 x Van der Waals radii of C, this reflects that C-C bonds are forming at the transition state.

=== Vibration Analysis ===

The imaginary frequency at -948.32 cm-1 corresponds to the reaction path at the transition state, which shows a synchronous bond formation, which agrees with the concerted mechanism of [4+2] cycloaddition, where both reaction centres converge at the same time to form two new bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 15;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Reaction Path at the Transition State
|}

The lowest positive frequency at 145.14 cm-1 is asynchronous as shown below, where one of the C from the ethene moves towards the butadiene reaction centre and the other C moves away. This suggests that bonds are formed one at a time.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 16;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Lowest positive frequency
|}

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

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via two different pathways, endo and exo, which are shown in the reaction scheme below. GaussView calculations could be carried out to compare the reaction barriers and reaction energies of the two pathways to determine the kinetic and thermodynamic products.

[[File:Ex2 reactionscheme.png|550px|center|thumb|Diagram 4: Reaction Scheme of Cyclohexadiene and 1,3-Dioxole]]

=== Frequency Analysis ===

Frequency calculations were run to confirm that reactants (cyclohexadiene and 1,3-dioxole), and both endo and exo products did not have imaginary vibrations, suggesting they are structures at relative minima to the transition state; whereas both endo and exo transition states each had one imaginary vibration.

=== Molecular Orbital Analysis ===

Cyclohexadiene and 1,3-dioxole were optimised to their minima at DFT-B3LYP 631-G level. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #9A03FE; color: #ffffff;" |'''Molecule'''
! '''Cyclohexadiene'''
! '''1,3-Dioxole'''
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Cyclo lumo 631g yhw14.png|center|150px]]
|[[File:Dioxole lumo 631g yhw14.png|center|150px]]
|-
|Corresponding to the s orbital
|Corresponding to the a orbital
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Cyclo homo 631g yhw14.png|center|150px]]
|[[File:Dioxole homo 631g yhw14.png|center|150px]]
|-
|Corresponding to the a orbital
|Corresponding to the s orbital
|}

The transition state was first optimised to its minimum, followed by a transition state calculation at DFT-B3LYP 631-G level. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #BD5CFE; color: #ffffff;" |'''Molecule'''
! '''Endo Transition State'''
! '''Exo Transition State'''
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Endo ts lumo+1 yhw14.png|center|150px]]
|[[File:Exo ts lumo+1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 5 orbital (asymmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Endo ts lumo yhw14.png|center|150px]]
|[[File:Exo ts lumo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 4 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Endo ts homo yhw14.png|center|150px]]
|[[File:Exo ts homo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 3 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Endo ts homo-1 yhw14.png|center|150px]]
|[[File:Exo ts homo-1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 2 orbital (asymmetric)
|}

The diagram below illustrates the π molecular orbitals of cyclohexadiene and 1,3-dioxole involved in the formation of the transition state.

[[File:Ex2 mo diagram yhw14.png|550px|center|thumb|Diagram 5: MO diagram of Reaction of Cyclohexadiene and 1,3-dioxole]]

=== Normal Demand vs Inverse Demand Diels-Alder Reaction ===

A normal electron demand Diels-Alder reaction can be defined as a reaction between electron rich diene and electron poor dienophile. An inverse electron demand is the reaction between electron poor diene and electron rich dienophile.

The LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are very close in energy, which results in strong bonding interaction between the two to form the HOMO and LUMO of both endo and exo TS. Since the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole have the correct symmetry (symmetric) to interact, they interact to form the symmetric HOMO and LUMO of both TS.

The presence of the two electron donating oxygen atoms on 1,3-dioxole raise the energy of both its HOMO and LUMO, making the overlap between the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole much better than the HOMO of cyclohexadiene and the LUMO of 1,3-dioxole. Thus, the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are now the frontier orbitals that interact the most, hence this is an inverse demand Diels-Alder reaction.

=== Reaction Energies and Secondary Orbital Interaction ===

The reaction paths at the endo and exo transition states are shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="text-align: center;"|Reaction Path at the Endo Transition State
! style="text-align: center;"|Reaction Path at the Exo Transition State
|-
|<jmol><jmolApplet>
<uploadedFileContents>ENDO TS OPT TS 631G yhw14.LOG</uploadedFileContents>
<color>white</color>
<size>300</size>
<script>frame 33;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|<jmol><jmolApplet>
<uploadedFileContents>EXO TS OPT TS 631G yhw14.LOG</uploadedFileContents>
<color>white</color>
<size>300</size>
<script>frame 17;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|}

The energies of reactants were taken using the sum of the energies of cyclohexadiene and 1,3-dioxole optimised to their minima at DFT-B3LYP 631-G. The calculations were done using DFT-B3LYP 631-G.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FF4AFF; color: #ffffff" |
! style="background: #FF4AFF; color: #ffffff" | Reactants
! style="background: #FF4AFF; color: #ffffff" | Transition State
! style="background: #FF4AFF; color: #ffffff" | Product
! style="background: #FF4AFF; color: #ffffff" | Activation Energy
! style="background: #FF4AFF; color: #ffffff" | Gibbs Free Energy
|-
|Endo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313622</nowiki>
|<nowiki>-1313849</nowiki>
|160
|<nowiki>-67</nowiki>
|-
|Exo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313614</nowiki>
|<nowiki>-1313846</nowiki>
|168
|<nowiki>-64</nowiki>
|+Table 3: Energies of Reactants, Transition States and Products of both Endo and Exo Pathways in Diels-Alder Reaction of Cyclohexadiene and 1,3-Dioxole (kJ mol-1)
|}

Kinetically favourable product of a reaction is the one that has the lowest activation energy; Thermodynamically favourable product is the product with lowest energy conformer, hence the more stabilised product.

The endo transition state is the kinetic product of this reaction as it has lower activation energy. This could be explained using the secondary orbital interaction between the lone pair orbital on the oxygen atom and the empty π* orbital of diene. This favourable effect stabilises the endo transition state.

As the oxygen atom lone pair is oriented away from the diene π system in the exo transition state, the secondary orbital effect is not present, hence the activation energy of exo reaction is higher.

However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, i.e. increasing temperature, formation of the exo product would be more favourable.

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

Xylylene can react with sulfur dioxide through Diels-Alder reaction via either endo or exo pathways to form a 6-membered ring, or through cheletropic reaction to form a 5-membered ring. The reaction scheme is shown below. Reaction barriers and reaction energies for each pathway were compared to determine the reaction that is most favourable.

[[File:Ex3 reactionscheme yhw14.png|550px|center|thumb|Diagram 6: Reaction Scheme of Xylylene and Sulfur Dioxide]]

=== Intrinsic Reaction Coordinate ===
The following files show the intrinsic reaction coordinates of the three different reaction pathways of xylylene and SO2. Please click to see animation.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Endo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Exo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Cheletropic TS
|-
|[[File:DA endo irc animation yhw14.gif|center]]
|[[File:DA exo irc animation yhw14.gif|center]]
|[[File:Cheletropic irc animation yhw14.gif|center]]
|-
|[[File:DA endo irc plot yhw14.png|center|500px]]
|[[File:DA exo irc plot yhw14.png|center|500px]]
|[[File:Cheletropic irc plot yhw14.png|center|650px]]
|}

=== Reaction Energies and Reaction Barriers ===

[[File:Ex3 reactionprofile yhw14.png|550px|center|thumb|Diagram 7: Reaction Profile of Xylylene and Sulfur Dioxide]]

The energies of reactants were taken using the sum of the energies of xylylene and SO2 optimised to their minima. All calculations were done using semi-empirical PM6 method.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FFD1C3; color: #ffffff" |
! style="background: #FFD1C3; color: #ffffff" | Reactants
! style="background: #FFD1C3; color: #ffffff" | Transition State
! style="background: #FFD1C3; color: #ffffff" | Product
! style="background: #FFD1C3; color: #ffffff" | Activation Energy
! style="background: #FFD1C3; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|237.767824
|56.9576013
|83.391038
|<nowiki>-97.4191847</nowiki>
|-
|Exo
|154.376786
|241.753433
|56.3196048
|87.406647
|<nowiki>-98.0571812</nowiki>
|-
|Cheletropic
|154.376786
|260.08205
|0.013127501
|105.705264
|<nowiki>-154.3636585</nowiki>
|+Table 4: Energies of Reactants, Transition States and Products of Reactions between Xylylene and Sulfur Dioxide (kJ mol-1)
|}

With reference to the reaction profile and Table 4, the Diels-Alder reaction via the endo pathway has the lowest activation energy, making it a more kinetically favourable product, i.e. the kinetic product; the Diels-Alder exo product has a lower energy than endo, however with a higher activation energy hence it will not form under low temperature condition; the cheletropic product is the most stabilised product out of the three and it has the lowest reaction energy, therefore is the thermodynamic product.

=== Instability of Xylylene ===

Xylylene does not follow the Hückel rule (4n+2 electrons) hence it is not aromatic. In addition, it is rich in double bonds, all these factors make xylylene a very unstable molecule.

[[File:Ex3 xylylene instability yhw14.png|550px|center|thumb|Diagram 8: Electrocyclic Reaction Xylylene]]

The driving force of this electrocyclic reaction is the formation of an aromatic 6-membered benzene ring in the benzocyclobutane, which could also be another possible reaction pathway apart from Diels-Alder reaction and cheletropic reaction.

=== Side Reaction between cis-diene in Xylylene 6-membered ring and SO2===

o-Xylylene contains another cis-butadiene fragment located in the 6-membered ring that can undergo a Diels-Alder reaction with SO2. The reaction energies and reaction barriers between endo and exo pathways are compared in the table below.

The energies of reactants were taken using the sum of the energies of xylylene and SO2 optimised to their minima. All calculations were done using semi-empirical PM6 method.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #4EBEBA; color: #ffffff" |
! style="background: #4EBEBA; color: #ffffff" | Reactants
! style="background: #4EBEBA; color: #ffffff" | Transition State
! style="background: #4EBEBA; color: #ffffff" | Product
! style="background: #4EBEBA; color: #ffffff" | Activation Energy
! style="background: #4EBEBA; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|267.984805
|172.272196
|113.608019
|17.89541
|-
|Exo
|154.376786
|275.821924
|176.711916
|121.445138
|22.33513
|+Table 5: Energies of Reactants, Transition States and Products of the Side Reaction in Xylylene 6-membered ring and Sulfur Dioxide (kJ mol-1)
|}

It is clear that both endo and exo Diels-Alder side reactions are kinetically and thermodynamically unfavourable at this site as the activation energies are much higher than the previous reactions mentioned above in Table 4 and the reaction energies show that the reactions are endothermic.

== Conclusion ==

The transition states of three pericyclic reactions were investigated in this computational lab, using GaussView to optimise the reactants, transition states and products respectively, and the vibrational frequencies and intrinsic reaction coordinates were computed.

In the reaction between butadiene and ethene, the importance of molecular orbital symmetry in the interaction of molecular orbitals was illustrated, such that a reaction is only allowed when the molecular orbitals with the same symmetry interact with each other and forbidden when symmetric molecular orbital interact with asymmetric orbitals. Furthermore, the vibration frequency calculation proved that this [4+2] Diels-Alder reaction proceeds via a concerted mechanism as synchronous bond formation was demonstrated. Bonding interaction can be further confirmed as the bond distance between the two termini carbon atoms in the transition state is shorter than the sum of two Van der Waals radii of carbon.

In the reaction of cyclohexadiene and 1,3-dioxole, both the endo and exo transition states were investigated. In general, the endo transition state is kinetically more favourable as it has lower activation barrier, possibly due to the secondary orbital interaction between the lone pair in p orbital on the oxygen atom and the empty π* orbital in the diene, which stabilises the transition state. However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, formation of the exo product could be possible.

The final reaction between xylylene and SO2 again proved that the endo Diels-Alder transition state has the lowest activation energy, making it kinetically favourable at low temperature. However, the cheletropic product is the most stabilised and thermodynamically favourable product. Therefore the reaction would yield the cheletropic product under thermodynamic control instead of the exo Diels-Alder product.

==References==
<references>
<ref name="C-C bond lengths">L. Pauling and L. O. Brockway, ''Journal of the American Chemical Society'', '''1937''', Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref>
<ref name="Van der Waals radius of C">S. S. Batsanov, ''Inorganic Materials'', '''2001''', Volume 37, Number 9, pp. 871-885, https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf.</ref>
</references>

Rep:Mod:yhw14cts

2017-02-10T03:22:59Z

Yhw14: /* Conclusion */

''' Transition States and Reactivity '''

'' Yi Hang Cherie WONG (yhw14) ''
'' CID: 00933828 ''

== Introduction ==
A potential energy surface is a mathematical or graphical function that gives relationship between the energy of a molecule and its geometry with the relative positions of the atoms participating in the reaction. The stationary points may be classified according to the first and second derivatives of the energy with respect to position. At the minimum of a reaction profile, the gradient is represented by the first derivative of the reaction coordinate, which is zero, while curvature is represented by the second derivative, is positive in this case; hence energy rises in all directions. Energy minima correspond to physically stable chemical species, which could be reactants and products. The transition state is defined as the maximum in a reaction profile, where the gradient is again, zero, while curvature is negative; hence energy decreases in one direction, which indicates the reaction pathway of the chemical reaction. The potential energy surface can be computed using Gaussview, which is a graphical interface for Gaussian, where structure and energy of reactants or products can be modelled to illustrate the transition states, which can rarely be obtained experimentally. The intrinsic reaction coordinate can then be calculated and compared to predict the reaction path at a transition state and follow it to the correct minima.

In this computational lab, all of the reactants and products were optimised to their minima, and the transition states were also optimised. The calculations were done by GaussView, using mainly semi-empirical method PM6 and Density Functional Theory-B3LYP-631G. The latter is a more detailed and accurate optimisation, which is more time consuming method as it involves a higher number of basis set. Frequency calculations were performed to show molecular vibrations to confirm the position on the potential energy surface. If all the vibrational frequencies are real, this confirms the structure is a minimum, and vice versa, the presence of imaginary frequency may suggest that the structure is at its transition state. Intrinsic reaction coordinate method was carried out using calculated force constants to predict which conformer a reaction path from the transition state would lead to.

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

The reaction between butadiene and ethene is a typical pericyclic [4+2] Diels-Alder reaction that proceeds via a concerted mechanism through a cyclic transition state. The reaction scheme is shown below.

[[File:Ex1 reactionscheme revised yhw14.png|550px|center|thumb|Diagram 1: Reaction Scheme of Butadiene and Ethene]]

=== Molecular Orbital Analysis ===

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of butadiene and ethene.

[[File:Ex1 mo diagram yhw14 revised v3.png|550px|center|thumb|Diagram 2: MO diagram of Reaction of Butadiene and Ethene]]

Butadiene and ethene were optimised to their minima at semi-empirical method PM6 level. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #06DCFB; color: #ffffff;" |'''Molecule'''
! '''Butadiene'''
! '''Ethene'''
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Butadiene lumo yhw14.png|center|150px]]
|[[File:Ethene lumo yhw14.png|center|150px]]
|-
|Corresponding to the s orbital (symmetric)
|Corresponding to the a orbital (asymmetric)
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Butadiene homo yhw14.png|center|150px]]
|[[File:Ethene homo yhw14.png|center|150px]]
|-
|Corresponding to the a orbital (antisymmetric)
|Corresponding to the s orbital (symmetric)
|}

The transition state was first optimised to its minimum, followed by a transition state calculation at semi-empirical method PM6 level. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #01FCEF; color: #ffffff;" |'''Molecule'''
! '''Transition State'''
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Ts lumo+1 yhw14.png|center|150px]]
|-
|Corresponding to the 5 orbital (asymmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Ts lumo 1 yhw14.png|center|150px]]
|-
|Corresponding to the 4 orbital (symmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Ts homo yhw14.png|center|150px]]
|-
|Corresponding to the 3 orbital (symmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Ts homo-1 yhw14.png|center|150px]]
|-
|Corresponding to the 2 orbital (asymmetrical)
|}

Based on the MO diagram and the computed MOs shown above, a reaction is only allowed when the MOs with the same symmetry interact with each other, i.e. symmetric-symmetric and asymmetric-asymmetric interactions; and a reaction is forbidden when the MOs with different symmetry interact with each other, i.e. symmetric-asymmetric interactions. The MOs have to be close in energy in order to overlap effectively.

In the reaction between butadiene and ethene, the butadiene asymmetric MO interacts with the ethene asymmetric MO to give the MOs 2 and 5 of the transition state, and the butadiene symmetric MO interacts with the ethene symmetric MO to give the MOs 3 and 4 of the transition state. Therefore, a reaction is allowed when the symmetry labels of the MOs of the reactants are the same; and forbidden when the symmetry labels are different.

The orbital overlap integral is zero in a symmetric-asymmetric interaction and non-zero in symmetric-symmetric and asymmetric-asymmetric interactions.

=== Bond Length Analysis ===

The changes in bond lengths between carbons in reactant, transition state and product as the reaction progresses were studied by comparing the bond lengths between carbons before and after the reaction. The summary of bond lengths is shown below.
[[File:Ex1 bondlength yhw14.png|470px|center|thumb|Diagram 3: Labelled carbons]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #0000FF; color: #ffffff" | State
! style="background: #0000FF; color: #ffffff" | C1-C2
! style="background: #0000FF; color: #ffffff" | C2-C3
! style="background: #0000FF; color: #ffffff" | C3-C4
! style="background: #0000FF; color: #ffffff" | C4-C5
! style="background: #0000FF; color: #ffffff" | C5-C6
! style="background: #0000FF; color: #ffffff" | C6-C1
|-
|Reactants
|1.335
|1.468
|1.335
|/
|1.327
|/
|-
|Transition State
|1.380
|1.411
|1.380
|2.115
|1.382
|2.114
|-
|Product
|1.500
|1.338
|1.500
|1.540
|1.540
|1.540
|+Table 1: Measurements of the C-C bond lengths of the reactants, transition state and products (Å)
|}

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #97A7ED; color: #ffffff" |
! style="background: #97A7ED; color: #ffffff" | sp3-sp3 (C-C single bond) <ref name="C-C bond lengths"/>
! style="background: #97A7ED; color: #ffffff" | sp2-sp2 (C-C double bond) <ref name="C-C bond lengths"/>
! style="background: #97A7ED; color: #ffffff" | Van der Waals radius of the C atom <ref name="Van der Waals radius of C"/>
|-
|Bond Lengths (Å)
|1.54
|1.33
|1.7
|+Table 2: Literature Values of C-C bond lengths and Van der Waals radius of the C atom (Å)
|}
As the reaction progresses, the bond lengths between C1-C2, C3-C4 and C5-C6 lengthen from ~1.3 Å to ~1.5 Å as the bond order decrease to one, whereas bond length of C2-C3 shortens from ~1.5 Å to ~1.3 Å as the bond order increases from one to two.
This could be explained as the increase in bond length suggest a change from sp2-sp2 (C-C double bond) with typical bond length of 1.33 Å <ref name="C-C bond lengths"/> to sp3-sp3 (C-C single bond) with typical bond length of 1.54 Å <ref name="C-C bond lengths"/>, and vice versa for the decrease in bond length. Based on the calculated bond lengths above in Table 1, it is clear that bond lengths and bond orders of the reactants changed during the reaction and the new bonds formed at C4-C5 and C6-C1 are single bonds as they have bond lengths of 1.54 Å.
The typical Van der Waals radius of the C atom is 1.7 Å <ref name="Van der Waals radius of C"/>. As the bond lengths between C4-C5 and C6-C1 of the transition state are shorter than 2 x Van der Waals radii of C, this reflects that C-C bonds are forming at the transition state.

=== Vibration Analysis ===

The imaginary frequency at -948.32 cm-1 corresponds to the reaction path at the transition state, which shows a synchronous bond formation, which agrees with the concerted mechanism of [4+2] cycloaddition, where both reaction centres converge at the same time to form two new bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 15;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Reaction Path at the Transition State
|}

The lowest positive frequency at 145.14 cm-1 is asynchronous as shown below, where one of the C from the ethene moves towards the butadiene reaction centre and the other C moves away. This suggests that bonds are formed one at a time.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 16;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Lowest positive frequency
|}

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

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via two different pathways, endo and exo, which are shown in the reaction scheme below. GaussView calculations could be carried out to compare the reaction barriers and reaction energies of the two pathways to determine the kinetic and thermodynamic products.

[[File:Ex2 reactionscheme.png|550px|center|thumb|Diagram 4: Reaction Scheme of Cyclohexadiene and 1,3-Dioxole]]

=== Frequency Analysis ===

Frequency calculations were run to confirm that reactants (cyclohexadiene and 1,3-dioxole), and both endo and exo products did not have imaginary vibrations, suggesting they are structures at relative minima to the transition state; whereas both endo and exo transition states each had one imaginary vibration.

=== Molecular Orbital Analysis ===

Cyclohexadiene and 1,3-dioxole were optimised to their minima at DFT-B3LYP 631-G level. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #9A03FE; color: #ffffff;" |'''Molecule'''
! '''Cyclohexadiene'''
! '''1,3-Dioxole'''
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Cyclo lumo 631g yhw14.png|center|150px]]
|[[File:Dioxole lumo 631g yhw14.png|center|150px]]
|-
|Corresponding to the s orbital
|Corresponding to the a orbital
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Cyclo homo 631g yhw14.png|center|150px]]
|[[File:Dioxole homo 631g yhw14.png|center|150px]]
|-
|Corresponding to the a orbital
|Corresponding to the s orbital
|}

The transition state was first optimised to its minimum, followed by a transition state calculation at DFT-B3LYP 631-G level. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #BD5CFE; color: #ffffff;" |'''Molecule'''
! '''Endo Transition State'''
! '''Exo Transition State'''
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Endo ts lumo+1 yhw14.png|center|150px]]
|[[File:Exo ts lumo+1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 5 orbital (asymmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Endo ts lumo yhw14.png|center|150px]]
|[[File:Exo ts lumo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 4 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Endo ts homo yhw14.png|center|150px]]
|[[File:Exo ts homo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 3 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Endo ts homo-1 yhw14.png|center|150px]]
|[[File:Exo ts homo-1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 2 orbital (asymmetric)
|}

The diagram below illustrates the π molecular orbitals of cyclohexadiene and 1,3-dioxole involved in the formation of the transition state.

[[File:Ex2 mo diagram yhw14.png|550px|center|thumb|Diagram 5: MO diagram of Reaction of Cyclohexadiene and 1,3-dioxole]]

=== Normal Demand vs Inverse Demand Diels-Alder Reaction ===

A normal electron demand Diels-Alder reaction can be defined as a reaction between electron rich diene and electron poor dienophile. An inverse electron demand is the reaction between electron poor diene and electron rich dienophile.

The LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are very close in energy, which results in strong bonding interaction between the two to form the HOMO and LUMO of both endo and exo TS. Since the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole have the correct symmetry (symmetric) to interact, they interact to form the symmetric HOMO and LUMO of both TS.

The presence of the two electron donating oxygen atoms on 1,3-dioxole raise the energy of both its HOMO and LUMO, making the overlap between the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole much better than the HOMO of cyclohexadiene and the LUMO of 1,3-dioxole. Thus, the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are now the frontier orbitals that interact the most, hence this is an inverse demand Diels-Alder reaction.

=== Reaction Energies and Secondary Orbital Interaction ===

The reaction paths at the endo and exo transition states are shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="text-align: center;"|Reaction Path at the Endo Transition State
! style="text-align: center;"|Reaction Path at the Exo Transition State
|-
|<jmol><jmolApplet>
<uploadedFileContents>ENDO TS OPT TS 631G yhw14.LOG</uploadedFileContents>
<color>white</color>
<size>300</size>
<script>frame 33;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|<jmol><jmolApplet>
<uploadedFileContents>EXO TS OPT TS 631G yhw14.LOG</uploadedFileContents>
<color>white</color>
<size>300</size>
<script>frame 17;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|}

The energies of reactants were taken using the sum of the energies of cyclohexadiene and 1,3-dioxole optimised to their minima at DFT-B3LYP 631-G. The calculations were done using DFT-B3LYP 631-G.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FF4AFF; color: #ffffff" |
! style="background: #FF4AFF; color: #ffffff" | Reactants
! style="background: #FF4AFF; color: #ffffff" | Transition State
! style="background: #FF4AFF; color: #ffffff" | Product
! style="background: #FF4AFF; color: #ffffff" | Activation Energy
! style="background: #FF4AFF; color: #ffffff" | Gibbs Free Energy
|-
|Endo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313622</nowiki>
|<nowiki>-1313849</nowiki>
|160
|<nowiki>-67</nowiki>
|-
|Exo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313614</nowiki>
|<nowiki>-1313846</nowiki>
|168
|<nowiki>-64</nowiki>
|+Table 3: Energies of Reactants, Transition States and Products of both Endo and Exo Pathways in Diels-Alder Reaction of Cyclohexadiene and 1,3-Dioxole (kJ mol-1)
|}

Kinetically favourable product of a reaction is the one that has the lowest activation energy; Thermodynamically favourable product is the product with lowest energy conformer, hence the more stabilised product.

The endo transition state is the kinetic product of this reaction as it has lower activation energy. This could be explained using the secondary orbital interaction between the lone pair orbital on the oxygen atom and the empty π* orbital of diene. This favourable effect stabilises the endo transition state.

As the oxygen atom lone pair is oriented away from the diene π system in the exo transition state, the secondary orbital effect is not present, hence the activation energy of exo reaction is higher.

However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, i.e. increasing temperature, formation of the exo product would be more favourable.

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

Xylylene can react with sulfur dioxide through Diels-Alder reaction via either endo or exo pathways to form a 6-membered ring, or through cheletropic reaction to form a 5-membered ring. The reaction scheme is shown below. Reaction barriers and reaction energies for each pathway were compared to determine the reaction that is most favourable.

[[File:Ex3 reactionscheme yhw14.png|550px|center|thumb|Diagram 6: Reaction Scheme of Xylylene and Sulfur Dioxide]]

=== Intrinsic Reaction Coordinate ===
The following files show the intrinsic reaction coordinates of the three different reaction pathways of xylylene and SO2. Please click to see animation.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Endo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Exo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Cheletropic TS
|-
|[[File:DA endo irc animation yhw14.gif|center]]
|[[File:DA exo irc animation yhw14.gif|center]]
|[[File:Cheletropic irc animation yhw14.gif|center]]
|-
|[[File:DA endo irc plot yhw14.png|center|500px]]
|[[File:DA exo irc plot yhw14.png|center|500px]]
|[[File:Cheletropic irc plot yhw14.png|center|650px]]
|}

=== Reaction Energies and Reaction Barriers ===

[[File:Ex3 reactionprofile yhw14.png|550px|center|thumb|Diagram 7: Reaction Profile of Xylylene and Sulfur Dioxide]]

The energies of reactants were taken using the sum of the energies of xylylene and SO2 optimised to their minima. All calculations were done using semi-empirical PM6 method.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FFD1C3; color: #ffffff" |
! style="background: #FFD1C3; color: #ffffff" | Reactants
! style="background: #FFD1C3; color: #ffffff" | Transition State
! style="background: #FFD1C3; color: #ffffff" | Product
! style="background: #FFD1C3; color: #ffffff" | Activation Energy
! style="background: #FFD1C3; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|237.767824
|56.9576013
|83.391038
|<nowiki>-97.4191847</nowiki>
|-
|Exo
|154.376786
|241.753433
|56.3196048
|87.406647
|<nowiki>-98.0571812</nowiki>
|-
|Cheletropic
|154.376786
|260.08205
|0.013127501
|105.705264
|<nowiki>-154.3636585</nowiki>
|+Table 4: Energies of Reactants, Transition States and Products of Reactions between Xylylene and Sulfur Dioxide (kJ mol-1)
|}

With reference to the reaction profile and Table 4, the Diels-Alder reaction via the endo pathway has the lowest activation energy, making it a more kinetically favourable product, i.e. the kinetic product; the Diels-Alder exo product has a lower energy than endo, however with a higher activation energy hence it will not form under low temperature condition; the cheletropic product is the most stabilised product out of the three and it has the lowest reaction energy, therefore is the thermodynamic product.

=== Instability of Xylylene ===

Xylylene does not follow the Hückel rule (4n+2 electrons) hence it is not aromatic. In addition, it is rich in double bonds, all these factors make xylylene a very unstable molecule.

[[File:Ex3 xylylene instability yhw14.png|550px|center|thumb|Diagram 8: Electrocyclic Reaction Xylylene]]

The driving force of this electrocyclic reaction is the formation of an aromatic 6-membered benzene ring in the benzocyclobutane, which could also be another possible reaction pathway apart from Diels-Alder reaction and cheletropic reaction.

=== Side Reaction between cis-diene in Xylylene 6-membered ring and SO2===

o-Xylylene contains another cis-butadiene fragment located in the 6-membered ring that can undergo a Diels-Alder reaction with SO2. The reaction energies and reaction barriers between endo and exo pathways are compared in the table below.

The energies of reactants were taken using the sum of the energies of xylylene and SO2 optimised to their minima. All calculations were done using semi-empirical PM6 method.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #4EBEBA; color: #ffffff" |
! style="background: #4EBEBA; color: #ffffff" | Reactants
! style="background: #4EBEBA; color: #ffffff" | Transition State
! style="background: #4EBEBA; color: #ffffff" | Product
! style="background: #4EBEBA; color: #ffffff" | Activation Energy
! style="background: #4EBEBA; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|267.984805
|172.272196
|113.608019
|17.89541
|-
|Exo
|154.376786
|275.821924
|176.711916
|121.445138
|22.33513
|+Table 5: Energies of Reactants, Transition States and Products of the Side Reaction in Xylylene 6-membered ring and Sulfur Dioxide (kJ mol-1)
|}

It is clear that both endo and exo Diels-Alder side reactions are kinetically and thermodynamically unfavourable at this site as the activation energies are much higher than the previous reactions mentioned above in Table 4 and the reaction energies show that the reactions are endothermic.

== Conclusion ==

The transition states of three pericyclic reactions were investigated in this computational lab, using GaussView to optimise the reactants, transition states and products respectively, and the vibrational frequencies and intrinsic reaction coordinates were computed.

In the reaction between butadiene and ethene, the importance of molecular orbital symmetry in the interaction of molecular orbitals was illustrated, such that a reaction is only allowed when the molecular orbitals with the same symmetry interact with each other and forbidden when symmetric molecular orbital interact with asymmetric orbitals. Furthermore, the vibration frequency calculation proved that this [4+2] Diels-Alder reaction proceeds via a concerted mechanism as synchronous bond formation was demonstrated. Bonding interaction can be further confirmed as the bond distance between the two termini carbon atoms in the transition state is shorter than the sum of two Van der Waals radii of carbon.

In the reaction of cyclohexadiene and 1,3-dioxole, both the endo and exo transition states were investigated. In general, the endo transition state is kinetically more favourable as it has lower activation barrier, possibly due to the secondary orbital interaction between the lone pair in p orbital on the oxygen atom and the empty π* orbital in the diene, which stabilises the transition state. However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, formation of the exo product could be possible.

The final reaction between xylylene and SO2 again proved that the endo Diels-Alder transition state has the lowest activation energy, making it kinetically favourable at low temperature. However, the cheletropic product is the most stabilised and thermodynamically favourable product. Therefore the reaction would yield the cheletropic product under thermodynamic control instead of the exo Diels-Alder product.

==References==
<references>
<ref name="C-C bond lengths">L. Pauling and L. O. Brockway, ''Journal of the American Chemical Society'', '''1937''', Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref>
<ref name="Van der Waals radius of C">S. S. Batsanov, ''Inorganic Materials'', '''2001''', Volume 37, Number 9, pp. 871-885, https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf.</ref>
</references>

Rep:Mod:yhw14cts

2017-02-10T03:20:28Z

Yhw14: /* Exercise 3: Diels-Alder vs Cheletropic */

''' Transition States and Reactivity '''

'' Yi Hang Cherie WONG (yhw14) ''
'' CID: 00933828 ''

== Introduction ==
A potential energy surface is a mathematical or graphical function that gives relationship between the energy of a molecule and its geometry with the relative positions of the atoms participating in the reaction. The stationary points may be classified according to the first and second derivatives of the energy with respect to position. At the minimum of a reaction profile, the gradient is represented by the first derivative of the reaction coordinate, which is zero, while curvature is represented by the second derivative, is positive in this case; hence energy rises in all directions. Energy minima correspond to physically stable chemical species, which could be reactants and products. The transition state is defined as the maximum in a reaction profile, where the gradient is again, zero, while curvature is negative; hence energy decreases in one direction, which indicates the reaction pathway of the chemical reaction. The potential energy surface can be computed using Gaussview, which is a graphical interface for Gaussian, where structure and energy of reactants or products can be modelled to illustrate the transition states, which can rarely be obtained experimentally. The intrinsic reaction coordinate can then be calculated and compared to predict the reaction path at a transition state and follow it to the correct minima.

In this computational lab, all of the reactants and products were optimised to their minima, and the transition states were also optimised. The calculations were done by GaussView, using mainly semi-empirical method PM6 and Density Functional Theory-B3LYP-631G. The latter is a more detailed and accurate optimisation, which is more time consuming method as it involves a higher number of basis set. Frequency calculations were performed to show molecular vibrations to confirm the position on the potential energy surface. If all the vibrational frequencies are real, this confirms the structure is a minimum, and vice versa, the presence of imaginary frequency may suggest that the structure is at its transition state. Intrinsic reaction coordinate method was carried out using calculated force constants to predict which conformer a reaction path from the transition state would lead to.

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

The reaction between butadiene and ethene is a typical pericyclic [4+2] Diels-Alder reaction that proceeds via a concerted mechanism through a cyclic transition state. The reaction scheme is shown below.

[[File:Ex1 reactionscheme revised yhw14.png|550px|center|thumb|Diagram 1: Reaction Scheme of Butadiene and Ethene]]

=== Molecular Orbital Analysis ===

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of butadiene and ethene.

[[File:Ex1 mo diagram yhw14 revised v3.png|550px|center|thumb|Diagram 2: MO diagram of Reaction of Butadiene and Ethene]]

Butadiene and ethene were optimised to their minima at semi-empirical method PM6 level. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #06DCFB; color: #ffffff;" |'''Molecule'''
! '''Butadiene'''
! '''Ethene'''
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Butadiene lumo yhw14.png|center|150px]]
|[[File:Ethene lumo yhw14.png|center|150px]]
|-
|Corresponding to the s orbital (symmetric)
|Corresponding to the a orbital (asymmetric)
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Butadiene homo yhw14.png|center|150px]]
|[[File:Ethene homo yhw14.png|center|150px]]
|-
|Corresponding to the a orbital (antisymmetric)
|Corresponding to the s orbital (symmetric)
|}

The transition state was first optimised to its minimum, followed by a transition state calculation at semi-empirical method PM6 level. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #01FCEF; color: #ffffff;" |'''Molecule'''
! '''Transition State'''
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Ts lumo+1 yhw14.png|center|150px]]
|-
|Corresponding to the 5 orbital (asymmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Ts lumo 1 yhw14.png|center|150px]]
|-
|Corresponding to the 4 orbital (symmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Ts homo yhw14.png|center|150px]]
|-
|Corresponding to the 3 orbital (symmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Ts homo-1 yhw14.png|center|150px]]
|-
|Corresponding to the 2 orbital (asymmetrical)
|}

Based on the MO diagram and the computed MOs shown above, a reaction is only allowed when the MOs with the same symmetry interact with each other, i.e. symmetric-symmetric and asymmetric-asymmetric interactions; and a reaction is forbidden when the MOs with different symmetry interact with each other, i.e. symmetric-asymmetric interactions. The MOs have to be close in energy in order to overlap effectively.

In the reaction between butadiene and ethene, the butadiene asymmetric MO interacts with the ethene asymmetric MO to give the MOs 2 and 5 of the transition state, and the butadiene symmetric MO interacts with the ethene symmetric MO to give the MOs 3 and 4 of the transition state. Therefore, a reaction is allowed when the symmetry labels of the MOs of the reactants are the same; and forbidden when the symmetry labels are different.

The orbital overlap integral is zero in a symmetric-asymmetric interaction and non-zero in symmetric-symmetric and asymmetric-asymmetric interactions.

=== Bond Length Analysis ===

The changes in bond lengths between carbons in reactant, transition state and product as the reaction progresses were studied by comparing the bond lengths between carbons before and after the reaction. The summary of bond lengths is shown below.
[[File:Ex1 bondlength yhw14.png|470px|center|thumb|Diagram 3: Labelled carbons]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #0000FF; color: #ffffff" | State
! style="background: #0000FF; color: #ffffff" | C1-C2
! style="background: #0000FF; color: #ffffff" | C2-C3
! style="background: #0000FF; color: #ffffff" | C3-C4
! style="background: #0000FF; color: #ffffff" | C4-C5
! style="background: #0000FF; color: #ffffff" | C5-C6
! style="background: #0000FF; color: #ffffff" | C6-C1
|-
|Reactants
|1.335
|1.468
|1.335
|/
|1.327
|/
|-
|Transition State
|1.380
|1.411
|1.380
|2.115
|1.382
|2.114
|-
|Product
|1.500
|1.338
|1.500
|1.540
|1.540
|1.540
|+Table 1: Measurements of the C-C bond lengths of the reactants, transition state and products (Å)
|}

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #97A7ED; color: #ffffff" |
! style="background: #97A7ED; color: #ffffff" | sp3-sp3 (C-C single bond) <ref name="C-C bond lengths"/>
! style="background: #97A7ED; color: #ffffff" | sp2-sp2 (C-C double bond) <ref name="C-C bond lengths"/>
! style="background: #97A7ED; color: #ffffff" | Van der Waals radius of the C atom <ref name="Van der Waals radius of C"/>
|-
|Bond Lengths (Å)
|1.54
|1.33
|1.7
|+Table 2: Literature Values of C-C bond lengths and Van der Waals radius of the C atom (Å)
|}
As the reaction progresses, the bond lengths between C1-C2, C3-C4 and C5-C6 lengthen from ~1.3 Å to ~1.5 Å as the bond order decrease to one, whereas bond length of C2-C3 shortens from ~1.5 Å to ~1.3 Å as the bond order increases from one to two.
This could be explained as the increase in bond length suggest a change from sp2-sp2 (C-C double bond) with typical bond length of 1.33 Å <ref name="C-C bond lengths"/> to sp3-sp3 (C-C single bond) with typical bond length of 1.54 Å <ref name="C-C bond lengths"/>, and vice versa for the decrease in bond length. Based on the calculated bond lengths above in Table 1, it is clear that bond lengths and bond orders of the reactants changed during the reaction and the new bonds formed at C4-C5 and C6-C1 are single bonds as they have bond lengths of 1.54 Å.
The typical Van der Waals radius of the C atom is 1.7 Å <ref name="Van der Waals radius of C"/>. As the bond lengths between C4-C5 and C6-C1 of the transition state are shorter than 2 x Van der Waals radii of C, this reflects that C-C bonds are forming at the transition state.

=== Vibration Analysis ===

The imaginary frequency at -948.32 cm-1 corresponds to the reaction path at the transition state, which shows a synchronous bond formation, which agrees with the concerted mechanism of [4+2] cycloaddition, where both reaction centres converge at the same time to form two new bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 15;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Reaction Path at the Transition State
|}

The lowest positive frequency at 145.14 cm-1 is asynchronous as shown below, where one of the C from the ethene moves towards the butadiene reaction centre and the other C moves away. This suggests that bonds are formed one at a time.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 16;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Lowest positive frequency
|}

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

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via two different pathways, endo and exo, which are shown in the reaction scheme below. GaussView calculations could be carried out to compare the reaction barriers and reaction energies of the two pathways to determine the kinetic and thermodynamic products.

[[File:Ex2 reactionscheme.png|550px|center|thumb|Diagram 4: Reaction Scheme of Cyclohexadiene and 1,3-Dioxole]]

=== Frequency Analysis ===

Frequency calculations were run to confirm that reactants (cyclohexadiene and 1,3-dioxole), and both endo and exo products did not have imaginary vibrations, suggesting they are structures at relative minima to the transition state; whereas both endo and exo transition states each had one imaginary vibration.

=== Molecular Orbital Analysis ===

Cyclohexadiene and 1,3-dioxole were optimised to their minima at DFT-B3LYP 631-G level. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #9A03FE; color: #ffffff;" |'''Molecule'''
! '''Cyclohexadiene'''
! '''1,3-Dioxole'''
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Cyclo lumo 631g yhw14.png|center|150px]]
|[[File:Dioxole lumo 631g yhw14.png|center|150px]]
|-
|Corresponding to the s orbital
|Corresponding to the a orbital
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Cyclo homo 631g yhw14.png|center|150px]]
|[[File:Dioxole homo 631g yhw14.png|center|150px]]
|-
|Corresponding to the a orbital
|Corresponding to the s orbital
|}

The transition state was first optimised to its minimum, followed by a transition state calculation at DFT-B3LYP 631-G level. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #BD5CFE; color: #ffffff;" |'''Molecule'''
! '''Endo Transition State'''
! '''Exo Transition State'''
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Endo ts lumo+1 yhw14.png|center|150px]]
|[[File:Exo ts lumo+1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 5 orbital (asymmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Endo ts lumo yhw14.png|center|150px]]
|[[File:Exo ts lumo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 4 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Endo ts homo yhw14.png|center|150px]]
|[[File:Exo ts homo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 3 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Endo ts homo-1 yhw14.png|center|150px]]
|[[File:Exo ts homo-1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 2 orbital (asymmetric)
|}

The diagram below illustrates the π molecular orbitals of cyclohexadiene and 1,3-dioxole involved in the formation of the transition state.

[[File:Ex2 mo diagram yhw14.png|550px|center|thumb|Diagram 5: MO diagram of Reaction of Cyclohexadiene and 1,3-dioxole]]

=== Normal Demand vs Inverse Demand Diels-Alder Reaction ===

A normal electron demand Diels-Alder reaction can be defined as a reaction between electron rich diene and electron poor dienophile. An inverse electron demand is the reaction between electron poor diene and electron rich dienophile.

The LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are very close in energy, which results in strong bonding interaction between the two to form the HOMO and LUMO of both endo and exo TS. Since the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole have the correct symmetry (symmetric) to interact, they interact to form the symmetric HOMO and LUMO of both TS.

The presence of the two electron donating oxygen atoms on 1,3-dioxole raise the energy of both its HOMO and LUMO, making the overlap between the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole much better than the HOMO of cyclohexadiene and the LUMO of 1,3-dioxole. Thus, the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are now the frontier orbitals that interact the most, hence this is an inverse demand Diels-Alder reaction.

=== Reaction Energies and Secondary Orbital Interaction ===

The reaction paths at the endo and exo transition states are shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="text-align: center;"|Reaction Path at the Endo Transition State
! style="text-align: center;"|Reaction Path at the Exo Transition State
|-
|<jmol><jmolApplet>
<uploadedFileContents>ENDO TS OPT TS 631G yhw14.LOG</uploadedFileContents>
<color>white</color>
<size>300</size>
<script>frame 33;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|<jmol><jmolApplet>
<uploadedFileContents>EXO TS OPT TS 631G yhw14.LOG</uploadedFileContents>
<color>white</color>
<size>300</size>
<script>frame 17;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|}

The energies of reactants were taken using the sum of the energies of cyclohexadiene and 1,3-dioxole optimised to their minima at DFT-B3LYP 631-G. The calculations were done using DFT-B3LYP 631-G.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FF4AFF; color: #ffffff" |
! style="background: #FF4AFF; color: #ffffff" | Reactants
! style="background: #FF4AFF; color: #ffffff" | Transition State
! style="background: #FF4AFF; color: #ffffff" | Product
! style="background: #FF4AFF; color: #ffffff" | Activation Energy
! style="background: #FF4AFF; color: #ffffff" | Gibbs Free Energy
|-
|Endo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313622</nowiki>
|<nowiki>-1313849</nowiki>
|160
|<nowiki>-67</nowiki>
|-
|Exo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313614</nowiki>
|<nowiki>-1313846</nowiki>
|168
|<nowiki>-64</nowiki>
|+Table 3: Energies of Reactants, Transition States and Products of both Endo and Exo Pathways in Diels-Alder Reaction of Cyclohexadiene and 1,3-Dioxole (kJ mol-1)
|}

Kinetically favourable product of a reaction is the one that has the lowest activation energy; Thermodynamically favourable product is the product with lowest energy conformer, hence the more stabilised product.

The endo transition state is the kinetic product of this reaction as it has lower activation energy. This could be explained using the secondary orbital interaction between the lone pair orbital on the oxygen atom and the empty π* orbital of diene. This favourable effect stabilises the endo transition state.

As the oxygen atom lone pair is oriented away from the diene π system in the exo transition state, the secondary orbital effect is not present, hence the activation energy of exo reaction is higher.

However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, i.e. increasing temperature, formation of the exo product would be more favourable.

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

Xylylene can react with sulfur dioxide through Diels-Alder reaction via either endo or exo pathways to form a 6-membered ring, or through cheletropic reaction to form a 5-membered ring. The reaction scheme is shown below. Reaction barriers and reaction energies for each pathway were compared to determine the reaction that is most favourable.

[[File:Ex3 reactionscheme yhw14.png|550px|center|thumb|Diagram 6: Reaction Scheme of Xylylene and Sulfur Dioxide]]

=== Intrinsic Reaction Coordinate ===
The following files show the intrinsic reaction coordinates of the three different reaction pathways of xylylene and SO2. Please click to see animation.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Endo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Exo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Cheletropic TS
|-
|[[File:DA endo irc animation yhw14.gif|center]]
|[[File:DA exo irc animation yhw14.gif|center]]
|[[File:Cheletropic irc animation yhw14.gif|center]]
|-
|[[File:DA endo irc plot yhw14.png|center|500px]]
|[[File:DA exo irc plot yhw14.png|center|500px]]
|[[File:Cheletropic irc plot yhw14.png|center|650px]]
|}

=== Reaction Energies and Reaction Barriers ===

[[File:Ex3 reactionprofile yhw14.png|550px|center|thumb|Diagram 7: Reaction Profile of Xylylene and Sulfur Dioxide]]

The energies of reactants were taken using the sum of the energies of xylylene and SO2 optimised to their minima. All calculations were done using semi-empirical PM6 method.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FFD1C3; color: #ffffff" |
! style="background: #FFD1C3; color: #ffffff" | Reactants
! style="background: #FFD1C3; color: #ffffff" | Transition State
! style="background: #FFD1C3; color: #ffffff" | Product
! style="background: #FFD1C3; color: #ffffff" | Activation Energy
! style="background: #FFD1C3; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|237.767824
|56.9576013
|83.391038
|<nowiki>-97.4191847</nowiki>
|-
|Exo
|154.376786
|241.753433
|56.3196048
|87.406647
|<nowiki>-98.0571812</nowiki>
|-
|Cheletropic
|154.376786
|260.08205
|0.013127501
|105.705264
|<nowiki>-154.3636585</nowiki>
|+Table 4: Energies of Reactants, Transition States and Products of Reactions between Xylylene and Sulfur Dioxide (kJ mol-1)
|}

With reference to the reaction profile and Table 4, the Diels-Alder reaction via the endo pathway has the lowest activation energy, making it a more kinetically favourable product, i.e. the kinetic product; the Diels-Alder exo product has a lower energy than endo, however with a higher activation energy hence it will not form under low temperature condition; the cheletropic product is the most stabilised product out of the three and it has the lowest reaction energy, therefore is the thermodynamic product.

=== Instability of Xylylene ===

Xylylene does not follow the Hückel rule (4n+2 electrons) hence it is not aromatic. In addition, it is rich in double bonds, all these factors make xylylene a very unstable molecule.

[[File:Ex3 xylylene instability yhw14.png|550px|center|thumb|Diagram 8: Electrocyclic Reaction Xylylene]]

The driving force of this electrocyclic reaction is the formation of an aromatic 6-membered benzene ring in the benzocyclobutane, which could also be another possible reaction pathway apart from Diels-Alder reaction and cheletropic reaction.

=== Side Reaction between cis-diene in Xylylene 6-membered ring and SO2===

o-Xylylene contains another cis-butadiene fragment located in the 6-membered ring that can undergo a Diels-Alder reaction with SO2. The reaction energies and reaction barriers between endo and exo pathways are compared in the table below.

The energies of reactants were taken using the sum of the energies of xylylene and SO2 optimised to their minima. All calculations were done using semi-empirical PM6 method.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #4EBEBA; color: #ffffff" |
! style="background: #4EBEBA; color: #ffffff" | Reactants
! style="background: #4EBEBA; color: #ffffff" | Transition State
! style="background: #4EBEBA; color: #ffffff" | Product
! style="background: #4EBEBA; color: #ffffff" | Activation Energy
! style="background: #4EBEBA; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|267.984805
|172.272196
|113.608019
|17.89541
|-
|Exo
|154.376786
|275.821924
|176.711916
|121.445138
|22.33513
|+Table 5: Energies of Reactants, Transition States and Products of the Side Reaction in Xylylene 6-membered ring and Sulfur Dioxide (kJ mol-1)
|}

It is clear that both endo and exo Diels-Alder side reactions are kinetically and thermodynamically unfavourable at this site as the activation energies are much higher than the previous reactions mentioned above in Table 4 and the reaction energies show that the reactions are endothermic.

== Conclusion ==

The transition states of three pericyclic reactions were investigated in this computational lab, using Gaussian to optimise the reactants, transition states and products respectively, and the vibrational frequencies and intrinsic reaction coordinates were computed.

In the reaction between butadiene and ethene, the importance of molecular orbital symmetry in the interaction of molecular orbitals was illustrated, such that a reaction is only allowed when the molecular orbitals with the same symmetry labels interact with each other and forbidden when symmetric molecular orbital interact with asymmetric orbitals. Furthermore, the vibration frequency calculation proved that this [4+2] Diels-Alder reaction proceeds via a concerted mechanism as synchronous bond formation was demonstrated. Bonding interaction can be further confirmed as the bond distance between the two termini carbon atoms in the transition state is shorter than the sum of two Van der Waals radii of carbon.

In the reaction of cyclohexadiene and 1,3-dioxole, both the endo and exo transition states were investigated. In general, the endo transition state is kinetically more favourable as it has lower activation barrier, possibly due to the secondary orbital interaction between the lone pair in p orbital on the oxygen atom and the empty pi* orbital in the diene, which stabilises the transition state. However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, formation of the exo product could be possible.

The final reaction between xylylene and SO2 again proved that the endo Diels-Alder transition state has the lowest activation energy, making it kinetically favourable at low temperature. However, the cheletropic product is the most stabilised and thermodynamically favourable product. Therefore the reaction would yield the cheletropic product under thermodynamic control instead of the exo Diels-Alder product.

==References==
<references>
<ref name="C-C bond lengths">L. Pauling and L. O. Brockway, ''Journal of the American Chemical Society'', '''1937''', Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref>
<ref name="Van der Waals radius of C">S. S. Batsanov, ''Inorganic Materials'', '''2001''', Volume 37, Number 9, pp. 871-885, https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf.</ref>
</references>

Rep:Mod:yhw14cts

2017-02-10T03:18:41Z

Yhw14: /* Exercise 3: Diels-Alder vs Cheletropic */

''' Transition States and Reactivity '''

'' Yi Hang Cherie WONG (yhw14) ''
'' CID: 00933828 ''

== Introduction ==
A potential energy surface is a mathematical or graphical function that gives relationship between the energy of a molecule and its geometry with the relative positions of the atoms participating in the reaction. The stationary points may be classified according to the first and second derivatives of the energy with respect to position. At the minimum of a reaction profile, the gradient is represented by the first derivative of the reaction coordinate, which is zero, while curvature is represented by the second derivative, is positive in this case; hence energy rises in all directions. Energy minima correspond to physically stable chemical species, which could be reactants and products. The transition state is defined as the maximum in a reaction profile, where the gradient is again, zero, while curvature is negative; hence energy decreases in one direction, which indicates the reaction pathway of the chemical reaction. The potential energy surface can be computed using Gaussview, which is a graphical interface for Gaussian, where structure and energy of reactants or products can be modelled to illustrate the transition states, which can rarely be obtained experimentally. The intrinsic reaction coordinate can then be calculated and compared to predict the reaction path at a transition state and follow it to the correct minima.

In this computational lab, all of the reactants and products were optimised to their minima, and the transition states were also optimised. The calculations were done by GaussView, using mainly semi-empirical method PM6 and Density Functional Theory-B3LYP-631G. The latter is a more detailed and accurate optimisation, which is more time consuming method as it involves a higher number of basis set. Frequency calculations were performed to show molecular vibrations to confirm the position on the potential energy surface. If all the vibrational frequencies are real, this confirms the structure is a minimum, and vice versa, the presence of imaginary frequency may suggest that the structure is at its transition state. Intrinsic reaction coordinate method was carried out using calculated force constants to predict which conformer a reaction path from the transition state would lead to.

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

The reaction between butadiene and ethene is a typical pericyclic [4+2] Diels-Alder reaction that proceeds via a concerted mechanism through a cyclic transition state. The reaction scheme is shown below.

[[File:Ex1 reactionscheme revised yhw14.png|550px|center|thumb|Diagram 1: Reaction Scheme of Butadiene and Ethene]]

=== Molecular Orbital Analysis ===

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of butadiene and ethene.

[[File:Ex1 mo diagram yhw14 revised v3.png|550px|center|thumb|Diagram 2: MO diagram of Reaction of Butadiene and Ethene]]

Butadiene and ethene were optimised to their minima at semi-empirical method PM6 level. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #06DCFB; color: #ffffff;" |'''Molecule'''
! '''Butadiene'''
! '''Ethene'''
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Butadiene lumo yhw14.png|center|150px]]
|[[File:Ethene lumo yhw14.png|center|150px]]
|-
|Corresponding to the s orbital (symmetric)
|Corresponding to the a orbital (asymmetric)
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Butadiene homo yhw14.png|center|150px]]
|[[File:Ethene homo yhw14.png|center|150px]]
|-
|Corresponding to the a orbital (antisymmetric)
|Corresponding to the s orbital (symmetric)
|}

The transition state was first optimised to its minimum, followed by a transition state calculation at semi-empirical method PM6 level. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #01FCEF; color: #ffffff;" |'''Molecule'''
! '''Transition State'''
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Ts lumo+1 yhw14.png|center|150px]]
|-
|Corresponding to the 5 orbital (asymmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Ts lumo 1 yhw14.png|center|150px]]
|-
|Corresponding to the 4 orbital (symmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Ts homo yhw14.png|center|150px]]
|-
|Corresponding to the 3 orbital (symmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Ts homo-1 yhw14.png|center|150px]]
|-
|Corresponding to the 2 orbital (asymmetrical)
|}

Based on the MO diagram and the computed MOs shown above, a reaction is only allowed when the MOs with the same symmetry interact with each other, i.e. symmetric-symmetric and asymmetric-asymmetric interactions; and a reaction is forbidden when the MOs with different symmetry interact with each other, i.e. symmetric-asymmetric interactions. The MOs have to be close in energy in order to overlap effectively.

In the reaction between butadiene and ethene, the butadiene asymmetric MO interacts with the ethene asymmetric MO to give the MOs 2 and 5 of the transition state, and the butadiene symmetric MO interacts with the ethene symmetric MO to give the MOs 3 and 4 of the transition state. Therefore, a reaction is allowed when the symmetry labels of the MOs of the reactants are the same; and forbidden when the symmetry labels are different.

The orbital overlap integral is zero in a symmetric-asymmetric interaction and non-zero in symmetric-symmetric and asymmetric-asymmetric interactions.

=== Bond Length Analysis ===

The changes in bond lengths between carbons in reactant, transition state and product as the reaction progresses were studied by comparing the bond lengths between carbons before and after the reaction. The summary of bond lengths is shown below.
[[File:Ex1 bondlength yhw14.png|470px|center|thumb|Diagram 3: Labelled carbons]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #0000FF; color: #ffffff" | State
! style="background: #0000FF; color: #ffffff" | C1-C2
! style="background: #0000FF; color: #ffffff" | C2-C3
! style="background: #0000FF; color: #ffffff" | C3-C4
! style="background: #0000FF; color: #ffffff" | C4-C5
! style="background: #0000FF; color: #ffffff" | C5-C6
! style="background: #0000FF; color: #ffffff" | C6-C1
|-
|Reactants
|1.335
|1.468
|1.335
|/
|1.327
|/
|-
|Transition State
|1.380
|1.411
|1.380
|2.115
|1.382
|2.114
|-
|Product
|1.500
|1.338
|1.500
|1.540
|1.540
|1.540
|+Table 1: Measurements of the C-C bond lengths of the reactants, transition state and products (Å)
|}

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #97A7ED; color: #ffffff" |
! style="background: #97A7ED; color: #ffffff" | sp3-sp3 (C-C single bond) <ref name="C-C bond lengths"/>
! style="background: #97A7ED; color: #ffffff" | sp2-sp2 (C-C double bond) <ref name="C-C bond lengths"/>
! style="background: #97A7ED; color: #ffffff" | Van der Waals radius of the C atom <ref name="Van der Waals radius of C"/>
|-
|Bond Lengths (Å)
|1.54
|1.33
|1.7
|+Table 2: Literature Values of C-C bond lengths and Van der Waals radius of the C atom (Å)
|}
As the reaction progresses, the bond lengths between C1-C2, C3-C4 and C5-C6 lengthen from ~1.3 Å to ~1.5 Å as the bond order decrease to one, whereas bond length of C2-C3 shortens from ~1.5 Å to ~1.3 Å as the bond order increases from one to two.
This could be explained as the increase in bond length suggest a change from sp2-sp2 (C-C double bond) with typical bond length of 1.33 Å <ref name="C-C bond lengths"/> to sp3-sp3 (C-C single bond) with typical bond length of 1.54 Å <ref name="C-C bond lengths"/>, and vice versa for the decrease in bond length. Based on the calculated bond lengths above in Table 1, it is clear that bond lengths and bond orders of the reactants changed during the reaction and the new bonds formed at C4-C5 and C6-C1 are single bonds as they have bond lengths of 1.54 Å.
The typical Van der Waals radius of the C atom is 1.7 Å <ref name="Van der Waals radius of C"/>. As the bond lengths between C4-C5 and C6-C1 of the transition state are shorter than 2 x Van der Waals radii of C, this reflects that C-C bonds are forming at the transition state.

=== Vibration Analysis ===

The imaginary frequency at -948.32 cm-1 corresponds to the reaction path at the transition state, which shows a synchronous bond formation, which agrees with the concerted mechanism of [4+2] cycloaddition, where both reaction centres converge at the same time to form two new bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 15;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Reaction Path at the Transition State
|}

The lowest positive frequency at 145.14 cm-1 is asynchronous as shown below, where one of the C from the ethene moves towards the butadiene reaction centre and the other C moves away. This suggests that bonds are formed one at a time.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 16;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Lowest positive frequency
|}

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

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via two different pathways, endo and exo, which are shown in the reaction scheme below. GaussView calculations could be carried out to compare the reaction barriers and reaction energies of the two pathways to determine the kinetic and thermodynamic products.

[[File:Ex2 reactionscheme.png|550px|center|thumb|Diagram 4: Reaction Scheme of Cyclohexadiene and 1,3-Dioxole]]

=== Frequency Analysis ===

Frequency calculations were run to confirm that reactants (cyclohexadiene and 1,3-dioxole), and both endo and exo products did not have imaginary vibrations, suggesting they are structures at relative minima to the transition state; whereas both endo and exo transition states each had one imaginary vibration.

=== Molecular Orbital Analysis ===

Cyclohexadiene and 1,3-dioxole were optimised to their minima at DFT-B3LYP 631-G level. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #9A03FE; color: #ffffff;" |'''Molecule'''
! '''Cyclohexadiene'''
! '''1,3-Dioxole'''
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Cyclo lumo 631g yhw14.png|center|150px]]
|[[File:Dioxole lumo 631g yhw14.png|center|150px]]
|-
|Corresponding to the s orbital
|Corresponding to the a orbital
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Cyclo homo 631g yhw14.png|center|150px]]
|[[File:Dioxole homo 631g yhw14.png|center|150px]]
|-
|Corresponding to the a orbital
|Corresponding to the s orbital
|}

The transition state was first optimised to its minimum, followed by a transition state calculation at DFT-B3LYP 631-G level. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #BD5CFE; color: #ffffff;" |'''Molecule'''
! '''Endo Transition State'''
! '''Exo Transition State'''
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Endo ts lumo+1 yhw14.png|center|150px]]
|[[File:Exo ts lumo+1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 5 orbital (asymmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Endo ts lumo yhw14.png|center|150px]]
|[[File:Exo ts lumo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 4 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Endo ts homo yhw14.png|center|150px]]
|[[File:Exo ts homo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 3 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Endo ts homo-1 yhw14.png|center|150px]]
|[[File:Exo ts homo-1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 2 orbital (asymmetric)
|}

The diagram below illustrates the π molecular orbitals of cyclohexadiene and 1,3-dioxole involved in the formation of the transition state.

[[File:Ex2 mo diagram yhw14.png|550px|center|thumb|Diagram 5: MO diagram of Reaction of Cyclohexadiene and 1,3-dioxole]]

=== Normal Demand vs Inverse Demand Diels-Alder Reaction ===

A normal electron demand Diels-Alder reaction can be defined as a reaction between electron rich diene and electron poor dienophile. An inverse electron demand is the reaction between electron poor diene and electron rich dienophile.

The LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are very close in energy, which results in strong bonding interaction between the two to form the HOMO and LUMO of both endo and exo TS. Since the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole have the correct symmetry (symmetric) to interact, they interact to form the symmetric HOMO and LUMO of both TS.

The presence of the two electron donating oxygen atoms on 1,3-dioxole raise the energy of both its HOMO and LUMO, making the overlap between the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole much better than the HOMO of cyclohexadiene and the LUMO of 1,3-dioxole. Thus, the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are now the frontier orbitals that interact the most, hence this is an inverse demand Diels-Alder reaction.

=== Reaction Energies and Secondary Orbital Interaction ===

The reaction paths at the endo and exo transition states are shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="text-align: center;"|Reaction Path at the Endo Transition State
! style="text-align: center;"|Reaction Path at the Exo Transition State
|-
|<jmol><jmolApplet>
<uploadedFileContents>ENDO TS OPT TS 631G yhw14.LOG</uploadedFileContents>
<color>white</color>
<size>300</size>
<script>frame 33;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|<jmol><jmolApplet>
<uploadedFileContents>EXO TS OPT TS 631G yhw14.LOG</uploadedFileContents>
<color>white</color>
<size>300</size>
<script>frame 17;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|}

The energies of reactants were taken using the sum of the energies of cyclohexadiene and 1,3-dioxole optimised to their minima at DFT-B3LYP 631-G. The calculations were done using DFT-B3LYP 631-G.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FF4AFF; color: #ffffff" |
! style="background: #FF4AFF; color: #ffffff" | Reactants
! style="background: #FF4AFF; color: #ffffff" | Transition State
! style="background: #FF4AFF; color: #ffffff" | Product
! style="background: #FF4AFF; color: #ffffff" | Activation Energy
! style="background: #FF4AFF; color: #ffffff" | Gibbs Free Energy
|-
|Endo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313622</nowiki>
|<nowiki>-1313849</nowiki>
|160
|<nowiki>-67</nowiki>
|-
|Exo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313614</nowiki>
|<nowiki>-1313846</nowiki>
|168
|<nowiki>-64</nowiki>
|+Table 3: Energies of Reactants, Transition States and Products of both Endo and Exo Pathways in Diels-Alder Reaction of Cyclohexadiene and 1,3-Dioxole (kJ mol-1)
|}

Kinetically favourable product of a reaction is the one that has the lowest activation energy; Thermodynamically favourable product is the product with lowest energy conformer, hence the more stabilised product.

The endo transition state is the kinetic product of this reaction as it has lower activation energy. This could be explained using the secondary orbital interaction between the lone pair orbital on the oxygen atom and the empty π* orbital of diene. This favourable effect stabilises the endo transition state.

As the oxygen atom lone pair is oriented away from the diene π system in the exo transition state, the secondary orbital effect is not present, hence the activation energy of exo reaction is higher.

However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, i.e. increasing temperature, formation of the exo product would be more favourable.

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

Xylylene can react with sulfur dioxide through Diels-Alder reaction via either endo or exo pathways to form a 6-membered ring, or through cheletropic reaction to form a 5-membered ring. The reaction scheme is shown below. Reaction barriers and reaction energies for each pathway were compared to determine the reaction that is most favourable.

[[File:Ex3 reactionscheme yhw14.png|550px|center|thumb|Diagram 6: Reaction Scheme of Xylylene and Sulfur Dioxide]]

=== Intrinsic Reaction Coordinate ===
The following files show the intrinsic reaction coordinates of the three different reaction pathways of xylylene and SO2. Please click to see animation.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Endo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Exo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Cheletropic TS
|-
|[[File:DA endo irc animation yhw14.gif|center]]
|[[File:DA exo irc animation yhw14.gif|center]]
|[[File:Cheletropic irc animation yhw14.gif|center]]
|-
|[[File:DA endo irc plot yhw14.png|center|500px]]
|[[File:DA exo irc plot yhw14.png|center|500px]]
|[[File:Cheletropic irc plot yhw14.png|center|650px]]
|}

=== Reaction Energies and Reaction Barriers ===

[[File:Ex3 reactionprofile yhw14.png|550px|center|thumb|Diagram 7: Reaction Profile of Xylylene and Sulfur Dioxide]]

The energies of reactants were taken using the sum of the energies of xylylene and SO2 optimised to their minima. All calculations were done using semi-empirical PM6 method.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FFD1C3; color: #ffffff" |
! style="background: #FFD1C3; color: #ffffff" | Reactants
! style="background: #FFD1C3; color: #ffffff" | Transition State
! style="background: #FFD1C3; color: #ffffff" | Product
! style="background: #FFD1C3; color: #ffffff" | Activation Energy
! style="background: #FFD1C3; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|237.767824
|56.9576013
|83.391038
|<nowiki>-97.4191847</nowiki>
|-
|Exo
|154.376786
|241.753433
|56.3196048
|87.406647
|<nowiki>-98.0571812</nowiki>
|-
|Cheletropic
|154.376786
|260.08205
|0.013127501
|105.705264
|<nowiki>-154.3636585</nowiki>
|+Table 3: Energies of Reactants, Transition States and Products of Reactions between Xylylene and Sulfur Dioxide (kJ mol-1)
|}

With reference to the reaction profile and Table 3, the Diels-Alder reaction via the endo pathway has the lowest activation energy, making it a more kinetically favourable product, i.e. the kinetic product; the Diels-Alder exo product has a lower energy than endo, however with a higher activation energy hence it will not form under low temperature condition; the cheletropic product is the most stabilised product out of the three and it has the lowest reaction energy, therefore is the thermodynamic product.

=== Instability of Xylylene ===

Xylylene does not follow the Hückel rule (4n+2 electrons) hence it is not aromatic. In addition, it is rich in double bonds, all these factors make xylylene a very unstable molecule.

[[File:Ex3 xylylene instability yhw14.png|550px|center|thumb|Diagram 8: Electrocyclic Reaction Xylylene]]

The driving force of this electrocyclic reaction is the formation of an aromatic 6-membered benzene ring in the benzocyclobutane, which could also be another possible reaction pathway apart from Diels-Alder reaction and cheletropic reaction.

=== Side Reaction between cis-diene in Xylylene 6-membered ring and SO2===

o-Xylylene contains another cis-butadiene fragment located in the 6-membered ring that can undergo a Diels-Alder reaction with SO2. The reaction energies and reaction barriers between endo and exo pathways are compared in the table below.

The energies of reactants were taken using the sum of the energies of xylylene and SO2 optimised to their minima. All calculations were done using semi-empirical PM6 method.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #4EBEBA; color: #ffffff" |
! style="background: #4EBEBA; color: #ffffff" | Reactants
! style="background: #4EBEBA; color: #ffffff" | Transition State
! style="background: #4EBEBA; color: #ffffff" | Product
! style="background: #4EBEBA; color: #ffffff" | Activation Energy
! style="background: #4EBEBA; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|267.984805
|172.272196
|113.608019
|17.89541
|-
|Exo
|154.376786
|275.821924
|176.711916
|121.445138
|22.33513
|+Table 4: Energies of Reactants, Transition States and Products of the Side Reaction in Xylylene 6-membered ring and Sulfur Dioxide (kJ mol-1)
|}

It is clear that both endo and exo Diels-Alder side reactions are kinetically and thermodynamically unfavourable at this site as the activation energies are much higher than the previous reactions mentioned above in Table 3 and the reaction energies show that the reactions are endothermic.

== Conclusion ==

The transition states of three pericyclic reactions were investigated in this computational lab, using Gaussian to optimise the reactants, transition states and products respectively, and the vibrational frequencies and intrinsic reaction coordinates were computed.

In the reaction between butadiene and ethene, the importance of molecular orbital symmetry in the interaction of molecular orbitals was illustrated, such that a reaction is only allowed when the molecular orbitals with the same symmetry labels interact with each other and forbidden when symmetric molecular orbital interact with asymmetric orbitals. Furthermore, the vibration frequency calculation proved that this [4+2] Diels-Alder reaction proceeds via a concerted mechanism as synchronous bond formation was demonstrated. Bonding interaction can be further confirmed as the bond distance between the two termini carbon atoms in the transition state is shorter than the sum of two Van der Waals radii of carbon.

In the reaction of cyclohexadiene and 1,3-dioxole, both the endo and exo transition states were investigated. In general, the endo transition state is kinetically more favourable as it has lower activation barrier, possibly due to the secondary orbital interaction between the lone pair in p orbital on the oxygen atom and the empty pi* orbital in the diene, which stabilises the transition state. However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, formation of the exo product could be possible.

The final reaction between xylylene and SO2 again proved that the endo Diels-Alder transition state has the lowest activation energy, making it kinetically favourable at low temperature. However, the cheletropic product is the most stabilised and thermodynamically favourable product. Therefore the reaction would yield the cheletropic product under thermodynamic control instead of the exo Diels-Alder product.

==References==
<references>
<ref name="C-C bond lengths">L. Pauling and L. O. Brockway, ''Journal of the American Chemical Society'', '''1937''', Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref>
<ref name="Van der Waals radius of C">S. S. Batsanov, ''Inorganic Materials'', '''2001''', Volume 37, Number 9, pp. 871-885, https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf.</ref>
</references>

File:Ex3 xylylene instability yhw14.png

2017-02-10T03:05:31Z

Yhw14:

Rep:Mod:yhw14cts

2017-02-10T02:47:53Z

Yhw14:

''' Transition States and Reactivity '''

'' Yi Hang Cherie WONG (yhw14) ''
'' CID: 00933828 ''

== Introduction ==
A potential energy surface is a mathematical or graphical function that gives relationship between the energy of a molecule and its geometry with the relative positions of the atoms participating in the reaction. The stationary points may be classified according to the first and second derivatives of the energy with respect to position. At the minimum of a reaction profile, the gradient is represented by the first derivative of the reaction coordinate, which is zero, while curvature is represented by the second derivative, is positive in this case; hence energy rises in all directions. Energy minima correspond to physically stable chemical species, which could be reactants and products. The transition state is defined as the maximum in a reaction profile, where the gradient is again, zero, while curvature is negative; hence energy decreases in one direction, which indicates the reaction pathway of the chemical reaction. The potential energy surface can be computed using Gaussview, which is a graphical interface for Gaussian, where structure and energy of reactants or products can be modelled to illustrate the transition states, which can rarely be obtained experimentally. The intrinsic reaction coordinate can then be calculated and compared to predict the reaction path at a transition state and follow it to the correct minima.

In this computational lab, all of the reactants and products were optimised to their minima, and the transition states were also optimised. The calculations were done by GaussView, using mainly semi-empirical method PM6 and Density Functional Theory-B3LYP-631G. The latter is a more detailed and accurate optimisation, which is more time consuming method as it involves a higher number of basis set. Frequency calculations were performed to show molecular vibrations to confirm the position on the potential energy surface. If all the vibrational frequencies are real, this confirms the structure is a minimum, and vice versa, the presence of imaginary frequency may suggest that the structure is at its transition state. Intrinsic reaction coordinate method was carried out using calculated force constants to predict which conformer a reaction path from the transition state would lead to.

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

The reaction between butadiene and ethene is a typical pericyclic [4+2] Diels-Alder reaction that proceeds via a concerted mechanism through a cyclic transition state. The reaction scheme is shown below.

[[File:Ex1 reactionscheme revised yhw14.png|550px|center|thumb|Diagram 1: Reaction Scheme of Butadiene and Ethene]]

=== Molecular Orbital Analysis ===

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of butadiene and ethene.

[[File:Ex1 mo diagram yhw14 revised v3.png|550px|center|thumb|Diagram 2: MO diagram of Reaction of Butadiene and Ethene]]

Butadiene and ethene were optimised to their minima at semi-empirical method PM6 level. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #06DCFB; color: #ffffff;" |'''Molecule'''
! '''Butadiene'''
! '''Ethene'''
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Butadiene lumo yhw14.png|center|150px]]
|[[File:Ethene lumo yhw14.png|center|150px]]
|-
|Corresponding to the s orbital (symmetric)
|Corresponding to the a orbital (asymmetric)
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Butadiene homo yhw14.png|center|150px]]
|[[File:Ethene homo yhw14.png|center|150px]]
|-
|Corresponding to the a orbital (antisymmetric)
|Corresponding to the s orbital (symmetric)
|}

The transition state was first optimised to its minimum, followed by a transition state calculation at semi-empirical method PM6 level. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #01FCEF; color: #ffffff;" |'''Molecule'''
! '''Transition State'''
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Ts lumo+1 yhw14.png|center|150px]]
|-
|Corresponding to the 5 orbital (asymmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Ts lumo 1 yhw14.png|center|150px]]
|-
|Corresponding to the 4 orbital (symmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Ts homo yhw14.png|center|150px]]
|-
|Corresponding to the 3 orbital (symmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Ts homo-1 yhw14.png|center|150px]]
|-
|Corresponding to the 2 orbital (asymmetrical)
|}

Based on the MO diagram and the computed MOs shown above, a reaction is only allowed when the MOs with the same symmetry interact with each other, i.e. symmetric-symmetric and asymmetric-asymmetric interactions; and a reaction is forbidden when the MOs with different symmetry interact with each other, i.e. symmetric-asymmetric interactions. The MOs have to be close in energy in order to overlap effectively.

In the reaction between butadiene and ethene, the butadiene asymmetric MO interacts with the ethene asymmetric MO to give the MOs 2 and 5 of the transition state, and the butadiene symmetric MO interacts with the ethene symmetric MO to give the MOs 3 and 4 of the transition state. Therefore, a reaction is allowed when the symmetry labels of the MOs of the reactants are the same; and forbidden when the symmetry labels are different.

The orbital overlap integral is zero in a symmetric-asymmetric interaction and non-zero in symmetric-symmetric and asymmetric-asymmetric interactions.

=== Bond Length Analysis ===

The changes in bond lengths between carbons in reactant, transition state and product as the reaction progresses were studied by comparing the bond lengths between carbons before and after the reaction. The summary of bond lengths is shown below.
[[File:Ex1 bondlength yhw14.png|470px|center|thumb|Diagram 3: Labelled carbons]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #0000FF; color: #ffffff" | State
! style="background: #0000FF; color: #ffffff" | C1-C2
! style="background: #0000FF; color: #ffffff" | C2-C3
! style="background: #0000FF; color: #ffffff" | C3-C4
! style="background: #0000FF; color: #ffffff" | C4-C5
! style="background: #0000FF; color: #ffffff" | C5-C6
! style="background: #0000FF; color: #ffffff" | C6-C1
|-
|Reactants
|1.335
|1.468
|1.335
|/
|1.327
|/
|-
|Transition State
|1.380
|1.411
|1.380
|2.115
|1.382
|2.114
|-
|Product
|1.500
|1.338
|1.500
|1.540
|1.540
|1.540
|+Table 1: Measurements of the C-C bond lengths of the reactants, transition state and products (Å)
|}

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #97A7ED; color: #ffffff" |
! style="background: #97A7ED; color: #ffffff" | sp3-sp3 (C-C single bond) <ref name="C-C bond lengths"/>
! style="background: #97A7ED; color: #ffffff" | sp2-sp2 (C-C double bond) <ref name="C-C bond lengths"/>
! style="background: #97A7ED; color: #ffffff" | Van der Waals radius of the C atom <ref name="Van der Waals radius of C"/>
|-
|Bond Lengths (Å)
|1.54
|1.33
|1.7
|+Table 2: Literature Values of C-C bond lengths and Van der Waals radius of the C atom (Å)
|}
As the reaction progresses, the bond lengths between C1-C2, C3-C4 and C5-C6 lengthen from ~1.3 Å to ~1.5 Å as the bond order decrease to one, whereas bond length of C2-C3 shortens from ~1.5 Å to ~1.3 Å as the bond order increases from one to two.
This could be explained as the increase in bond length suggest a change from sp2-sp2 (C-C double bond) with typical bond length of 1.33 Å <ref name="C-C bond lengths"/> to sp3-sp3 (C-C single bond) with typical bond length of 1.54 Å <ref name="C-C bond lengths"/>, and vice versa for the decrease in bond length. Based on the calculated bond lengths above in Table 1, it is clear that bond lengths and bond orders of the reactants changed during the reaction and the new bonds formed at C4-C5 and C6-C1 are single bonds as they have bond lengths of 1.54 Å.
The typical Van der Waals radius of the C atom is 1.7 Å <ref name="Van der Waals radius of C"/>. As the bond lengths between C4-C5 and C6-C1 of the transition state are shorter than 2 x Van der Waals radii of C, this reflects that C-C bonds are forming at the transition state.

=== Vibration Analysis ===

The imaginary frequency at -948.32 cm-1 corresponds to the reaction path at the transition state, which shows a synchronous bond formation, which agrees with the concerted mechanism of [4+2] cycloaddition, where both reaction centres converge at the same time to form two new bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 15;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Reaction Path at the Transition State
|}

The lowest positive frequency at 145.14 cm-1 is asynchronous as shown below, where one of the C from the ethene moves towards the butadiene reaction centre and the other C moves away. This suggests that bonds are formed one at a time.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 16;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Lowest positive frequency
|}

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

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via two different pathways, endo and exo, which are shown in the reaction scheme below. GaussView calculations could be carried out to compare the reaction barriers and reaction energies of the two pathways to determine the kinetic and thermodynamic products.

[[File:Ex2 reactionscheme.png|550px|center|thumb|Diagram 4: Reaction Scheme of Cyclohexadiene and 1,3-Dioxole]]

=== Frequency Analysis ===

Frequency calculations were run to confirm that reactants (cyclohexadiene and 1,3-dioxole), and both endo and exo products did not have imaginary vibrations, suggesting they are structures at relative minima to the transition state; whereas both endo and exo transition states each had one imaginary vibration.

=== Molecular Orbital Analysis ===

Cyclohexadiene and 1,3-dioxole were optimised to their minima at DFT-B3LYP 631-G level. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #9A03FE; color: #ffffff;" |'''Molecule'''
! '''Cyclohexadiene'''
! '''1,3-Dioxole'''
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Cyclo lumo 631g yhw14.png|center|150px]]
|[[File:Dioxole lumo 631g yhw14.png|center|150px]]
|-
|Corresponding to the s orbital
|Corresponding to the a orbital
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Cyclo homo 631g yhw14.png|center|150px]]
|[[File:Dioxole homo 631g yhw14.png|center|150px]]
|-
|Corresponding to the a orbital
|Corresponding to the s orbital
|}

The transition state was first optimised to its minimum, followed by a transition state calculation at DFT-B3LYP 631-G level. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #BD5CFE; color: #ffffff;" |'''Molecule'''
! '''Endo Transition State'''
! '''Exo Transition State'''
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Endo ts lumo+1 yhw14.png|center|150px]]
|[[File:Exo ts lumo+1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 5 orbital (asymmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Endo ts lumo yhw14.png|center|150px]]
|[[File:Exo ts lumo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 4 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Endo ts homo yhw14.png|center|150px]]
|[[File:Exo ts homo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 3 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Endo ts homo-1 yhw14.png|center|150px]]
|[[File:Exo ts homo-1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 2 orbital (asymmetric)
|}

The diagram below illustrates the π molecular orbitals of cyclohexadiene and 1,3-dioxole involved in the formation of the transition state.

[[File:Ex2 mo diagram yhw14.png|550px|center|thumb|Diagram 5: MO diagram of Reaction of Cyclohexadiene and 1,3-dioxole]]

=== Normal Demand vs Inverse Demand Diels-Alder Reaction ===

A normal electron demand Diels-Alder reaction can be defined as a reaction between electron rich diene and electron poor dienophile. An inverse electron demand is the reaction between electron poor diene and electron rich dienophile.

The LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are very close in energy, which results in strong bonding interaction between the two to form the HOMO and LUMO of both endo and exo TS. Since the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole have the correct symmetry (symmetric) to interact, they interact to form the symmetric HOMO and LUMO of both TS.

The presence of the two electron donating oxygen atoms on 1,3-dioxole raise the energy of both its HOMO and LUMO, making the overlap between the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole much better than the HOMO of cyclohexadiene and the LUMO of 1,3-dioxole. Thus, the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are now the frontier orbitals that interact the most, hence this is an inverse demand Diels-Alder reaction.

=== Reaction Energies and Secondary Orbital Interaction ===

The reaction paths at the endo and exo transition states are shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="text-align: center;"|Reaction Path at the Endo Transition State
! style="text-align: center;"|Reaction Path at the Exo Transition State
|-
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<uploadedFileContents>ENDO TS OPT TS 631G yhw14.LOG</uploadedFileContents>
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<script>frame 33;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|<jmol><jmolApplet>
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The energies of reactants were taken using the sum of the energies of cyclohexadiene and 1,3-dioxole optimised to their minima at DFT-B3LYP 631-G. The calculations were done using DFT-B3LYP 631-G.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FF4AFF; color: #ffffff" |
! style="background: #FF4AFF; color: #ffffff" | Reactants
! style="background: #FF4AFF; color: #ffffff" | Transition State
! style="background: #FF4AFF; color: #ffffff" | Product
! style="background: #FF4AFF; color: #ffffff" | Activation Energy
! style="background: #FF4AFF; color: #ffffff" | Gibbs Free Energy
|-
|Endo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313622</nowiki>
|<nowiki>-1313849</nowiki>
|160
|<nowiki>-67</nowiki>
|-
|Exo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313614</nowiki>
|<nowiki>-1313846</nowiki>
|168
|<nowiki>-64</nowiki>
|+Table 3: Energies of Reactants, Transition States and Products of both Endo and Exo Pathways in Diels-Alder Reaction of Cyclohexadiene and 1,3-Dioxole (kJ mol-1)
|}

Kinetically favourable product of a reaction is the one that has the lowest activation energy; Thermodynamically favourable product is the product with lowest energy conformer, hence the more stabilised product.

The endo transition state is the kinetic product of this reaction as it has lower activation energy. This could be explained using the secondary orbital interaction between the lone pair orbital on the oxygen atom and the empty π* orbital of diene. This favourable effect stabilises the endo transition state.

As the oxygen atom lone pair is oriented away from the diene π system in the exo transition state, the secondary orbital effect is not present, hence the activation energy of exo reaction is higher.

However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, i.e. increasing temperature, formation of the exo product would be more favourable.

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

Xylylene can react with sulfur dioxide through Diels-Alder reaction via either endo or exo pathways to form a 6-membered ring, or through cheletropic reaction to form a 5-membered ring. The reaction scheme is shown below. Reaction barriers and reaction energies for each pathway are compared to determine the reaction that is most favourable.

[[File:Ex3 reactionscheme yhw14.png|550px|center|thumb|Diagram 6: Reaction Scheme of Xylylene and Sulfur Dioxide]]

=== Intrinsic Reaction Coordinate ===
The following files show the intrinsic reaction coordinates of the three different reaction pathways of xylylene and SO2. Please click to see animation.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Endo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Exo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Cheletropic TS
|-
|[[File:DA endo irc animation yhw14.gif|center]]
|[[File:DA exo irc animation yhw14.gif|center]]
|[[File:Cheletropic irc animation yhw14.gif|center]]
|-
|[[File:DA endo irc plot yhw14.png|center|500px]]
|[[File:DA exo irc plot yhw14.png|center|500px]]
|[[File:Cheletropic irc plot yhw14.png|center|650px]]
|}

=== Reaction Energies and Reaction Barriers ===

[[File:Ex3 reactionprofile yhw14.png|550px|center|thumb|Diagram 7: Reaction Profile of Xylylene and Sulfur Dioxide]]

The energies of reactants were taken using the sum of the energies of xylylene and SO2 optimised to their minima at semi-empirical PM6 level. The calculations were done using semi-empirical PM6.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FFD1C3; color: #ffffff" |
! style="background: #FFD1C3; color: #ffffff" | Reactants
! style="background: #FFD1C3; color: #ffffff" | Transition State
! style="background: #FFD1C3; color: #ffffff" | Product
! style="background: #FFD1C3; color: #ffffff" | Activation Energy
! style="background: #FFD1C3; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|237.767824
|56.9576013
|83.391038
|<nowiki>-97.4191847</nowiki>
|-
|Exo
|154.376786
|241.753433
|56.3196048
|87.406647
|<nowiki>-98.0571812</nowiki>
|-
|Cheletropic
|154.376786
|260.08205
|0.013127501
|105.705264
|<nowiki>-154.3636585</nowiki>
|+Table 3: Energies of Reactants, Transition States and Products of Reactions between Xylylene and Sulfur Dioxide (kJ mol-1)
|}

With reference to the reaction profile and Table 3, the Diels-Alder reaction via the endo pathway has the lowest activation energy, making it a more kinetically favourable product, i.e. the kinetic product; the Diels-Alder exo product has a lower energy than endo, however with a higher activation energy hence it will not form under low temperature condition; the cheletropic product is the most stabilised product out of the three and it has the lowest reaction energy, therefore is the thermodynamic product.

=== Side Reaction between cis-diene in Xylylene 6-membered ring and SO2===

o-Xylylene contains another cis-butadiene fragment located in the 6-membered ring that can undergo a Diels-Alder reaction with SO2. The reaction energies and reaction barriers between endo and exo pathways are compared in the table below.

The energies of reactants were taken using the sum of the energies of xylylene and SO2 optimised to their minima at semi-empirical PM6 level. The calculations were done using semi-empirical PM6.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #4EBEBA; color: #ffffff" |
! style="background: #4EBEBA; color: #ffffff" | Reactants
! style="background: #4EBEBA; color: #ffffff" | Transition State
! style="background: #4EBEBA; color: #ffffff" | Product
! style="background: #4EBEBA; color: #ffffff" | Activation Energy
! style="background: #4EBEBA; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|267.984805
|172.272196
|113.608019
|17.89541
|-
|Exo
|154.376786
|275.821924
|176.711916
|121.445138
|22.33513
|+Table 4: Energies of Reactants, Transition States and Products of the Side Reaction in Xylylene 6-membered ring and Sulfur Dioxide (kJ mol-1)
|}

It is clear that both endo and exo Diels-Alder side reactions are kinetically and thermodynamically unfavourable at this site as the activation energies are much higher than the previous reactions mentioned above in Table 3 and the reaction energies show that the reactions are endothermic.

== Conclusion ==

The transition states of three pericyclic reactions were investigated in this computational lab, using Gaussian to optimise the reactants, transition states and products respectively, and the vibrational frequencies and intrinsic reaction coordinates were computed.

In the reaction between butadiene and ethene, the importance of molecular orbital symmetry in the interaction of molecular orbitals was illustrated, such that a reaction is only allowed when the molecular orbitals with the same symmetry labels interact with each other and forbidden when symmetric molecular orbital interact with asymmetric orbitals. Furthermore, the vibration frequency calculation proved that this [4+2] Diels-Alder reaction proceeds via a concerted mechanism as synchronous bond formation was demonstrated. Bonding interaction can be further confirmed as the bond distance between the two termini carbon atoms in the transition state is shorter than the sum of two Van der Waals radii of carbon.

In the reaction of cyclohexadiene and 1,3-dioxole, both the endo and exo transition states were investigated. In general, the endo transition state is kinetically more favourable as it has lower activation barrier, possibly due to the secondary orbital interaction between the lone pair in p orbital on the oxygen atom and the empty pi* orbital in the diene, which stabilises the transition state. However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, formation of the exo product could be possible.

The final reaction between xylylene and SO2 again proved that the endo Diels-Alder transition state has the lowest activation energy, making it kinetically favourable at low temperature. However, the cheletropic product is the most stabilised and thermodynamically favourable product. Therefore the reaction would yield the cheletropic product under thermodynamic control instead of the exo Diels-Alder product.

==References==
<references>
<ref name="C-C bond lengths">L. Pauling and L. O. Brockway, ''Journal of the American Chemical Society'', '''1937''', Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref>
<ref name="Van der Waals radius of C">S. S. Batsanov, ''Inorganic Materials'', '''2001''', Volume 37, Number 9, pp. 871-885, https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf.</ref>
</references>

File:EXO TS OPT TS 631G yhw14.LOG

2017-02-10T02:41:49Z

Yhw14:

File:ENDO TS OPT TS 631G yhw14.LOG

2017-02-10T02:41:48Z

Yhw14:

Rep:Mod:yhw14cts

2017-02-10T02:25:43Z

Yhw14: /* Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole */

''' Transition States and Reactivity '''

'' Yi Hang Cherie WONG (yhw14) ''
'' CID: 00933828 ''

== Introduction ==
A potential energy surface is a mathematical or graphical function that gives relationship between the energy of a molecule and its geometry with the relative positions of the atoms participating in the reaction. The stationary points may be classified according to the first and second derivatives of the energy with respect to position. At the minimum of a reaction profile, the gradient is represented by the first derivative of the reaction coordinate, which is zero, while curvature is represented by the second derivative, is positive in this case; hence energy rises in all directions. Energy minima correspond to physically stable chemical species, which could be reactants and products. The transition state is defined as the maximum in a reaction profile, where the gradient is again, zero, while curvature is negative; hence energy decreases in one direction, which indicates the reaction pathway of the chemical reaction. The potential energy surface can be computed using Gaussview, which is a graphical interface for Gaussian, where structure and energy of reactants or products can be modelled to illustrate the transition states, which can rarely be obtained experimentally. The intrinsic reaction coordinate can then be calculated and compared to predict the reaction path at a transition state and follow it to the correct minima.

In this computational lab, all of the reactants and products were optimised to their minima, and the transition states were also optimised. The calculations were done by GaussView, using mainly semi-empirical method PM6 and Density Functional Theory-B3LYP-631G. The latter is a more detailed and accurate optimisation, which is more time consuming method as it involves a higher number of basis set. Frequency calculations were performed to show molecular vibrations to confirm the position on the potential energy surface. If all the vibrational frequencies are real, this confirms the structure is a minimum, and vice versa, the presence of imaginary frequency may suggest that the structure is at its transition state. Intrinsic reaction coordinate method was carried out using calculated force constants to predict which conformer a reaction path from the transition state would lead to.

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

The reaction between butadiene and ethene is a typical pericyclic [4+2] Diels-Alder reaction that proceeds via a concerted mechanism through a cyclic transition state. The reaction scheme is shown below.

[[File:Ex1 reactionscheme revised yhw14.png|550px|center|thumb|Diagram 1: Reaction Scheme of Butadiene and Ethene]]

=== Molecular Orbital Analysis ===

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of butadiene and ethene.

[[File:Ex1 mo diagram yhw14 revised v3.png|550px|center|thumb|Diagram 2: MO diagram of Reaction of Butadiene and Ethene]]

Butadiene and ethene were optimised to their minima at semi-empirical method PM6 level. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #06DCFB; color: #ffffff;" |'''Molecule'''
! '''Butadiene'''
! '''Ethene'''
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Butadiene lumo yhw14.png|center|150px]]
|[[File:Ethene lumo yhw14.png|center|150px]]
|-
|Corresponding to the s orbital (symmetric)
|Corresponding to the a orbital (asymmetric)
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Butadiene homo yhw14.png|center|150px]]
|[[File:Ethene homo yhw14.png|center|150px]]
|-
|Corresponding to the a orbital (antisymmetric)
|Corresponding to the s orbital (symmetric)
|}

The transition state was first optimised to its minimum, followed by a transition state calculation at semi-empirical method PM6 level. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #01FCEF; color: #ffffff;" |'''Molecule'''
! '''Transition State'''
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Ts lumo+1 yhw14.png|center|150px]]
|-
|Corresponding to the 5 orbital (asymmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Ts lumo 1 yhw14.png|center|150px]]
|-
|Corresponding to the 4 orbital (symmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Ts homo yhw14.png|center|150px]]
|-
|Corresponding to the 3 orbital (symmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Ts homo-1 yhw14.png|center|150px]]
|-
|Corresponding to the 2 orbital (asymmetrical)
|}

Based on the MO diagram and the computed MOs shown above, a reaction is only allowed when the MOs with the same symmetry interact with each other, i.e. symmetric-symmetric and asymmetric-asymmetric interactions; and a reaction is forbidden when the MOs with different symmetry interact with each other, i.e. symmetric-asymmetric interactions. The MOs have to be close in energy in order to overlap effectively.

In the reaction between butadiene and ethene, the butadiene asymmetric MO interacts with the ethene asymmetric MO to give the MOs 2 and 5 of the transition state, and the butadiene symmetric MO interacts with the ethene symmetric MO to give the MOs 3 and 4 of the transition state. Therefore, a reaction is allowed when the symmetry labels of the MOs of the reactants are the same; and forbidden when the symmetry labels are different.

The orbital overlap integral is zero in a symmetric-asymmetric interaction and non-zero in symmetric-symmetric and asymmetric-asymmetric interactions.

=== Bond Length Analysis ===

The changes in bond lengths between carbons in reactant, transition state and product as the reaction progresses were studied by comparing the bond lengths between carbons before and after the reaction. The summary of bond lengths is shown below.
[[File:Ex1 bondlength yhw14.png|470px|center|thumb|Diagram 3: Labelled carbons]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #0000FF; color: #ffffff" | State
! style="background: #0000FF; color: #ffffff" | C1-C2
! style="background: #0000FF; color: #ffffff" | C2-C3
! style="background: #0000FF; color: #ffffff" | C3-C4
! style="background: #0000FF; color: #ffffff" | C4-C5
! style="background: #0000FF; color: #ffffff" | C5-C6
! style="background: #0000FF; color: #ffffff" | C6-C1
|-
|Reactants
|1.335
|1.468
|1.335
|/
|1.327
|/
|-
|Transition State
|1.380
|1.411
|1.380
|2.115
|1.382
|2.114
|-
|Product
|1.500
|1.338
|1.500
|1.540
|1.540
|1.540
|+Table 1: Measurements of the C-C bond lengths of the reactants, transition state and products (Å)
|}

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #97A7ED; color: #ffffff" |
! style="background: #97A7ED; color: #ffffff" | sp3-sp3 (C-C single bond) <ref name="C-C bond lengths"/>
! style="background: #97A7ED; color: #ffffff" | sp2-sp2 (C-C double bond) <ref name="C-C bond lengths"/>
! style="background: #97A7ED; color: #ffffff" | Van der Waals radius of the C atom <ref name="Van der Waals radius of C"/>
|-
|Bond Lengths (Å)
|1.54
|1.33
|1.7
|+Table 2: Literature Values of C-C bond lengths and Van der Waals radius of the C atom (Å)
|}
As the reaction progresses, the bond lengths between C1-C2, C3-C4 and C5-C6 lengthen from ~1.3 Å to ~1.5 Å as the bond order decrease to one, whereas bond length of C2-C3 shortens from ~1.5 Å to ~1.3 Å as the bond order increases from one to two.
This could be explained as the increase in bond length suggest a change from sp2-sp2 (C-C double bond) with typical bond length of 1.33 Å <ref name="C-C bond lengths"/> to sp3-sp3 (C-C single bond) with typical bond length of 1.54 Å <ref name="C-C bond lengths"/>, and vice versa for the decrease in bond length. Based on the calculated bond lengths above in Table 1, it is clear that bond lengths and bond orders of the reactants changed during the reaction and the new bonds formed at C4-C5 and C6-C1 are single bonds as they have bond lengths of 1.54 Å.
The typical Van der Waals radius of the C atom is 1.7 Å <ref name="Van der Waals radius of C"/>. As the bond lengths between C4-C5 and C6-C1 of the transition state are shorter than 2 x Van der Waals radii of C, this reflects that C-C bonds are forming at the transition state.

=== Vibration Analysis ===

The imaginary frequency at -948.32 cm-1 corresponds to the reaction path at the transition state, which shows a synchronous bond formation, which agrees with the concerted mechanism of [4+2] cycloaddition, where both reaction centres converge at the same time to form two new bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 15;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Reaction Path at the Transition State
|}

The lowest positive frequency at 145.14 cm-1 is asynchronous as shown below, where one of the C from the ethene moves towards the butadiene reaction centre and the other C moves away. This suggests that bonds are formed one at a time.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 16;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Lowest positive frequency
|}

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

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via two different pathways, endo and exo, which are shown in the reaction scheme below. GaussView calculations could be carried out to compare the reaction barriers and reaction energies of the two pathways to determine the kinetic and thermodynamic products.

[[File:Ex2 reactionscheme.png|550px|center|thumb|Diagram 4: Reaction Scheme of Cyclohexadiene and 1,3-Dioxole]]

=== Frequency Analysis ===

Frequency calculations were run to confirm that reactants (cyclohexadiene and 1,3-dioxole), and both endo and exo products did not have imaginary vibrations, suggesting they are structures at relative minima to the transition state; whereas both endo and exo transition states each had one imaginary vibration.

=== Molecular Orbital Analysis ===

Cyclohexadiene and 1,3-dioxole were optimised to their minima at DFT-B3LYP 631-G level. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #9A03FE; color: #ffffff;" |'''Molecule'''
! '''Cyclohexadiene'''
! '''1,3-Dioxole'''
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Cyclo lumo 631g yhw14.png|center|150px]]
|[[File:Dioxole lumo 631g yhw14.png|center|150px]]
|-
|Corresponding to the s orbital
|Corresponding to the a orbital
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Cyclo homo 631g yhw14.png|center|150px]]
|[[File:Dioxole homo 631g yhw14.png|center|150px]]
|-
|Corresponding to the a orbital
|Corresponding to the s orbital
|}

The transition state was first optimised to its minimum, followed by a transition state calculation at DFT-B3LYP 631-G level. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #BD5CFE; color: #ffffff;" |'''Molecule'''
! '''Endo Transition State'''
! '''Exo Transition State'''
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Endo ts lumo+1 yhw14.png|center|150px]]
|[[File:Exo ts lumo+1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 5 orbital (asymmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Endo ts lumo yhw14.png|center|150px]]
|[[File:Exo ts lumo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 4 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Endo ts homo yhw14.png|center|150px]]
|[[File:Exo ts homo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 3 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Endo ts homo-1 yhw14.png|center|150px]]
|[[File:Exo ts homo-1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 2 orbital (asymmetric)
|}

The diagram below illustrates the π molecular orbitals of cyclohexadiene and 1,3-dioxole involved in the formation of the transition state.

[[File:Ex2 mo diagram yhw14.png|550px|center|thumb|Diagram 5: MO diagram of Reaction of Cyclohexadiene and 1,3-dioxole]]

=== Normal Demand vs Inverse Demand Diels-Alder Reaction ===

A normal electron demand Diels-Alder reaction can be defined as a reaction between electron rich diene and electron poor dienophile. An inverse electron demand is the reaction between electron poor diene and electron rich dienophile.

The LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are very close in energy, which results in strong bonding interaction between the two to form the HOMO and LUMO of both endo and exo TS. Since the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole have the correct symmetry (symmetric) to interact, they interact to form the symmetric HOMO and LUMO of both TS.

The presence of the two electron donating oxygen atoms on 1,3-dioxole raise the energy of both its HOMO and LUMO, making the overlap between the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole much better than the HOMO of cyclohexadiene and the LUMO of 1,3-dioxole. Thus, the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are now the frontier orbitals that interact the most, hence this is an inverse demand Diels-Alder reaction.

=== Reaction Energies and Secondary Orbital Interaction ===

The energies of reactants were taken using the sum of the energies of cyclohexadiene and 1,3-dioxole optimised to their minima at DFT-B3LYP 631-G. The calculations were done using DFT-B3LYP 631-G.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FF4AFF; color: #ffffff" |
! style="background: #FF4AFF; color: #ffffff" | Reactants
! style="background: #FF4AFF; color: #ffffff" | Transition State
! style="background: #FF4AFF; color: #ffffff" | Product
! style="background: #FF4AFF; color: #ffffff" | Activation Energy
! style="background: #FF4AFF; color: #ffffff" | Gibbs Free Energy
|-
|Endo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313622</nowiki>
|<nowiki>-1313849</nowiki>
|160
|<nowiki>-67</nowiki>
|-
|Exo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313614</nowiki>
|<nowiki>-1313846</nowiki>
|168
|<nowiki>-64</nowiki>
|+Table 3: Energies of Reactants, Transition States and Products of both Endo and Exo Pathways in Diels-Alder Reaction of Cyclohexadiene and 1,3-Dioxole (kJ mol-1)
|}

Kinetically favourable product of a reaction is the one that has the lowest activation energy; Thermodynamically favourable product is the product with lowest energy conformer, hence the more stabilised product.

The endo transition state is the kinetic product of this reaction as it has lower activation energy. This could be explained using the secondary orbital interaction between the lone pair orbital on the oxygen atom and the empty π* orbital of diene. This favourable effect stabilises the endo transition state.

As the oxygen atom lone pair is oriented away from the diene π system in the exo transition state, the secondary orbital effect is not present, hence the activation energy of exo reaction is higher.

However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, i.e. increasing temperature, formation of the exo product would be more favourable.

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

Xylylene can react with sulfur dioxide through Diels-Alder reaction via either endo or exo pathways to form a 6-membered ring, or through cheletropic reaction to form a 5-membered ring. The reaction scheme is shown below. Reaction barriers and reaction energies for each pathway are compared to determine the reaction that is most favourable.

[[File:Ex3 reactionscheme yhw14.png|550px|center|thumb|Diagram 6: Reaction Scheme of Xylylene and Sulfur Dioxide]]

=== Intrinsic Reaction Coordinate ===
The following files show the intrinsic reaction coordinates of the three different reaction pathways of xylylene and SO2. Please click to see animation.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Endo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Exo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Cheletropic TS
|-
|[[File:DA endo irc animation yhw14.gif|center]]
|[[File:DA exo irc animation yhw14.gif|center]]
|[[File:Cheletropic irc animation yhw14.gif|center]]
|-
|[[File:DA endo irc plot yhw14.png|center|500px]]
|[[File:DA exo irc plot yhw14.png|center|500px]]
|[[File:Cheletropic irc plot yhw14.png|center|650px]]
|}

=== Reaction Energies and Reaction Barriers ===

[[File:Ex3 reactionprofile yhw14.png|550px|center|thumb|Diagram 7: Reaction Profile of Xylylene and Sulfur Dioxide]]

The energies of reactants were taken using the sum of the energies of xylylene and SO2 optimised to their minima at semi-empirical PM6 level. The calculations were done using semi-empirical PM6.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FFD1C3; color: #ffffff" |
! style="background: #FFD1C3; color: #ffffff" | Reactants
! style="background: #FFD1C3; color: #ffffff" | Transition State
! style="background: #FFD1C3; color: #ffffff" | Product
! style="background: #FFD1C3; color: #ffffff" | Activation Energy
! style="background: #FFD1C3; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|237.767824
|56.9576013
|83.391038
|<nowiki>-97.4191847</nowiki>
|-
|Exo
|154.376786
|241.753433
|56.3196048
|87.406647
|<nowiki>-98.0571812</nowiki>
|-
|Cheletropic
|154.376786
|260.08205
|0.013127501
|105.705264
|<nowiki>-154.3636585</nowiki>
|+Table 3: Energies of Reactants, Transition States and Products of Reactions between Xylylene and Sulfur Dioxide (kJ mol-1)
|}

With reference to the reaction profile and Table 3, the Diels-Alder reaction via the endo pathway has the lowest activation energy, making it a more kinetically favourable product, i.e. the kinetic product; the Diels-Alder exo product has a lower energy than endo, however with a higher activation energy hence it will not form under low temperature condition; the cheletropic product is the most stabilised product out of the three and it has the lowest reaction energy, therefore is the thermodynamic product.

=== Side Reaction between cis-diene in Xylylene 6-membered ring and SO2===

o-Xylylene contains another cis-butadiene fragment located in the 6-membered ring that can undergo a Diels-Alder reaction with SO2. The reaction energies and reaction barriers between endo and exo pathways are compared in the table below.

The energies of reactants were taken using the sum of the energies of xylylene and SO2 optimised to their minima at semi-empirical PM6 level. The calculations were done using semi-empirical PM6.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #4EBEBA; color: #ffffff" |
! style="background: #4EBEBA; color: #ffffff" | Reactants
! style="background: #4EBEBA; color: #ffffff" | Transition State
! style="background: #4EBEBA; color: #ffffff" | Product
! style="background: #4EBEBA; color: #ffffff" | Activation Energy
! style="background: #4EBEBA; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|267.984805
|172.272196
|113.608019
|17.89541
|-
|Exo
|154.376786
|275.821924
|176.711916
|121.445138
|22.33513
|+Table 4: Energies of Reactants, Transition States and Products of the Side Reaction in Xylylene 6-membered ring and Sulfur Dioxide (kJ mol-1)
|}

It is clear that both endo and exo Diels-Alder side reactions are kinetically and thermodynamically unfavourable at this site as the activation energies are much higher than the previous reactions mentioned above in Table 3 and the reaction energies show that the reactions are endothermic.

== Conclusion ==

The transition states of three pericyclic reactions were investigated in this computational lab, using Gaussian to optimise the reactants, transition states and products respectively, and the vibrational frequencies and intrinsic reaction coordinates were computed.

In the reaction between butadiene and ethene, the importance of molecular orbital symmetry in the interaction of molecular orbitals was illustrated, such that a reaction is only allowed when the molecular orbitals with the same symmetry labels interact with each other and forbidden when symmetric molecular orbital interact with asymmetric orbitals. Furthermore, the vibration frequency calculation proved that this [4+2] Diels-Alder reaction proceeds via a concerted mechanism as synchronous bond formation was demonstrated. Bonding interaction can be further confirmed as the bond distance between the two termini carbon atoms in the transition state is shorter than the sum of two Van der Waals radii of carbon.

In the reaction of cyclohexadiene and 1,3-dioxole, both the endo and exo transition states were investigated. In general, the endo transition state is kinetically more favourable as it has lower activation barrier, possibly due to the secondary orbital interaction between the lone pair in p orbital on the oxygen atom and the empty pi* orbital in the diene, which stabilises the transition state. However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, formation of the exo product could be possible.

The final reaction between xylylene and SO2 again proved that the endo Diels-Alder transition state has the lowest activation energy, making it kinetically favourable at low temperature. However, the cheletropic product is the most stabilised and thermodynamically favourable product. Therefore the reaction would yield the cheletropic product under thermodynamic control instead of the exo Diels-Alder product.

==References==
<references>
<ref name="C-C bond lengths">L. Pauling and L. O. Brockway, ''Journal of the American Chemical Society'', '''1937''', Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref>
<ref name="Van der Waals radius of C">S. S. Batsanov, ''Inorganic Materials'', '''2001''', Volume 37, Number 9, pp. 871-885, https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf.</ref>
</references>

Rep:Mod:yhw14cts

2017-02-10T02:05:25Z

Yhw14: /* Vibration Analysis */

''' Transition States and Reactivity '''

'' Yi Hang Cherie WONG (yhw14) ''
'' CID: 00933828 ''

== Introduction ==
A potential energy surface is a mathematical or graphical function that gives relationship between the energy of a molecule and its geometry with the relative positions of the atoms participating in the reaction. The stationary points may be classified according to the first and second derivatives of the energy with respect to position. At the minimum of a reaction profile, the gradient is represented by the first derivative of the reaction coordinate, which is zero, while curvature is represented by the second derivative, is positive in this case; hence energy rises in all directions. Energy minima correspond to physically stable chemical species, which could be reactants and products. The transition state is defined as the maximum in a reaction profile, where the gradient is again, zero, while curvature is negative; hence energy decreases in one direction, which indicates the reaction pathway of the chemical reaction. The potential energy surface can be computed using Gaussview, which is a graphical interface for Gaussian, where structure and energy of reactants or products can be modelled to illustrate the transition states, which can rarely be obtained experimentally. The intrinsic reaction coordinate can then be calculated and compared to predict the reaction path at a transition state and follow it to the correct minima.

In this computational lab, all of the reactants and products were optimised to their minima, and the transition states were also optimised. The calculations were done by GaussView, using mainly semi-empirical method PM6 and Density Functional Theory-B3LYP-631G. The latter is a more detailed and accurate optimisation, which is more time consuming method as it involves a higher number of basis set. Frequency calculations were performed to show molecular vibrations to confirm the position on the potential energy surface. If all the vibrational frequencies are real, this confirms the structure is a minimum, and vice versa, the presence of imaginary frequency may suggest that the structure is at its transition state. Intrinsic reaction coordinate method was carried out using calculated force constants to predict which conformer a reaction path from the transition state would lead to.

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

The reaction between butadiene and ethene is a typical pericyclic [4+2] Diels-Alder reaction that proceeds via a concerted mechanism through a cyclic transition state. The reaction scheme is shown below.

[[File:Ex1 reactionscheme revised yhw14.png|550px|center|thumb|Diagram 1: Reaction Scheme of Butadiene and Ethene]]

=== Molecular Orbital Analysis ===

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of butadiene and ethene.

[[File:Ex1 mo diagram yhw14 revised v3.png|550px|center|thumb|Diagram 2: MO diagram of Reaction of Butadiene and Ethene]]

Butadiene and ethene were optimised to their minima at semi-empirical method PM6 level. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #06DCFB; color: #ffffff;" |'''Molecule'''
! '''Butadiene'''
! '''Ethene'''
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Butadiene lumo yhw14.png|center|150px]]
|[[File:Ethene lumo yhw14.png|center|150px]]
|-
|Corresponding to the s orbital (symmetric)
|Corresponding to the a orbital (asymmetric)
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Butadiene homo yhw14.png|center|150px]]
|[[File:Ethene homo yhw14.png|center|150px]]
|-
|Corresponding to the a orbital (antisymmetric)
|Corresponding to the s orbital (symmetric)
|}

The transition state was first optimised to its minimum, followed by a transition state calculation at semi-empirical method PM6 level. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #01FCEF; color: #ffffff;" |'''Molecule'''
! '''Transition State'''
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Ts lumo+1 yhw14.png|center|150px]]
|-
|Corresponding to the 5 orbital (asymmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Ts lumo 1 yhw14.png|center|150px]]
|-
|Corresponding to the 4 orbital (symmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Ts homo yhw14.png|center|150px]]
|-
|Corresponding to the 3 orbital (symmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Ts homo-1 yhw14.png|center|150px]]
|-
|Corresponding to the 2 orbital (asymmetrical)
|}

Based on the MO diagram and the computed MOs shown above, a reaction is only allowed when the MOs with the same symmetry interact with each other, i.e. symmetric-symmetric and asymmetric-asymmetric interactions; and a reaction is forbidden when the MOs with different symmetry interact with each other, i.e. symmetric-asymmetric interactions. The MOs have to be close in energy in order to overlap effectively.

In the reaction between butadiene and ethene, the butadiene asymmetric MO interacts with the ethene asymmetric MO to give the MOs 2 and 5 of the transition state, and the butadiene symmetric MO interacts with the ethene symmetric MO to give the MOs 3 and 4 of the transition state. Therefore, a reaction is allowed when the symmetry labels of the MOs of the reactants are the same; and forbidden when the symmetry labels are different.

The orbital overlap integral is zero in a symmetric-asymmetric interaction and non-zero in symmetric-symmetric and asymmetric-asymmetric interactions.

=== Bond Length Analysis ===

The changes in bond lengths between carbons in reactant, transition state and product as the reaction progresses were studied by comparing the bond lengths between carbons before and after the reaction. The summary of bond lengths is shown below.
[[File:Ex1 bondlength yhw14.png|470px|center|thumb|Diagram 3: Labelled carbons]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #0000FF; color: #ffffff" | State
! style="background: #0000FF; color: #ffffff" | C1-C2
! style="background: #0000FF; color: #ffffff" | C2-C3
! style="background: #0000FF; color: #ffffff" | C3-C4
! style="background: #0000FF; color: #ffffff" | C4-C5
! style="background: #0000FF; color: #ffffff" | C5-C6
! style="background: #0000FF; color: #ffffff" | C6-C1
|-
|Reactants
|1.335
|1.468
|1.335
|/
|1.327
|/
|-
|Transition State
|1.380
|1.411
|1.380
|2.115
|1.382
|2.114
|-
|Product
|1.500
|1.338
|1.500
|1.540
|1.540
|1.540
|+Table 1: Measurements of the C-C bond lengths of the reactants, transition state and products (Å)
|}

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #97A7ED; color: #ffffff" |
! style="background: #97A7ED; color: #ffffff" | sp3-sp3 (C-C single bond) <ref name="C-C bond lengths"/>
! style="background: #97A7ED; color: #ffffff" | sp2-sp2 (C-C double bond) <ref name="C-C bond lengths"/>
! style="background: #97A7ED; color: #ffffff" | Van der Waals radius of the C atom <ref name="Van der Waals radius of C"/>
|-
|Bond Lengths (Å)
|1.54
|1.33
|1.7
|+Table 2: Literature Values of C-C bond lengths and Van der Waals radius of the C atom (Å)
|}
As the reaction progresses, the bond lengths between C1-C2, C3-C4 and C5-C6 lengthen from ~1.3 Å to ~1.5 Å as the bond order decrease to one, whereas bond length of C2-C3 shortens from ~1.5 Å to ~1.3 Å as the bond order increases from one to two.
This could be explained as the increase in bond length suggest a change from sp2-sp2 (C-C double bond) with typical bond length of 1.33 Å <ref name="C-C bond lengths"/> to sp3-sp3 (C-C single bond) with typical bond length of 1.54 Å <ref name="C-C bond lengths"/>, and vice versa for the decrease in bond length. Based on the calculated bond lengths above in Table 1, it is clear that bond lengths and bond orders of the reactants changed during the reaction and the new bonds formed at C4-C5 and C6-C1 are single bonds as they have bond lengths of 1.54 Å.
The typical Van der Waals radius of the C atom is 1.7 Å <ref name="Van der Waals radius of C"/>. As the bond lengths between C4-C5 and C6-C1 of the transition state are shorter than 2 x Van der Waals radii of C, this reflects that C-C bonds are forming at the transition state.

=== Vibration Analysis ===

The imaginary frequency at -948.32 cm-1 corresponds to the reaction path at the transition state, which shows a synchronous bond formation, which agrees with the concerted mechanism of [4+2] cycloaddition, where both reaction centres converge at the same time to form two new bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 15;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Reaction Path at the Transition State
|}

The lowest positive frequency at 145.14 cm-1 is asynchronous as shown below, where one of the C from the ethene moves towards the butadiene reaction centre and the other C moves away. This suggests that bonds are formed one at a time.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 16;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Lowest positive frequency
|}

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

[[File:Ex2 reactionscheme.png|550px|center|thumb|Diagram 4: Reaction Scheme of Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

Cyclohexadiene and 1,3-dioxole were optimised to their minima at DFT-B3LYP 631-G level. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #9A03FE; color: #ffffff;" |'''Molecule'''
! '''Cyclohexadiene'''
! '''1,3-Dioxole'''
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Cyclo lumo 631g yhw14.png|center|150px]]
|[[File:Dioxole lumo 631g yhw14.png|center|150px]]
|-
|Corresponding to the s orbital
|Corresponding to the a orbital
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Cyclo homo 631g yhw14.png|center|150px]]
|[[File:Dioxole homo 631g yhw14.png|center|150px]]
|-
|Corresponding to the a orbital
|Corresponding to the s orbital
|}

The transition state was first optimised to its minimum, followed by a transition state calculation at DFT-B3LYP 631-G level. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #BD5CFE; color: #ffffff;" |'''Molecule'''
! '''Endo Transition State'''
! '''Exo Transition State'''
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Endo ts lumo+1 yhw14.png|center|150px]]
|[[File:Exo ts lumo+1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 5 orbital (asymmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Endo ts lumo yhw14.png|center|150px]]
|[[File:Exo ts lumo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 4 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Endo ts homo yhw14.png|center|150px]]
|[[File:Exo ts homo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 3 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Endo ts homo-1 yhw14.png|center|150px]]
|[[File:Exo ts homo-1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 2 orbital (asymmetric)
|}

The diagram below illustrates the π molecular orbitals of cyclohexadiene and 1,3-dioxole involved in the formation of the transition state.

[[File:Ex2 mo diagram yhw14.png|550px|center|thumb|Diagram 5: MO diagram of Reaction of Cyclohexadiene and 1,3-dioxole]]

=== Normal Demand vs Inverse Demand Diels-Alder Reaction ===

A normal electron demand Diels-Alder reaction can be defined as a reaction between electron rich diene and electron poor dienophile. An inverse electron demand is the reaction between electron poor diene and electron rich dienophile.

The LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are very close in energy, which results in strong bonding interaction between the two to form the HOMO and LUMO of both endo and exo TS. Since the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole have the correct symmetry (symmetric) to interact, they interact to form the symmetric HOMO and LUMO of both TS.

The presence of electron rich O on 1,3-dioxole raise the energy of both its HOMO and LUMO, making the overlap between the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole much better than the HOMO of cyclohexadiene and the LUMO of 1,3-dioxole. Thus, the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are now the frontier orbitals that interact the most, hence this is an inverse demand Diels-Alder reaction.

=== Reaction Energies and Secondary Orbital Interaction ===

The energies of reactants were taken using the sum of the energies of cyclohexadiene and 1,3-dioxole optimised to their minima at DFT-B3LYP 631-G. The calculations were done using DFT-B3LYP 631-G.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FF4AFF; color: #ffffff" |
! style="background: #FF4AFF; color: #ffffff" | Reactants
! style="background: #FF4AFF; color: #ffffff" | Transition State
! style="background: #FF4AFF; color: #ffffff" | Product
! style="background: #FF4AFF; color: #ffffff" | Activation Energy
! style="background: #FF4AFF; color: #ffffff" | Gibbs Free Energy
|-
|Endo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313622</nowiki>
|<nowiki>-1313849</nowiki>
|160
|<nowiki>-67</nowiki>
|-
|Exo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313614</nowiki>
|<nowiki>-1313846</nowiki>
|168
|<nowiki>-64</nowiki>
|+Table 2: Energies of Reactants, Transition States and Products of both Endo and Exo Pathways in Diels-Alder Reaction of Cyclohexadiene and 1,3-Dioxole (kJ mol-1)
|}

Kinetically favourable product of a reaction is the one that has the lowest activation energy; Thermodynamically favourable product is the product with lowest energy conformer, hence the more stabilised product.

The endo transition state is the kinetic product of this reaction as it has lower activation energy. This could be explained using the secondary orbital interaction between the lone pair orbital on the oxygen atom and the empty π* orbital of diene. This favourable effect stabilises the endo transition state.

As the oxygen atom lone pair is oriented away from the diene π system in the exo transition state, the secondary orbital effect is not present, hence the activation energy of exo reaction is higher.

However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, i.e. increasing temperature, formation of the exo product would be more favourable.

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

Xylylene can react with sulfur dioxide through Diels-Alder reaction via either endo or exo pathways to form a 6-membered ring, or through cheletropic reaction to form a 5-membered ring. The reaction scheme is shown below. Reaction barriers and reaction energies for each pathway are compared to determine the reaction that is most favourable.

[[File:Ex3 reactionscheme yhw14.png|550px|center|thumb|Diagram 6: Reaction Scheme of Xylylene and Sulfur Dioxide]]

=== Intrinsic Reaction Coordinate ===
The following files show the intrinsic reaction coordinates of the three different reaction pathways of xylylene and SO2. Please click to see animation.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Endo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Exo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Cheletropic TS
|-
|[[File:DA endo irc animation yhw14.gif|center]]
|[[File:DA exo irc animation yhw14.gif|center]]
|[[File:Cheletropic irc animation yhw14.gif|center]]
|-
|[[File:DA endo irc plot yhw14.png|center|500px]]
|[[File:DA exo irc plot yhw14.png|center|500px]]
|[[File:Cheletropic irc plot yhw14.png|center|650px]]
|}

=== Reaction Energies and Reaction Barriers ===

[[File:Ex3 reactionprofile yhw14.png|550px|center|thumb|Diagram 7: Reaction Profile of Xylylene and Sulfur Dioxide]]

The energies of reactants were taken using the sum of the energies of xylylene and SO2 optimised to their minima at semi-empirical PM6 level. The calculations were done using semi-empirical PM6.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FFD1C3; color: #ffffff" |
! style="background: #FFD1C3; color: #ffffff" | Reactants
! style="background: #FFD1C3; color: #ffffff" | Transition State
! style="background: #FFD1C3; color: #ffffff" | Product
! style="background: #FFD1C3; color: #ffffff" | Activation Energy
! style="background: #FFD1C3; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|237.767824
|56.9576013
|83.391038
|<nowiki>-97.4191847</nowiki>
|-
|Exo
|154.376786
|241.753433
|56.3196048
|87.406647
|<nowiki>-98.0571812</nowiki>
|-
|Cheletropic
|154.376786
|260.08205
|0.013127501
|105.705264
|<nowiki>-154.3636585</nowiki>
|+Table 3: Energies of Reactants, Transition States and Products of Reactions between Xylylene and Sulfur Dioxide (kJ mol-1)
|}

With reference to the reaction profile and Table 3, the Diels-Alder reaction via the endo pathway has the lowest activation energy, making it a more kinetically favourable product, i.e. the kinetic product; the Diels-Alder exo product has a lower energy than endo, however with a higher activation energy hence it will not form under low temperature condition; the cheletropic product is the most stabilised product out of the three and it has the lowest reaction energy, therefore is the thermodynamic product.

=== Side Reaction between cis-diene in Xylylene 6-membered ring and SO2===

o-Xylylene contains another cis-butadiene fragment located in the 6-membered ring that can undergo a Diels-Alder reaction with SO2. The reaction energies and reaction barriers between endo and exo pathways are compared in the table below.

The energies of reactants were taken using the sum of the energies of xylylene and SO2 optimised to their minima at semi-empirical PM6 level. The calculations were done using semi-empirical PM6.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #4EBEBA; color: #ffffff" |
! style="background: #4EBEBA; color: #ffffff" | Reactants
! style="background: #4EBEBA; color: #ffffff" | Transition State
! style="background: #4EBEBA; color: #ffffff" | Product
! style="background: #4EBEBA; color: #ffffff" | Activation Energy
! style="background: #4EBEBA; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|267.984805
|172.272196
|113.608019
|17.89541
|-
|Exo
|154.376786
|275.821924
|176.711916
|121.445138
|22.33513
|+Table 4: Energies of Reactants, Transition States and Products of the Side Reaction in Xylylene 6-membered ring and Sulfur Dioxide (kJ mol-1)
|}

It is clear that both endo and exo Diels-Alder side reactions are kinetically and thermodynamically unfavourable at this site as the activation energies are much higher than the previous reactions mentioned above in Table 3 and the reaction energies show that the reactions are endothermic.

== Conclusion ==

The transition states of three pericyclic reactions were investigated in this computational lab, using Gaussian to optimise the reactants, transition states and products respectively, and the vibrational frequencies and intrinsic reaction coordinates were computed.

In the reaction between butadiene and ethene, the importance of molecular orbital symmetry in the interaction of molecular orbitals was illustrated, such that a reaction is only allowed when the molecular orbitals with the same symmetry labels interact with each other and forbidden when symmetric molecular orbital interact with asymmetric orbitals. Furthermore, the vibration frequency calculation proved that this [4+2] Diels-Alder reaction proceeds via a concerted mechanism as synchronous bond formation was demonstrated. Bonding interaction can be further confirmed as the bond distance between the two termini carbon atoms in the transition state is shorter than the sum of two Van der Waals radii of carbon.

In the reaction of cyclohexadiene and 1,3-dioxole, both the endo and exo transition states were investigated. In general, the endo transition state is kinetically more favourable as it has lower activation barrier, possibly due to the secondary orbital interaction between the lone pair in p orbital on the oxygen atom and the empty pi* orbital in the diene, which stabilises the transition state. However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, formation of the exo product could be possible.

The final reaction between xylylene and SO2 again proved that the endo Diels-Alder transition state has the lowest activation energy, making it kinetically favourable at low temperature. However, the cheletropic product is the most stabilised and thermodynamically favourable product. Therefore the reaction would yield the cheletropic product under thermodynamic control instead of the exo Diels-Alder product.

==References==
<references>
<ref name="C-C bond lengths">L. Pauling and L. O. Brockway, ''Journal of the American Chemical Society'', '''1937''', Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref>
<ref name="Van der Waals radius of C">S. S. Batsanov, ''Inorganic Materials'', '''2001''', Volume 37, Number 9, pp. 871-885, https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf.</ref>
</references>

Rep:Mod:yhw14cts

2017-02-10T02:01:12Z

Yhw14: /* Bond Length Analysis */

''' Transition States and Reactivity '''

'' Yi Hang Cherie WONG (yhw14) ''
'' CID: 00933828 ''

== Introduction ==
A potential energy surface is a mathematical or graphical function that gives relationship between the energy of a molecule and its geometry with the relative positions of the atoms participating in the reaction. The stationary points may be classified according to the first and second derivatives of the energy with respect to position. At the minimum of a reaction profile, the gradient is represented by the first derivative of the reaction coordinate, which is zero, while curvature is represented by the second derivative, is positive in this case; hence energy rises in all directions. Energy minima correspond to physically stable chemical species, which could be reactants and products. The transition state is defined as the maximum in a reaction profile, where the gradient is again, zero, while curvature is negative; hence energy decreases in one direction, which indicates the reaction pathway of the chemical reaction. The potential energy surface can be computed using Gaussview, which is a graphical interface for Gaussian, where structure and energy of reactants or products can be modelled to illustrate the transition states, which can rarely be obtained experimentally. The intrinsic reaction coordinate can then be calculated and compared to predict the reaction path at a transition state and follow it to the correct minima.

In this computational lab, all of the reactants and products were optimised to their minima, and the transition states were also optimised. The calculations were done by GaussView, using mainly semi-empirical method PM6 and Density Functional Theory-B3LYP-631G. The latter is a more detailed and accurate optimisation, which is more time consuming method as it involves a higher number of basis set. Frequency calculations were performed to show molecular vibrations to confirm the position on the potential energy surface. If all the vibrational frequencies are real, this confirms the structure is a minimum, and vice versa, the presence of imaginary frequency may suggest that the structure is at its transition state. Intrinsic reaction coordinate method was carried out using calculated force constants to predict which conformer a reaction path from the transition state would lead to.

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

The reaction between butadiene and ethene is a typical pericyclic [4+2] Diels-Alder reaction that proceeds via a concerted mechanism through a cyclic transition state. The reaction scheme is shown below.

[[File:Ex1 reactionscheme revised yhw14.png|550px|center|thumb|Diagram 1: Reaction Scheme of Butadiene and Ethene]]

=== Molecular Orbital Analysis ===

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of butadiene and ethene.

[[File:Ex1 mo diagram yhw14 revised v3.png|550px|center|thumb|Diagram 2: MO diagram of Reaction of Butadiene and Ethene]]

Butadiene and ethene were optimised to their minima at semi-empirical method PM6 level. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #06DCFB; color: #ffffff;" |'''Molecule'''
! '''Butadiene'''
! '''Ethene'''
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Butadiene lumo yhw14.png|center|150px]]
|[[File:Ethene lumo yhw14.png|center|150px]]
|-
|Corresponding to the s orbital (symmetric)
|Corresponding to the a orbital (asymmetric)
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Butadiene homo yhw14.png|center|150px]]
|[[File:Ethene homo yhw14.png|center|150px]]
|-
|Corresponding to the a orbital (antisymmetric)
|Corresponding to the s orbital (symmetric)
|}

The transition state was first optimised to its minimum, followed by a transition state calculation at semi-empirical method PM6 level. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #01FCEF; color: #ffffff;" |'''Molecule'''
! '''Transition State'''
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Ts lumo+1 yhw14.png|center|150px]]
|-
|Corresponding to the 5 orbital (asymmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Ts lumo 1 yhw14.png|center|150px]]
|-
|Corresponding to the 4 orbital (symmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Ts homo yhw14.png|center|150px]]
|-
|Corresponding to the 3 orbital (symmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Ts homo-1 yhw14.png|center|150px]]
|-
|Corresponding to the 2 orbital (asymmetrical)
|}

Based on the MO diagram and the computed MOs shown above, a reaction is only allowed when the MOs with the same symmetry interact with each other, i.e. symmetric-symmetric and asymmetric-asymmetric interactions; and a reaction is forbidden when the MOs with different symmetry interact with each other, i.e. symmetric-asymmetric interactions. The MOs have to be close in energy in order to overlap effectively.

In the reaction between butadiene and ethene, the butadiene asymmetric MO interacts with the ethene asymmetric MO to give the MOs 2 and 5 of the transition state, and the butadiene symmetric MO interacts with the ethene symmetric MO to give the MOs 3 and 4 of the transition state. Therefore, a reaction is allowed when the symmetry labels of the MOs of the reactants are the same; and forbidden when the symmetry labels are different.

The orbital overlap integral is zero in a symmetric-asymmetric interaction and non-zero in symmetric-symmetric and asymmetric-asymmetric interactions.

=== Bond Length Analysis ===

The changes in bond lengths between carbons in reactant, transition state and product as the reaction progresses were studied by comparing the bond lengths between carbons before and after the reaction. The summary of bond lengths is shown below.
[[File:Ex1 bondlength yhw14.png|470px|center|thumb|Diagram 3: Labelled carbons]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #0000FF; color: #ffffff" | State
! style="background: #0000FF; color: #ffffff" | C1-C2
! style="background: #0000FF; color: #ffffff" | C2-C3
! style="background: #0000FF; color: #ffffff" | C3-C4
! style="background: #0000FF; color: #ffffff" | C4-C5
! style="background: #0000FF; color: #ffffff" | C5-C6
! style="background: #0000FF; color: #ffffff" | C6-C1
|-
|Reactants
|1.335
|1.468
|1.335
|/
|1.327
|/
|-
|Transition State
|1.380
|1.411
|1.380
|2.115
|1.382
|2.114
|-
|Product
|1.500
|1.338
|1.500
|1.540
|1.540
|1.540
|+Table 1: Measurements of the C-C bond lengths of the reactants, transition state and products (Å)
|}

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #97A7ED; color: #ffffff" |
! style="background: #97A7ED; color: #ffffff" | sp3-sp3 (C-C single bond) <ref name="C-C bond lengths"/>
! style="background: #97A7ED; color: #ffffff" | sp2-sp2 (C-C double bond) <ref name="C-C bond lengths"/>
! style="background: #97A7ED; color: #ffffff" | Van der Waals radius of the C atom <ref name="Van der Waals radius of C"/>
|-
|Bond Lengths (Å)
|1.54
|1.33
|1.7
|+Table 2: Literature Values of C-C bond lengths and Van der Waals radius of the C atom (Å)
|}
As the reaction progresses, the bond lengths between C1-C2, C3-C4 and C5-C6 lengthen from ~1.3 Å to ~1.5 Å as the bond order decrease to one, whereas bond length of C2-C3 shortens from ~1.5 Å to ~1.3 Å as the bond order increases from one to two.
This could be explained as the increase in bond length suggest a change from sp2-sp2 (C-C double bond) with typical bond length of 1.33 Å <ref name="C-C bond lengths"/> to sp3-sp3 (C-C single bond) with typical bond length of 1.54 Å <ref name="C-C bond lengths"/>, and vice versa for the decrease in bond length. Based on the calculated bond lengths above in Table 1, it is clear that bond lengths and bond orders of the reactants changed during the reaction and the new bonds formed at C4-C5 and C6-C1 are single bonds as they have bond lengths of 1.54 Å.
The typical Van der Waals radius of the C atom is 1.7 Å <ref name="Van der Waals radius of C"/>. As the bond lengths between C4-C5 and C6-C1 of the transition state are shorter than 2 x Van der Waals radii of C, this reflects that C-C bonds are forming at the transition state.

=== Vibration Analysis ===

The imaginary frequency at -948.32 cm-1 corresponds to the reaction path at the transition state, which shows a synchronous bond formation, which agrees with the concerted mechanism of [4+2] cycloaddition, where both reaction centres converge at the same time to form bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 15;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Reaction Path at the Transition State
|}

The lowest positive frequency at 145.14 cm-1 is asynchronous as shown below, where one of the C from the ethene moves towards the butadiene reaction centre and the other C moves away. This suggests that bonds are formed one at a time.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 16;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Lowest positive frequency
|}

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

[[File:Ex2 reactionscheme.png|550px|center|thumb|Diagram 4: Reaction Scheme of Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

Cyclohexadiene and 1,3-dioxole were optimised to their minima at DFT-B3LYP 631-G level. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #9A03FE; color: #ffffff;" |'''Molecule'''
! '''Cyclohexadiene'''
! '''1,3-Dioxole'''
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Cyclo lumo 631g yhw14.png|center|150px]]
|[[File:Dioxole lumo 631g yhw14.png|center|150px]]
|-
|Corresponding to the s orbital
|Corresponding to the a orbital
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Cyclo homo 631g yhw14.png|center|150px]]
|[[File:Dioxole homo 631g yhw14.png|center|150px]]
|-
|Corresponding to the a orbital
|Corresponding to the s orbital
|}

The transition state was first optimised to its minimum, followed by a transition state calculation at DFT-B3LYP 631-G level. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #BD5CFE; color: #ffffff;" |'''Molecule'''
! '''Endo Transition State'''
! '''Exo Transition State'''
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Endo ts lumo+1 yhw14.png|center|150px]]
|[[File:Exo ts lumo+1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 5 orbital (asymmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Endo ts lumo yhw14.png|center|150px]]
|[[File:Exo ts lumo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 4 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Endo ts homo yhw14.png|center|150px]]
|[[File:Exo ts homo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 3 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Endo ts homo-1 yhw14.png|center|150px]]
|[[File:Exo ts homo-1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 2 orbital (asymmetric)
|}

The diagram below illustrates the π molecular orbitals of cyclohexadiene and 1,3-dioxole involved in the formation of the transition state.

[[File:Ex2 mo diagram yhw14.png|550px|center|thumb|Diagram 5: MO diagram of Reaction of Cyclohexadiene and 1,3-dioxole]]

=== Normal Demand vs Inverse Demand Diels-Alder Reaction ===

A normal electron demand Diels-Alder reaction can be defined as a reaction between electron rich diene and electron poor dienophile. An inverse electron demand is the reaction between electron poor diene and electron rich dienophile.

The LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are very close in energy, which results in strong bonding interaction between the two to form the HOMO and LUMO of both endo and exo TS. Since the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole have the correct symmetry (symmetric) to interact, they interact to form the symmetric HOMO and LUMO of both TS.

The presence of electron rich O on 1,3-dioxole raise the energy of both its HOMO and LUMO, making the overlap between the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole much better than the HOMO of cyclohexadiene and the LUMO of 1,3-dioxole. Thus, the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are now the frontier orbitals that interact the most, hence this is an inverse demand Diels-Alder reaction.

=== Reaction Energies and Secondary Orbital Interaction ===

The energies of reactants were taken using the sum of the energies of cyclohexadiene and 1,3-dioxole optimised to their minima at DFT-B3LYP 631-G. The calculations were done using DFT-B3LYP 631-G.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FF4AFF; color: #ffffff" |
! style="background: #FF4AFF; color: #ffffff" | Reactants
! style="background: #FF4AFF; color: #ffffff" | Transition State
! style="background: #FF4AFF; color: #ffffff" | Product
! style="background: #FF4AFF; color: #ffffff" | Activation Energy
! style="background: #FF4AFF; color: #ffffff" | Gibbs Free Energy
|-
|Endo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313622</nowiki>
|<nowiki>-1313849</nowiki>
|160
|<nowiki>-67</nowiki>
|-
|Exo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313614</nowiki>
|<nowiki>-1313846</nowiki>
|168
|<nowiki>-64</nowiki>
|+Table 2: Energies of Reactants, Transition States and Products of both Endo and Exo Pathways in Diels-Alder Reaction of Cyclohexadiene and 1,3-Dioxole (kJ mol-1)
|}

Kinetically favourable product of a reaction is the one that has the lowest activation energy; Thermodynamically favourable product is the product with lowest energy conformer, hence the more stabilised product.

The endo transition state is the kinetic product of this reaction as it has lower activation energy. This could be explained using the secondary orbital interaction between the lone pair orbital on the oxygen atom and the empty π* orbital of diene. This favourable effect stabilises the endo transition state.

As the oxygen atom lone pair is oriented away from the diene π system in the exo transition state, the secondary orbital effect is not present, hence the activation energy of exo reaction is higher.

However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, i.e. increasing temperature, formation of the exo product would be more favourable.

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

Xylylene can react with sulfur dioxide through Diels-Alder reaction via either endo or exo pathways to form a 6-membered ring, or through cheletropic reaction to form a 5-membered ring. The reaction scheme is shown below. Reaction barriers and reaction energies for each pathway are compared to determine the reaction that is most favourable.

[[File:Ex3 reactionscheme yhw14.png|550px|center|thumb|Diagram 6: Reaction Scheme of Xylylene and Sulfur Dioxide]]

=== Intrinsic Reaction Coordinate ===
The following files show the intrinsic reaction coordinates of the three different reaction pathways of xylylene and SO2. Please click to see animation.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Endo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Exo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Cheletropic TS
|-
|[[File:DA endo irc animation yhw14.gif|center]]
|[[File:DA exo irc animation yhw14.gif|center]]
|[[File:Cheletropic irc animation yhw14.gif|center]]
|-
|[[File:DA endo irc plot yhw14.png|center|500px]]
|[[File:DA exo irc plot yhw14.png|center|500px]]
|[[File:Cheletropic irc plot yhw14.png|center|650px]]
|}

=== Reaction Energies and Reaction Barriers ===

[[File:Ex3 reactionprofile yhw14.png|550px|center|thumb|Diagram 7: Reaction Profile of Xylylene and Sulfur Dioxide]]

The energies of reactants were taken using the sum of the energies of xylylene and SO2 optimised to their minima at semi-empirical PM6 level. The calculations were done using semi-empirical PM6.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FFD1C3; color: #ffffff" |
! style="background: #FFD1C3; color: #ffffff" | Reactants
! style="background: #FFD1C3; color: #ffffff" | Transition State
! style="background: #FFD1C3; color: #ffffff" | Product
! style="background: #FFD1C3; color: #ffffff" | Activation Energy
! style="background: #FFD1C3; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|237.767824
|56.9576013
|83.391038
|<nowiki>-97.4191847</nowiki>
|-
|Exo
|154.376786
|241.753433
|56.3196048
|87.406647
|<nowiki>-98.0571812</nowiki>
|-
|Cheletropic
|154.376786
|260.08205
|0.013127501
|105.705264
|<nowiki>-154.3636585</nowiki>
|+Table 3: Energies of Reactants, Transition States and Products of Reactions between Xylylene and Sulfur Dioxide (kJ mol-1)
|}

With reference to the reaction profile and Table 3, the Diels-Alder reaction via the endo pathway has the lowest activation energy, making it a more kinetically favourable product, i.e. the kinetic product; the Diels-Alder exo product has a lower energy than endo, however with a higher activation energy hence it will not form under low temperature condition; the cheletropic product is the most stabilised product out of the three and it has the lowest reaction energy, therefore is the thermodynamic product.

=== Side Reaction between cis-diene in Xylylene 6-membered ring and SO2===

o-Xylylene contains another cis-butadiene fragment located in the 6-membered ring that can undergo a Diels-Alder reaction with SO2. The reaction energies and reaction barriers between endo and exo pathways are compared in the table below.

The energies of reactants were taken using the sum of the energies of xylylene and SO2 optimised to their minima at semi-empirical PM6 level. The calculations were done using semi-empirical PM6.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #4EBEBA; color: #ffffff" |
! style="background: #4EBEBA; color: #ffffff" | Reactants
! style="background: #4EBEBA; color: #ffffff" | Transition State
! style="background: #4EBEBA; color: #ffffff" | Product
! style="background: #4EBEBA; color: #ffffff" | Activation Energy
! style="background: #4EBEBA; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|267.984805
|172.272196
|113.608019
|17.89541
|-
|Exo
|154.376786
|275.821924
|176.711916
|121.445138
|22.33513
|+Table 4: Energies of Reactants, Transition States and Products of the Side Reaction in Xylylene 6-membered ring and Sulfur Dioxide (kJ mol-1)
|}

It is clear that both endo and exo Diels-Alder side reactions are kinetically and thermodynamically unfavourable at this site as the activation energies are much higher than the previous reactions mentioned above in Table 3 and the reaction energies show that the reactions are endothermic.

== Conclusion ==

The transition states of three pericyclic reactions were investigated in this computational lab, using Gaussian to optimise the reactants, transition states and products respectively, and the vibrational frequencies and intrinsic reaction coordinates were computed.

In the reaction between butadiene and ethene, the importance of molecular orbital symmetry in the interaction of molecular orbitals was illustrated, such that a reaction is only allowed when the molecular orbitals with the same symmetry labels interact with each other and forbidden when symmetric molecular orbital interact with asymmetric orbitals. Furthermore, the vibration frequency calculation proved that this [4+2] Diels-Alder reaction proceeds via a concerted mechanism as synchronous bond formation was demonstrated. Bonding interaction can be further confirmed as the bond distance between the two termini carbon atoms in the transition state is shorter than the sum of two Van der Waals radii of carbon.

In the reaction of cyclohexadiene and 1,3-dioxole, both the endo and exo transition states were investigated. In general, the endo transition state is kinetically more favourable as it has lower activation barrier, possibly due to the secondary orbital interaction between the lone pair in p orbital on the oxygen atom and the empty pi* orbital in the diene, which stabilises the transition state. However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, formation of the exo product could be possible.

The final reaction between xylylene and SO2 again proved that the endo Diels-Alder transition state has the lowest activation energy, making it kinetically favourable at low temperature. However, the cheletropic product is the most stabilised and thermodynamically favourable product. Therefore the reaction would yield the cheletropic product under thermodynamic control instead of the exo Diels-Alder product.

==References==
<references>
<ref name="C-C bond lengths">L. Pauling and L. O. Brockway, ''Journal of the American Chemical Society'', '''1937''', Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref>
<ref name="Van der Waals radius of C">S. S. Batsanov, ''Inorganic Materials'', '''2001''', Volume 37, Number 9, pp. 871-885, https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf.</ref>
</references>

Rep:Mod:yhw14cts

2017-02-10T01:45:41Z

Yhw14: /* Molecular Orbital Analysis */

''' Transition States and Reactivity '''

'' Yi Hang Cherie WONG (yhw14) ''
'' CID: 00933828 ''

== Introduction ==
A potential energy surface is a mathematical or graphical function that gives relationship between the energy of a molecule and its geometry with the relative positions of the atoms participating in the reaction. The stationary points may be classified according to the first and second derivatives of the energy with respect to position. At the minimum of a reaction profile, the gradient is represented by the first derivative of the reaction coordinate, which is zero, while curvature is represented by the second derivative, is positive in this case; hence energy rises in all directions. Energy minima correspond to physically stable chemical species, which could be reactants and products. The transition state is defined as the maximum in a reaction profile, where the gradient is again, zero, while curvature is negative; hence energy decreases in one direction, which indicates the reaction pathway of the chemical reaction. The potential energy surface can be computed using Gaussview, which is a graphical interface for Gaussian, where structure and energy of reactants or products can be modelled to illustrate the transition states, which can rarely be obtained experimentally. The intrinsic reaction coordinate can then be calculated and compared to predict the reaction path at a transition state and follow it to the correct minima.

In this computational lab, all of the reactants and products were optimised to their minima, and the transition states were also optimised. The calculations were done by GaussView, using mainly semi-empirical method PM6 and Density Functional Theory-B3LYP-631G. The latter is a more detailed and accurate optimisation, which is more time consuming method as it involves a higher number of basis set. Frequency calculations were performed to show molecular vibrations to confirm the position on the potential energy surface. If all the vibrational frequencies are real, this confirms the structure is a minimum, and vice versa, the presence of imaginary frequency may suggest that the structure is at its transition state. Intrinsic reaction coordinate method was carried out using calculated force constants to predict which conformer a reaction path from the transition state would lead to.

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

The reaction between butadiene and ethene is a typical pericyclic [4+2] Diels-Alder reaction that proceeds via a concerted mechanism through a cyclic transition state. The reaction scheme is shown below.

[[File:Ex1 reactionscheme revised yhw14.png|550px|center|thumb|Diagram 1: Reaction Scheme of Butadiene and Ethene]]

=== Molecular Orbital Analysis ===

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of butadiene and ethene.

[[File:Ex1 mo diagram yhw14 revised v3.png|550px|center|thumb|Diagram 2: MO diagram of Reaction of Butadiene and Ethene]]

Butadiene and ethene were optimised to their minima at semi-empirical method PM6 level. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #06DCFB; color: #ffffff;" |'''Molecule'''
! '''Butadiene'''
! '''Ethene'''
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Butadiene lumo yhw14.png|center|150px]]
|[[File:Ethene lumo yhw14.png|center|150px]]
|-
|Corresponding to the s orbital (symmetric)
|Corresponding to the a orbital (asymmetric)
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Butadiene homo yhw14.png|center|150px]]
|[[File:Ethene homo yhw14.png|center|150px]]
|-
|Corresponding to the a orbital (antisymmetric)
|Corresponding to the s orbital (symmetric)
|}

The transition state was first optimised to its minimum, followed by a transition state calculation at semi-empirical method PM6 level. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #01FCEF; color: #ffffff;" |'''Molecule'''
! '''Transition State'''
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Ts lumo+1 yhw14.png|center|150px]]
|-
|Corresponding to the 5 orbital (asymmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Ts lumo 1 yhw14.png|center|150px]]
|-
|Corresponding to the 4 orbital (symmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Ts homo yhw14.png|center|150px]]
|-
|Corresponding to the 3 orbital (symmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Ts homo-1 yhw14.png|center|150px]]
|-
|Corresponding to the 2 orbital (asymmetrical)
|}

Based on the MO diagram and the computed MOs shown above, a reaction is only allowed when the MOs with the same symmetry interact with each other, i.e. symmetric-symmetric and asymmetric-asymmetric interactions; and a reaction is forbidden when the MOs with different symmetry interact with each other, i.e. symmetric-asymmetric interactions. The MOs have to be close in energy in order to overlap effectively.

In the reaction between butadiene and ethene, the butadiene asymmetric MO interacts with the ethene asymmetric MO to give the MOs 2 and 5 of the transition state, and the butadiene symmetric MO interacts with the ethene symmetric MO to give the MOs 3 and 4 of the transition state. Therefore, a reaction is allowed when the symmetry labels of the MOs of the reactants are the same; and forbidden when the symmetry labels are different.

The orbital overlap integral is zero in a symmetric-asymmetric interaction and non-zero in symmetric-symmetric and asymmetric-asymmetric interactions.

=== Bond Length Analysis ===

The changes in bond lengths between carbons in reactant, transition state and product as the reaction progresses were studied by comparing the bond lengths between carbons before and after the reaction. The summary of bond lengths is shown below.
[[File:Ex1 bondlength yhw14.png|470px|center|thumb|Diagram 3: Labelled carbons]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #0000FF; color: #ffffff" | State
! style="background: #0000FF; color: #ffffff" | C1-C2
! style="background: #0000FF; color: #ffffff" | C2-C3
! style="background: #0000FF; color: #ffffff" | C3-C4
! style="background: #0000FF; color: #ffffff" | C4-C5
! style="background: #0000FF; color: #ffffff" | C5-C6
! style="background: #0000FF; color: #ffffff" | C6-C1
|-
|Reactants
|1.335
|1.468
|1.335
|/
|1.327
|/
|-
|Transition State
|1.380
|1.411
|1.380
|2.115
|1.382
|2.114
|-
|Product
|1.500
|1.338
|1.500
|1.540
|1.540
|1.540
|+Table 1: Measurements of the C-C bond lengths of the reactants, transition state and products (Å)
|}
As the reaction progresses, the bond lengths between C1-C2, C3-C4 and C5-C6 increase from ~1.3 Å to ~1.5 Å as the bond order decrease to one, whereas bond length of C2-C3 decreases from ~1.5 Å to ~1.3 Å as the bond order increases from one to two.
This could be explained as the increase in bond length suggest a change from sp2-sp2 (C-C double bond) with typical bond length of 1.33 Å <ref name="C-C bond lengths"/> to sp3-sp3 (C-C single bond) with typical bond length of 1.54 Å <ref name="C-C bond lengths"/>, and vice versa for the decrease in bond length. Based on the calculated bond lengths above in Table 1, it is clear that bond lengths and bond orders of the reactants changed during the reaction and the new bonds formed at C4-C5 and C6-C1 are single bonds as they have bond lengths of 1.54 Å.
The typical Van der Waals radius of the C atom is 1.7 Å <ref name="Van der Waals radius of C"/>. As the bond lengths between C4-C5 and C6-C1 of the transition state are shorter than 2 x Van der Waals radii of C, this reflects that C-C bonds are forming at the transition state.

=== Vibration Analysis ===

The imaginary frequency at -948.32 cm-1 corresponds to the reaction path at the transition state, which shows a synchronous bond formation, which agrees with the concerted mechanism of [4+2] cycloaddition, where both reaction centres converge at the same time to form bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 15;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Reaction Path at the Transition State
|}

The lowest positive frequency at 145.14 cm-1 is asynchronous as shown below, where one of the C from the ethene moves towards the butadiene reaction centre and the other C moves away. This suggests that bonds are formed one at a time.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 16;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Lowest positive frequency
|}

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

[[File:Ex2 reactionscheme.png|550px|center|thumb|Diagram 4: Reaction Scheme of Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

Cyclohexadiene and 1,3-dioxole were optimised to their minima at DFT-B3LYP 631-G level. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #9A03FE; color: #ffffff;" |'''Molecule'''
! '''Cyclohexadiene'''
! '''1,3-Dioxole'''
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Cyclo lumo 631g yhw14.png|center|150px]]
|[[File:Dioxole lumo 631g yhw14.png|center|150px]]
|-
|Corresponding to the s orbital
|Corresponding to the a orbital
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Cyclo homo 631g yhw14.png|center|150px]]
|[[File:Dioxole homo 631g yhw14.png|center|150px]]
|-
|Corresponding to the a orbital
|Corresponding to the s orbital
|}

The transition state was first optimised to its minimum, followed by a transition state calculation at DFT-B3LYP 631-G level. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #BD5CFE; color: #ffffff;" |'''Molecule'''
! '''Endo Transition State'''
! '''Exo Transition State'''
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Endo ts lumo+1 yhw14.png|center|150px]]
|[[File:Exo ts lumo+1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 5 orbital (asymmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Endo ts lumo yhw14.png|center|150px]]
|[[File:Exo ts lumo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 4 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Endo ts homo yhw14.png|center|150px]]
|[[File:Exo ts homo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 3 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Endo ts homo-1 yhw14.png|center|150px]]
|[[File:Exo ts homo-1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 2 orbital (asymmetric)
|}

The diagram below illustrates the π molecular orbitals of cyclohexadiene and 1,3-dioxole involved in the formation of the transition state.

[[File:Ex2 mo diagram yhw14.png|550px|center|thumb|Diagram 5: MO diagram of Reaction of Cyclohexadiene and 1,3-dioxole]]

=== Normal Demand vs Inverse Demand Diels-Alder Reaction ===

A normal electron demand Diels-Alder reaction can be defined as a reaction between electron rich diene and electron poor dienophile. An inverse electron demand is the reaction between electron poor diene and electron rich dienophile.

The LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are very close in energy, which results in strong bonding interaction between the two to form the HOMO and LUMO of both endo and exo TS. Since the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole have the correct symmetry (symmetric) to interact, they interact to form the symmetric HOMO and LUMO of both TS.

The presence of electron rich O on 1,3-dioxole raise the energy of both its HOMO and LUMO, making the overlap between the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole much better than the HOMO of cyclohexadiene and the LUMO of 1,3-dioxole. Thus, the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are now the frontier orbitals that interact the most, hence this is an inverse demand Diels-Alder reaction.

=== Reaction Energies and Secondary Orbital Interaction ===

The energies of reactants were taken using the sum of the energies of cyclohexadiene and 1,3-dioxole optimised to their minima at DFT-B3LYP 631-G. The calculations were done using DFT-B3LYP 631-G.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FF4AFF; color: #ffffff" |
! style="background: #FF4AFF; color: #ffffff" | Reactants
! style="background: #FF4AFF; color: #ffffff" | Transition State
! style="background: #FF4AFF; color: #ffffff" | Product
! style="background: #FF4AFF; color: #ffffff" | Activation Energy
! style="background: #FF4AFF; color: #ffffff" | Gibbs Free Energy
|-
|Endo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313622</nowiki>
|<nowiki>-1313849</nowiki>
|160
|<nowiki>-67</nowiki>
|-
|Exo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313614</nowiki>
|<nowiki>-1313846</nowiki>
|168
|<nowiki>-64</nowiki>
|+Table 2: Energies of Reactants, Transition States and Products of both Endo and Exo Pathways in Diels-Alder Reaction of Cyclohexadiene and 1,3-Dioxole (kJ mol-1)
|}

Kinetically favourable product of a reaction is the one that has the lowest activation energy; Thermodynamically favourable product is the product with lowest energy conformer, hence the more stabilised product.

The endo transition state is the kinetic product of this reaction as it has lower activation energy. This could be explained using the secondary orbital interaction between the lone pair orbital on the oxygen atom and the empty π* orbital of diene. This favourable effect stabilises the endo transition state.

As the oxygen atom lone pair is oriented away from the diene π system in the exo transition state, the secondary orbital effect is not present, hence the activation energy of exo reaction is higher.

However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, i.e. increasing temperature, formation of the exo product would be more favourable.

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

Xylylene can react with sulfur dioxide through Diels-Alder reaction via either endo or exo pathways to form a 6-membered ring, or through cheletropic reaction to form a 5-membered ring. The reaction scheme is shown below. Reaction barriers and reaction energies for each pathway are compared to determine the reaction that is most favourable.

[[File:Ex3 reactionscheme yhw14.png|550px|center|thumb|Diagram 6: Reaction Scheme of Xylylene and Sulfur Dioxide]]

=== Intrinsic Reaction Coordinate ===
The following files show the intrinsic reaction coordinates of the three different reaction pathways of xylylene and SO2. Please click to see animation.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Endo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Exo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Cheletropic TS
|-
|[[File:DA endo irc animation yhw14.gif|center]]
|[[File:DA exo irc animation yhw14.gif|center]]
|[[File:Cheletropic irc animation yhw14.gif|center]]
|-
|[[File:DA endo irc plot yhw14.png|center|500px]]
|[[File:DA exo irc plot yhw14.png|center|500px]]
|[[File:Cheletropic irc plot yhw14.png|center|650px]]
|}

=== Reaction Energies and Reaction Barriers ===

[[File:Ex3 reactionprofile yhw14.png|550px|center|thumb|Diagram 7: Reaction Profile of Xylylene and Sulfur Dioxide]]

The energies of reactants were taken using the sum of the energies of xylylene and SO2 optimised to their minima at semi-empirical PM6 level. The calculations were done using semi-empirical PM6.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FFD1C3; color: #ffffff" |
! style="background: #FFD1C3; color: #ffffff" | Reactants
! style="background: #FFD1C3; color: #ffffff" | Transition State
! style="background: #FFD1C3; color: #ffffff" | Product
! style="background: #FFD1C3; color: #ffffff" | Activation Energy
! style="background: #FFD1C3; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|237.767824
|56.9576013
|83.391038
|<nowiki>-97.4191847</nowiki>
|-
|Exo
|154.376786
|241.753433
|56.3196048
|87.406647
|<nowiki>-98.0571812</nowiki>
|-
|Cheletropic
|154.376786
|260.08205
|0.013127501
|105.705264
|<nowiki>-154.3636585</nowiki>
|+Table 3: Energies of Reactants, Transition States and Products of Reactions between Xylylene and Sulfur Dioxide (kJ mol-1)
|}

With reference to the reaction profile and Table 3, the Diels-Alder reaction via the endo pathway has the lowest activation energy, making it a more kinetically favourable product, i.e. the kinetic product; the Diels-Alder exo product has a lower energy than endo, however with a higher activation energy hence it will not form under low temperature condition; the cheletropic product is the most stabilised product out of the three and it has the lowest reaction energy, therefore is the thermodynamic product.

=== Side Reaction between cis-diene in Xylylene 6-membered ring and SO2===

o-Xylylene contains another cis-butadiene fragment located in the 6-membered ring that can undergo a Diels-Alder reaction with SO2. The reaction energies and reaction barriers between endo and exo pathways are compared in the table below.

The energies of reactants were taken using the sum of the energies of xylylene and SO2 optimised to their minima at semi-empirical PM6 level. The calculations were done using semi-empirical PM6.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #4EBEBA; color: #ffffff" |
! style="background: #4EBEBA; color: #ffffff" | Reactants
! style="background: #4EBEBA; color: #ffffff" | Transition State
! style="background: #4EBEBA; color: #ffffff" | Product
! style="background: #4EBEBA; color: #ffffff" | Activation Energy
! style="background: #4EBEBA; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|267.984805
|172.272196
|113.608019
|17.89541
|-
|Exo
|154.376786
|275.821924
|176.711916
|121.445138
|22.33513
|+Table 4: Energies of Reactants, Transition States and Products of the Side Reaction in Xylylene 6-membered ring and Sulfur Dioxide (kJ mol-1)
|}

It is clear that both endo and exo Diels-Alder side reactions are kinetically and thermodynamically unfavourable at this site as the activation energies are much higher than the previous reactions mentioned above in Table 3 and the reaction energies show that the reactions are endothermic.

== Conclusion ==

The transition states of three pericyclic reactions were investigated in this computational lab, using Gaussian to optimise the reactants, transition states and products respectively, and the vibrational frequencies and intrinsic reaction coordinates were computed.

In the reaction between butadiene and ethene, the importance of molecular orbital symmetry in the interaction of molecular orbitals was illustrated, such that a reaction is only allowed when the molecular orbitals with the same symmetry labels interact with each other and forbidden when symmetric molecular orbital interact with asymmetric orbitals. Furthermore, the vibration frequency calculation proved that this [4+2] Diels-Alder reaction proceeds via a concerted mechanism as synchronous bond formation was demonstrated. Bonding interaction can be further confirmed as the bond distance between the two termini carbon atoms in the transition state is shorter than the sum of two Van der Waals radii of carbon.

In the reaction of cyclohexadiene and 1,3-dioxole, both the endo and exo transition states were investigated. In general, the endo transition state is kinetically more favourable as it has lower activation barrier, possibly due to the secondary orbital interaction between the lone pair in p orbital on the oxygen atom and the empty pi* orbital in the diene, which stabilises the transition state. However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, formation of the exo product could be possible.

The final reaction between xylylene and SO2 again proved that the endo Diels-Alder transition state has the lowest activation energy, making it kinetically favourable at low temperature. However, the cheletropic product is the most stabilised and thermodynamically favourable product. Therefore the reaction would yield the cheletropic product under thermodynamic control instead of the exo Diels-Alder product.

==References==
<references>
<ref name="C-C bond lengths">L. Pauling and L. O. Brockway, ''Journal of the American Chemical Society'', '''1937''', Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref>
<ref name="Van der Waals radius of C">S. S. Batsanov, ''Inorganic Materials'', '''2001''', Volume 37, Number 9, pp. 871-885, https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf.</ref>
</references>

Rep:Mod:yhw14cts

2017-02-10T01:28:40Z

Yhw14: /* Introduction */

''' Transition States and Reactivity '''

'' Yi Hang Cherie WONG (yhw14) ''
'' CID: 00933828 ''

== Introduction ==
A potential energy surface is a mathematical or graphical function that gives relationship between the energy of a molecule and its geometry with the relative positions of the atoms participating in the reaction. The stationary points may be classified according to the first and second derivatives of the energy with respect to position. At the minimum of a reaction profile, the gradient is represented by the first derivative of the reaction coordinate, which is zero, while curvature is represented by the second derivative, is positive in this case; hence energy rises in all directions. Energy minima correspond to physically stable chemical species, which could be reactants and products. The transition state is defined as the maximum in a reaction profile, where the gradient is again, zero, while curvature is negative; hence energy decreases in one direction, which indicates the reaction pathway of the chemical reaction. The potential energy surface can be computed using Gaussview, which is a graphical interface for Gaussian, where structure and energy of reactants or products can be modelled to illustrate the transition states, which can rarely be obtained experimentally. The intrinsic reaction coordinate can then be calculated and compared to predict the reaction path at a transition state and follow it to the correct minima.

In this computational lab, all of the reactants and products were optimised to their minima, and the transition states were also optimised. The calculations were done by GaussView, using mainly semi-empirical method PM6 and Density Functional Theory-B3LYP-631G. The latter is a more detailed and accurate optimisation, which is more time consuming method as it involves a higher number of basis set. Frequency calculations were performed to show molecular vibrations to confirm the position on the potential energy surface. If all the vibrational frequencies are real, this confirms the structure is a minimum, and vice versa, the presence of imaginary frequency may suggest that the structure is at its transition state. Intrinsic reaction coordinate method was carried out using calculated force constants to predict which conformer a reaction path from the transition state would lead to.

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

The reaction between butadiene and ethene is a typical pericyclic [4+2] Diels-Alder reaction that proceeds via a concerted mechanism through a cyclic transition state. The reaction scheme is shown below.

[[File:Ex1 reactionscheme revised yhw14.png|550px|center|thumb|Diagram 1: Reaction Scheme of Butadiene and Ethene]]

=== Molecular Orbital Analysis ===

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of butadiene and ethene.

[[File:Ex1 mo diagram yhw14 revised v3.png|550px|center|thumb|Diagram 2: MO diagram of Reaction of Butadiene and Ethene]]

Butadiene and ethene were optimised to their minima at semi-empirical method PM6 level. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #06DCFB; color: #ffffff;" |'''Molecule'''
! '''Butadiene'''
! '''Ethene'''
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Butadiene lumo yhw14.png|center|150px]]
|[[File:Ethene lumo yhw14.png|center|150px]]
|-
|Corresponding to the s orbital (symmetric)
|Corresponding to the a orbital (asymmetric)
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Butadiene homo yhw14.png|center|150px]]
|[[File:Ethene homo yhw14.png|center|150px]]
|-
|Corresponding to the a orbital (antisymmetric)
|Corresponding to the s orbital (symmetric)
|}

The transition state was first optimised to its minimum, followed by a transition state calculation at semi-empirical method PM6 level. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #01FCEF; color: #ffffff;" |'''Molecule'''
! '''Transition State'''
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Ts lumo+1 yhw14.png|center|150px]]
|-
|Corresponding to the 5 orbital (asymmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Ts lumo 1 yhw14.png|center|150px]]
|-
|Corresponding to the 4 orbital (symmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Ts homo yhw14.png|center|150px]]
|-
|Corresponding to the 3 orbital (symmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Ts homo-1 yhw14.png|center|150px]]
|-
|Corresponding to the 2 orbital (asymmetrical)
|}

Based on the MO diagram and the computed MOs shown above, a reaction is only allowed when the MOs with the same symmetry labels interact with each other, i.e. symmetric-symmetric and asymmetric-asymmetric interactions; and a reaction is forbidden when the MOs with different symmetry labels interact with each other, i.e. symmetric-asymmetric interactions.
In the reaction between butadiene and ethene, the butadiene asymmetric MO interacts with the ethene asymmetric MO to give the 2 and 5 MOs of the transition state, and the butadiene symmetric MO interacts with the ethene symmetric MO to give the 3 and 4 MOs of the transition state. Therefore, a reaction is allowed when the symmetry labels of the MOs of the reactants are the same; and forbidden when the symmetry labels are different.

The orbital overlap integral is zero in a symmetric-asymmetric interaction and non-zero in symmetric-symmetric and asymmetric-asymmetric interactions.

=== Bond Length Analysis ===

The changes in bond lengths between carbons in reactant, transition state and product as the reaction progresses were studied by comparing the bond lengths between carbons before and after the reaction. The summary of bond lengths is shown below.
[[File:Ex1 bondlength yhw14.png|470px|center|thumb|Diagram 3: Labelled carbons]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #0000FF; color: #ffffff" | State
! style="background: #0000FF; color: #ffffff" | C1-C2
! style="background: #0000FF; color: #ffffff" | C2-C3
! style="background: #0000FF; color: #ffffff" | C3-C4
! style="background: #0000FF; color: #ffffff" | C4-C5
! style="background: #0000FF; color: #ffffff" | C5-C6
! style="background: #0000FF; color: #ffffff" | C6-C1
|-
|Reactants
|1.335
|1.468
|1.335
|/
|1.327
|/
|-
|Transition State
|1.380
|1.411
|1.380
|2.115
|1.382
|2.114
|-
|Product
|1.500
|1.338
|1.500
|1.540
|1.540
|1.540
|+Table 1: Measurements of the C-C bond lengths of the reactants, transition state and products (Å)
|}
As the reaction progresses, the bond lengths between C1-C2, C3-C4 and C5-C6 increase from ~1.3 Å to ~1.5 Å as the bond order decrease to one, whereas bond length of C2-C3 decreases from ~1.5 Å to ~1.3 Å as the bond order increases from one to two.
This could be explained as the increase in bond length suggest a change from sp2-sp2 (C-C double bond) with typical bond length of 1.33 Å <ref name="C-C bond lengths"/> to sp3-sp3 (C-C single bond) with typical bond length of 1.54 Å <ref name="C-C bond lengths"/>, and vice versa for the decrease in bond length. Based on the calculated bond lengths above in Table 1, it is clear that bond lengths and bond orders of the reactants changed during the reaction and the new bonds formed at C4-C5 and C6-C1 are single bonds as they have bond lengths of 1.54 Å.
The typical Van der Waals radius of the C atom is 1.7 Å <ref name="Van der Waals radius of C"/>. As the bond lengths between C4-C5 and C6-C1 of the transition state are shorter than 2 x Van der Waals radii of C, this reflects that C-C bonds are forming at the transition state.

=== Vibration Analysis ===

The imaginary frequency at -948.32 cm-1 corresponds to the reaction path at the transition state, which shows a synchronous bond formation, which agrees with the concerted mechanism of [4+2] cycloaddition, where both reaction centres converge at the same time to form bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 15;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Reaction Path at the Transition State
|}

The lowest positive frequency at 145.14 cm-1 is asynchronous as shown below, where one of the C from the ethene moves towards the butadiene reaction centre and the other C moves away. This suggests that bonds are formed one at a time.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 16;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Lowest positive frequency
|}

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

[[File:Ex2 reactionscheme.png|550px|center|thumb|Diagram 4: Reaction Scheme of Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

Cyclohexadiene and 1,3-dioxole were optimised to their minima at DFT-B3LYP 631-G level. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #9A03FE; color: #ffffff;" |'''Molecule'''
! '''Cyclohexadiene'''
! '''1,3-Dioxole'''
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Cyclo lumo 631g yhw14.png|center|150px]]
|[[File:Dioxole lumo 631g yhw14.png|center|150px]]
|-
|Corresponding to the s orbital
|Corresponding to the a orbital
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Cyclo homo 631g yhw14.png|center|150px]]
|[[File:Dioxole homo 631g yhw14.png|center|150px]]
|-
|Corresponding to the a orbital
|Corresponding to the s orbital
|}

The transition state was first optimised to its minimum, followed by a transition state calculation at DFT-B3LYP 631-G level. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #BD5CFE; color: #ffffff;" |'''Molecule'''
! '''Endo Transition State'''
! '''Exo Transition State'''
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Endo ts lumo+1 yhw14.png|center|150px]]
|[[File:Exo ts lumo+1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 5 orbital (asymmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Endo ts lumo yhw14.png|center|150px]]
|[[File:Exo ts lumo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 4 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Endo ts homo yhw14.png|center|150px]]
|[[File:Exo ts homo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 3 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Endo ts homo-1 yhw14.png|center|150px]]
|[[File:Exo ts homo-1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 2 orbital (asymmetric)
|}

The diagram below illustrates the π molecular orbitals of cyclohexadiene and 1,3-dioxole involved in the formation of the transition state.

[[File:Ex2 mo diagram yhw14.png|550px|center|thumb|Diagram 5: MO diagram of Reaction of Cyclohexadiene and 1,3-dioxole]]

=== Normal Demand vs Inverse Demand Diels-Alder Reaction ===

A normal electron demand Diels-Alder reaction can be defined as a reaction between electron rich diene and electron poor dienophile. An inverse electron demand is the reaction between electron poor diene and electron rich dienophile.

The LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are very close in energy, which results in strong bonding interaction between the two to form the HOMO and LUMO of both endo and exo TS. Since the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole have the correct symmetry (symmetric) to interact, they interact to form the symmetric HOMO and LUMO of both TS.

The presence of electron rich O on 1,3-dioxole raise the energy of both its HOMO and LUMO, making the overlap between the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole much better than the HOMO of cyclohexadiene and the LUMO of 1,3-dioxole. Thus, the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are now the frontier orbitals that interact the most, hence this is an inverse demand Diels-Alder reaction.

=== Reaction Energies and Secondary Orbital Interaction ===

The energies of reactants were taken using the sum of the energies of cyclohexadiene and 1,3-dioxole optimised to their minima at DFT-B3LYP 631-G. The calculations were done using DFT-B3LYP 631-G.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FF4AFF; color: #ffffff" |
! style="background: #FF4AFF; color: #ffffff" | Reactants
! style="background: #FF4AFF; color: #ffffff" | Transition State
! style="background: #FF4AFF; color: #ffffff" | Product
! style="background: #FF4AFF; color: #ffffff" | Activation Energy
! style="background: #FF4AFF; color: #ffffff" | Gibbs Free Energy
|-
|Endo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313622</nowiki>
|<nowiki>-1313849</nowiki>
|160
|<nowiki>-67</nowiki>
|-
|Exo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313614</nowiki>
|<nowiki>-1313846</nowiki>
|168
|<nowiki>-64</nowiki>
|+Table 2: Energies of Reactants, Transition States and Products of both Endo and Exo Pathways in Diels-Alder Reaction of Cyclohexadiene and 1,3-Dioxole (kJ mol-1)
|}

Kinetically favourable product of a reaction is the one that has the lowest activation energy; Thermodynamically favourable product is the product with lowest energy conformer, hence the more stabilised product.

The endo transition state is the kinetic product of this reaction as it has lower activation energy. This could be explained using the secondary orbital interaction between the lone pair orbital on the oxygen atom and the empty π* orbital of diene. This favourable effect stabilises the endo transition state.

As the oxygen atom lone pair is oriented away from the diene π system in the exo transition state, the secondary orbital effect is not present, hence the activation energy of exo reaction is higher.

However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, i.e. increasing temperature, formation of the exo product would be more favourable.

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

Xylylene can react with sulfur dioxide through Diels-Alder reaction via either endo or exo pathways to form a 6-membered ring, or through cheletropic reaction to form a 5-membered ring. The reaction scheme is shown below. Reaction barriers and reaction energies for each pathway are compared to determine the reaction that is most favourable.

[[File:Ex3 reactionscheme yhw14.png|550px|center|thumb|Diagram 6: Reaction Scheme of Xylylene and Sulfur Dioxide]]

=== Intrinsic Reaction Coordinate ===
The following files show the intrinsic reaction coordinates of the three different reaction pathways of xylylene and SO2. Please click to see animation.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Endo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Exo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Cheletropic TS
|-
|[[File:DA endo irc animation yhw14.gif|center]]
|[[File:DA exo irc animation yhw14.gif|center]]
|[[File:Cheletropic irc animation yhw14.gif|center]]
|-
|[[File:DA endo irc plot yhw14.png|center|500px]]
|[[File:DA exo irc plot yhw14.png|center|500px]]
|[[File:Cheletropic irc plot yhw14.png|center|650px]]
|}

=== Reaction Energies and Reaction Barriers ===

[[File:Ex3 reactionprofile yhw14.png|550px|center|thumb|Diagram 7: Reaction Profile of Xylylene and Sulfur Dioxide]]

The energies of reactants were taken using the sum of the energies of xylylene and SO2 optimised to their minima at semi-empirical PM6 level. The calculations were done using semi-empirical PM6.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FFD1C3; color: #ffffff" |
! style="background: #FFD1C3; color: #ffffff" | Reactants
! style="background: #FFD1C3; color: #ffffff" | Transition State
! style="background: #FFD1C3; color: #ffffff" | Product
! style="background: #FFD1C3; color: #ffffff" | Activation Energy
! style="background: #FFD1C3; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|237.767824
|56.9576013
|83.391038
|<nowiki>-97.4191847</nowiki>
|-
|Exo
|154.376786
|241.753433
|56.3196048
|87.406647
|<nowiki>-98.0571812</nowiki>
|-
|Cheletropic
|154.376786
|260.08205
|0.013127501
|105.705264
|<nowiki>-154.3636585</nowiki>
|+Table 3: Energies of Reactants, Transition States and Products of Reactions between Xylylene and Sulfur Dioxide (kJ mol-1)
|}

With reference to the reaction profile and Table 3, the Diels-Alder reaction via the endo pathway has the lowest activation energy, making it a more kinetically favourable product, i.e. the kinetic product; the Diels-Alder exo product has a lower energy than endo, however with a higher activation energy hence it will not form under low temperature condition; the cheletropic product is the most stabilised product out of the three and it has the lowest reaction energy, therefore is the thermodynamic product.

=== Side Reaction between cis-diene in Xylylene 6-membered ring and SO2===

o-Xylylene contains another cis-butadiene fragment located in the 6-membered ring that can undergo a Diels-Alder reaction with SO2. The reaction energies and reaction barriers between endo and exo pathways are compared in the table below.

The energies of reactants were taken using the sum of the energies of xylylene and SO2 optimised to their minima at semi-empirical PM6 level. The calculations were done using semi-empirical PM6.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #4EBEBA; color: #ffffff" |
! style="background: #4EBEBA; color: #ffffff" | Reactants
! style="background: #4EBEBA; color: #ffffff" | Transition State
! style="background: #4EBEBA; color: #ffffff" | Product
! style="background: #4EBEBA; color: #ffffff" | Activation Energy
! style="background: #4EBEBA; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|267.984805
|172.272196
|113.608019
|17.89541
|-
|Exo
|154.376786
|275.821924
|176.711916
|121.445138
|22.33513
|+Table 4: Energies of Reactants, Transition States and Products of the Side Reaction in Xylylene 6-membered ring and Sulfur Dioxide (kJ mol-1)
|}

It is clear that both endo and exo Diels-Alder side reactions are kinetically and thermodynamically unfavourable at this site as the activation energies are much higher than the previous reactions mentioned above in Table 3 and the reaction energies show that the reactions are endothermic.

== Conclusion ==

The transition states of three pericyclic reactions were investigated in this computational lab, using Gaussian to optimise the reactants, transition states and products respectively, and the vibrational frequencies and intrinsic reaction coordinates were computed.

In the reaction between butadiene and ethene, the importance of molecular orbital symmetry in the interaction of molecular orbitals was illustrated, such that a reaction is only allowed when the molecular orbitals with the same symmetry labels interact with each other and forbidden when symmetric molecular orbital interact with asymmetric orbitals. Furthermore, the vibration frequency calculation proved that this [4+2] Diels-Alder reaction proceeds via a concerted mechanism as synchronous bond formation was demonstrated. Bonding interaction can be further confirmed as the bond distance between the two termini carbon atoms in the transition state is shorter than the sum of two Van der Waals radii of carbon.

In the reaction of cyclohexadiene and 1,3-dioxole, both the endo and exo transition states were investigated. In general, the endo transition state is kinetically more favourable as it has lower activation barrier, possibly due to the secondary orbital interaction between the lone pair in p orbital on the oxygen atom and the empty pi* orbital in the diene, which stabilises the transition state. However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, formation of the exo product could be possible.

The final reaction between xylylene and SO2 again proved that the endo Diels-Alder transition state has the lowest activation energy, making it kinetically favourable at low temperature. However, the cheletropic product is the most stabilised and thermodynamically favourable product. Therefore the reaction would yield the cheletropic product under thermodynamic control instead of the exo Diels-Alder product.

==References==
<references>
<ref name="C-C bond lengths">L. Pauling and L. O. Brockway, ''Journal of the American Chemical Society'', '''1937''', Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref>
<ref name="Van der Waals radius of C">S. S. Batsanov, ''Inorganic Materials'', '''2001''', Volume 37, Number 9, pp. 871-885, https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf.</ref>
</references>

Rep:Mod:yhw14cts

2017-02-10T01:22:04Z

Yhw14: /* Introduction */

''' Transition States and Reactivity '''

'' Yi Hang Cherie WONG (yhw14) ''
'' CID: 00933828 ''

== Introduction ==
A potential energy surface is a mathematical or graphical function that gives relationship between the energy of a molecule and its geometry with the relative positions of the atoms participating in the reaction. The stationary points may be classified according to the first and second derivatives of the energy with respect to position. At the minimum of a reaction profile, the gradient is represented by the first derivative of the reaction coordinate, which is zero, while curvature is represented by the second derivative, is positive in this case; hence energy rises in all directions. Energy minima correspond to physically stable chemical species, which could be reactants and products. The transition state is defined as the maximum in a reaction profile, where the gradient is again, zero, while curvature is negative; hence energy decreases in one direction, which indicates the reaction pathway of the chemical reaction. The potential energy surface can be computed using Gaussview 09, where structure and energy of reactants or products can be modelled to illustrate the transition states, which can rarely be obtained experimentally. The intrinsic reaction coordinate can then be calculated and compared to predict the reaction path at a transition state and follow it to the correct minima.

In this computational lab, all of the reactants and products were optimised to their minima, and the transition states were also optimised. The calculations were done by Gaussian 09, using mainly semi-empirical method PM6 and Density Functional Theory-B3LYP-631G. The latter is a more detailed and accurate optimisation, which is more time consuming method as it involves a higher number of basis set. Frequency calculations were performed to show molecular vibrations to confirm the position on the potential energy surface. If all the vibrational frequencies are real, this confirms the structure is a minimum, and vice versa, the presence of imaginary frequency may suggest that the structure is at its transition state. Intrinsic reaction coordinate method was carried out using calculated force constants to predict which conformer a reaction path from the transition state would lead to.

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

The reaction between butadiene and ethene is a typical pericyclic [4+2] Diels-Alder reaction that proceeds via a concerted mechanism through a cyclic transition state. The reaction scheme is shown below.

[[File:Ex1 reactionscheme revised yhw14.png|550px|center|thumb|Diagram 1: Reaction Scheme of Butadiene and Ethene]]

=== Molecular Orbital Analysis ===

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of butadiene and ethene.

[[File:Ex1 mo diagram yhw14 revised v3.png|550px|center|thumb|Diagram 2: MO diagram of Reaction of Butadiene and Ethene]]

Butadiene and ethene were optimised to their minima at semi-empirical method PM6 level. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #06DCFB; color: #ffffff;" |'''Molecule'''
! '''Butadiene'''
! '''Ethene'''
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Butadiene lumo yhw14.png|center|150px]]
|[[File:Ethene lumo yhw14.png|center|150px]]
|-
|Corresponding to the s orbital (symmetric)
|Corresponding to the a orbital (asymmetric)
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Butadiene homo yhw14.png|center|150px]]
|[[File:Ethene homo yhw14.png|center|150px]]
|-
|Corresponding to the a orbital (antisymmetric)
|Corresponding to the s orbital (symmetric)
|}

The transition state was first optimised to its minimum, followed by a transition state calculation at semi-empirical method PM6 level. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #01FCEF; color: #ffffff;" |'''Molecule'''
! '''Transition State'''
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Ts lumo+1 yhw14.png|center|150px]]
|-
|Corresponding to the 5 orbital (asymmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Ts lumo 1 yhw14.png|center|150px]]
|-
|Corresponding to the 4 orbital (symmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Ts homo yhw14.png|center|150px]]
|-
|Corresponding to the 3 orbital (symmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Ts homo-1 yhw14.png|center|150px]]
|-
|Corresponding to the 2 orbital (asymmetrical)
|}

Based on the MO diagram and the computed MOs shown above, a reaction is only allowed when the MOs with the same symmetry labels interact with each other, i.e. symmetric-symmetric and asymmetric-asymmetric interactions; and a reaction is forbidden when the MOs with different symmetry labels interact with each other, i.e. symmetric-asymmetric interactions.
In the reaction between butadiene and ethene, the butadiene asymmetric MO interacts with the ethene asymmetric MO to give the 2 and 5 MOs of the transition state, and the butadiene symmetric MO interacts with the ethene symmetric MO to give the 3 and 4 MOs of the transition state. Therefore, a reaction is allowed when the symmetry labels of the MOs of the reactants are the same; and forbidden when the symmetry labels are different.

The orbital overlap integral is zero in a symmetric-asymmetric interaction and non-zero in symmetric-symmetric and asymmetric-asymmetric interactions.

=== Bond Length Analysis ===

The changes in bond lengths between carbons in reactant, transition state and product as the reaction progresses were studied by comparing the bond lengths between carbons before and after the reaction. The summary of bond lengths is shown below.
[[File:Ex1 bondlength yhw14.png|470px|center|thumb|Diagram 3: Labelled carbons]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #0000FF; color: #ffffff" | State
! style="background: #0000FF; color: #ffffff" | C1-C2
! style="background: #0000FF; color: #ffffff" | C2-C3
! style="background: #0000FF; color: #ffffff" | C3-C4
! style="background: #0000FF; color: #ffffff" | C4-C5
! style="background: #0000FF; color: #ffffff" | C5-C6
! style="background: #0000FF; color: #ffffff" | C6-C1
|-
|Reactants
|1.335
|1.468
|1.335
|/
|1.327
|/
|-
|Transition State
|1.380
|1.411
|1.380
|2.115
|1.382
|2.114
|-
|Product
|1.500
|1.338
|1.500
|1.540
|1.540
|1.540
|+Table 1: Measurements of the C-C bond lengths of the reactants, transition state and products (Å)
|}
As the reaction progresses, the bond lengths between C1-C2, C3-C4 and C5-C6 increase from ~1.3 Å to ~1.5 Å as the bond order decrease to one, whereas bond length of C2-C3 decreases from ~1.5 Å to ~1.3 Å as the bond order increases from one to two.
This could be explained as the increase in bond length suggest a change from sp2-sp2 (C-C double bond) with typical bond length of 1.33 Å <ref name="C-C bond lengths"/> to sp3-sp3 (C-C single bond) with typical bond length of 1.54 Å <ref name="C-C bond lengths"/>, and vice versa for the decrease in bond length. Based on the calculated bond lengths above in Table 1, it is clear that bond lengths and bond orders of the reactants changed during the reaction and the new bonds formed at C4-C5 and C6-C1 are single bonds as they have bond lengths of 1.54 Å.
The typical Van der Waals radius of the C atom is 1.7 Å <ref name="Van der Waals radius of C"/>. As the bond lengths between C4-C5 and C6-C1 of the transition state are shorter than 2 x Van der Waals radii of C, this reflects that C-C bonds are forming at the transition state.

=== Vibration Analysis ===

The imaginary frequency at -948.32 cm-1 corresponds to the reaction path at the transition state, which shows a synchronous bond formation, which agrees with the concerted mechanism of [4+2] cycloaddition, where both reaction centres converge at the same time to form bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 15;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Reaction Path at the Transition State
|}

The lowest positive frequency at 145.14 cm-1 is asynchronous as shown below, where one of the C from the ethene moves towards the butadiene reaction centre and the other C moves away. This suggests that bonds are formed one at a time.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 16;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Lowest positive frequency
|}

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

[[File:Ex2 reactionscheme.png|550px|center|thumb|Diagram 4: Reaction Scheme of Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

Cyclohexadiene and 1,3-dioxole were optimised to their minima at DFT-B3LYP 631-G level. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #9A03FE; color: #ffffff;" |'''Molecule'''
! '''Cyclohexadiene'''
! '''1,3-Dioxole'''
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Cyclo lumo 631g yhw14.png|center|150px]]
|[[File:Dioxole lumo 631g yhw14.png|center|150px]]
|-
|Corresponding to the s orbital
|Corresponding to the a orbital
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Cyclo homo 631g yhw14.png|center|150px]]
|[[File:Dioxole homo 631g yhw14.png|center|150px]]
|-
|Corresponding to the a orbital
|Corresponding to the s orbital
|}

The transition state was first optimised to its minimum, followed by a transition state calculation at DFT-B3LYP 631-G level. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #BD5CFE; color: #ffffff;" |'''Molecule'''
! '''Endo Transition State'''
! '''Exo Transition State'''
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Endo ts lumo+1 yhw14.png|center|150px]]
|[[File:Exo ts lumo+1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 5 orbital (asymmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Endo ts lumo yhw14.png|center|150px]]
|[[File:Exo ts lumo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 4 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Endo ts homo yhw14.png|center|150px]]
|[[File:Exo ts homo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 3 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Endo ts homo-1 yhw14.png|center|150px]]
|[[File:Exo ts homo-1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 2 orbital (asymmetric)
|}

The diagram below illustrates the π molecular orbitals of cyclohexadiene and 1,3-dioxole involved in the formation of the transition state.

[[File:Ex2 mo diagram yhw14.png|550px|center|thumb|Diagram 5: MO diagram of Reaction of Cyclohexadiene and 1,3-dioxole]]

=== Normal Demand vs Inverse Demand Diels-Alder Reaction ===

A normal electron demand Diels-Alder reaction can be defined as a reaction between electron rich diene and electron poor dienophile. An inverse electron demand is the reaction between electron poor diene and electron rich dienophile.

The LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are very close in energy, which results in strong bonding interaction between the two to form the HOMO and LUMO of both endo and exo TS. Since the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole have the correct symmetry (symmetric) to interact, they interact to form the symmetric HOMO and LUMO of both TS.

The presence of electron rich O on 1,3-dioxole raise the energy of both its HOMO and LUMO, making the overlap between the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole much better than the HOMO of cyclohexadiene and the LUMO of 1,3-dioxole. Thus, the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are now the frontier orbitals that interact the most, hence this is an inverse demand Diels-Alder reaction.

=== Reaction Energies and Secondary Orbital Interaction ===

The energies of reactants were taken using the sum of the energies of cyclohexadiene and 1,3-dioxole optimised to their minima at DFT-B3LYP 631-G. The calculations were done using DFT-B3LYP 631-G.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FF4AFF; color: #ffffff" |
! style="background: #FF4AFF; color: #ffffff" | Reactants
! style="background: #FF4AFF; color: #ffffff" | Transition State
! style="background: #FF4AFF; color: #ffffff" | Product
! style="background: #FF4AFF; color: #ffffff" | Activation Energy
! style="background: #FF4AFF; color: #ffffff" | Gibbs Free Energy
|-
|Endo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313622</nowiki>
|<nowiki>-1313849</nowiki>
|160
|<nowiki>-67</nowiki>
|-
|Exo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313614</nowiki>
|<nowiki>-1313846</nowiki>
|168
|<nowiki>-64</nowiki>
|+Table 2: Energies of Reactants, Transition States and Products of both Endo and Exo Pathways in Diels-Alder Reaction of Cyclohexadiene and 1,3-Dioxole (kJ mol-1)
|}

Kinetically favourable product of a reaction is the one that has the lowest activation energy; Thermodynamically favourable product is the product with lowest energy conformer, hence the more stabilised product.

The endo transition state is the kinetic product of this reaction as it has lower activation energy. This could be explained using the secondary orbital interaction between the lone pair orbital on the oxygen atom and the empty π* orbital of diene. This favourable effect stabilises the endo transition state.

As the oxygen atom lone pair is oriented away from the diene π system in the exo transition state, the secondary orbital effect is not present, hence the activation energy of exo reaction is higher.

However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, i.e. increasing temperature, formation of the exo product would be more favourable.

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

Xylylene can react with sulfur dioxide through Diels-Alder reaction via either endo or exo pathways to form a 6-membered ring, or through cheletropic reaction to form a 5-membered ring. The reaction scheme is shown below. Reaction barriers and reaction energies for each pathway are compared to determine the reaction that is most favourable.

[[File:Ex3 reactionscheme yhw14.png|550px|center|thumb|Diagram 6: Reaction Scheme of Xylylene and Sulfur Dioxide]]

=== Intrinsic Reaction Coordinate ===
The following files show the intrinsic reaction coordinates of the three different reaction pathways of xylylene and SO2. Please click to see animation.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Endo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Exo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Cheletropic TS
|-
|[[File:DA endo irc animation yhw14.gif|center]]
|[[File:DA exo irc animation yhw14.gif|center]]
|[[File:Cheletropic irc animation yhw14.gif|center]]
|-
|[[File:DA endo irc plot yhw14.png|center|500px]]
|[[File:DA exo irc plot yhw14.png|center|500px]]
|[[File:Cheletropic irc plot yhw14.png|center|650px]]
|}

=== Reaction Energies and Reaction Barriers ===

[[File:Ex3 reactionprofile yhw14.png|550px|center|thumb|Diagram 7: Reaction Profile of Xylylene and Sulfur Dioxide]]

The energies of reactants were taken using the sum of the energies of xylylene and SO2 optimised to their minima at semi-empirical PM6 level. The calculations were done using semi-empirical PM6.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FFD1C3; color: #ffffff" |
! style="background: #FFD1C3; color: #ffffff" | Reactants
! style="background: #FFD1C3; color: #ffffff" | Transition State
! style="background: #FFD1C3; color: #ffffff" | Product
! style="background: #FFD1C3; color: #ffffff" | Activation Energy
! style="background: #FFD1C3; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|237.767824
|56.9576013
|83.391038
|<nowiki>-97.4191847</nowiki>
|-
|Exo
|154.376786
|241.753433
|56.3196048
|87.406647
|<nowiki>-98.0571812</nowiki>
|-
|Cheletropic
|154.376786
|260.08205
|0.013127501
|105.705264
|<nowiki>-154.3636585</nowiki>
|+Table 3: Energies of Reactants, Transition States and Products of Reactions between Xylylene and Sulfur Dioxide (kJ mol-1)
|}

With reference to the reaction profile and Table 3, the Diels-Alder reaction via the endo pathway has the lowest activation energy, making it a more kinetically favourable product, i.e. the kinetic product; the Diels-Alder exo product has a lower energy than endo, however with a higher activation energy hence it will not form under low temperature condition; the cheletropic product is the most stabilised product out of the three and it has the lowest reaction energy, therefore is the thermodynamic product.

=== Side Reaction between cis-diene in Xylylene 6-membered ring and SO2===

o-Xylylene contains another cis-butadiene fragment located in the 6-membered ring that can undergo a Diels-Alder reaction with SO2. The reaction energies and reaction barriers between endo and exo pathways are compared in the table below.

The energies of reactants were taken using the sum of the energies of xylylene and SO2 optimised to their minima at semi-empirical PM6 level. The calculations were done using semi-empirical PM6.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #4EBEBA; color: #ffffff" |
! style="background: #4EBEBA; color: #ffffff" | Reactants
! style="background: #4EBEBA; color: #ffffff" | Transition State
! style="background: #4EBEBA; color: #ffffff" | Product
! style="background: #4EBEBA; color: #ffffff" | Activation Energy
! style="background: #4EBEBA; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|267.984805
|172.272196
|113.608019
|17.89541
|-
|Exo
|154.376786
|275.821924
|176.711916
|121.445138
|22.33513
|+Table 4: Energies of Reactants, Transition States and Products of the Side Reaction in Xylylene 6-membered ring and Sulfur Dioxide (kJ mol-1)
|}

It is clear that both endo and exo Diels-Alder side reactions are kinetically and thermodynamically unfavourable at this site as the activation energies are much higher than the previous reactions mentioned above in Table 3 and the reaction energies show that the reactions are endothermic.

== Conclusion ==

The transition states of three pericyclic reactions were investigated in this computational lab, using Gaussian to optimise the reactants, transition states and products respectively, and the vibrational frequencies and intrinsic reaction coordinates were computed.

In the reaction between butadiene and ethene, the importance of molecular orbital symmetry in the interaction of molecular orbitals was illustrated, such that a reaction is only allowed when the molecular orbitals with the same symmetry labels interact with each other and forbidden when symmetric molecular orbital interact with asymmetric orbitals. Furthermore, the vibration frequency calculation proved that this [4+2] Diels-Alder reaction proceeds via a concerted mechanism as synchronous bond formation was demonstrated. Bonding interaction can be further confirmed as the bond distance between the two termini carbon atoms in the transition state is shorter than the sum of two Van der Waals radii of carbon.

In the reaction of cyclohexadiene and 1,3-dioxole, both the endo and exo transition states were investigated. In general, the endo transition state is kinetically more favourable as it has lower activation barrier, possibly due to the secondary orbital interaction between the lone pair in p orbital on the oxygen atom and the empty pi* orbital in the diene, which stabilises the transition state. However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, formation of the exo product could be possible.

The final reaction between xylylene and SO2 again proved that the endo Diels-Alder transition state has the lowest activation energy, making it kinetically favourable at low temperature. However, the cheletropic product is the most stabilised and thermodynamically favourable product. Therefore the reaction would yield the cheletropic product under thermodynamic control instead of the exo Diels-Alder product.

==References==
<references>
<ref name="C-C bond lengths">L. Pauling and L. O. Brockway, ''Journal of the American Chemical Society'', '''1937''', Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref>
<ref name="Van der Waals radius of C">S. S. Batsanov, ''Inorganic Materials'', '''2001''', Volume 37, Number 9, pp. 871-885, https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf.</ref>
</references>

Rep:Mod:yhw14cts

2017-02-09T21:16:16Z

Yhw14: /* Side Reaction between cis-diene in Xylylene 6-membered ring and SO2 */

''' Transition States and Reactivity '''

'' Yi Hang Cherie WONG (yhw14) ''
'' CID: 00933828 ''

== Introduction ==
A potential energy surface is a mathematical function that gives the energy of a molecule as a function of its geometry with the relative positions of the atoms participating in the reaction. The stationary points may be classified according to the first and second derivatives of the energy with respect to position. At the minimum of a reaction profile, the gradient is represented by the first derivative of the reaction coordinate, which is zero, while curvature is represented by the second derivative, is positive in this case; hence energy rises in all directions. Energy minima correspond to physically stable chemical species, which could be reactants and products. The transition state is defined as the maximum in a reaction profile, where the gradient is again, zero, while curvature is negative; hence energy decreases in one direction, which indicates the reaction pathway of the chemical reaction. The potential energy surface can be computed using Gaussview 09, where structure and energy of reactants or products can be modelled to illustrate the transition states, which can rarely be obtained experimentally. The intrinsic reaction coordinate can then be calculated and compared to predict the reaction path at a transition state and follow it to the correct minima.

In this computational lab, all of the reactants and products were optimised to their minima, and the transition states were also optimised. The calculations were done by Gaussian 09, using mainly semi-empirical method PM6 and DFT-B3LYP. Frequency calculations were performed to show molecular vibrations to confirm the position on the potential energy surface. If all the vibrational frequencies are real, this confirms the structure is a minimum, and vice versa, the presence of imaginary frequency may suggest that the structure is at its transition state. Intrinsic reaction coordinate method was carried out using calculated force constants to predict which conformer a reaction path from the transition state would lead to.

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

The reaction between butadiene and ethene is a typical pericyclic [4+2] Diels-Alder reaction that proceeds via a concerted mechanism through a cyclic transition state. The reaction scheme is shown below.

[[File:Ex1 reactionscheme revised yhw14.png|550px|center|thumb|Diagram 1: Reaction Scheme of Butadiene and Ethene]]

=== Molecular Orbital Analysis ===

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of butadiene and ethene.

[[File:Ex1 mo diagram yhw14 revised v3.png|550px|center|thumb|Diagram 2: MO diagram of Reaction of Butadiene and Ethene]]

Butadiene and ethene were optimised to their minima at semi-empirical method PM6 level. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #06DCFB; color: #ffffff;" |'''Molecule'''
! '''Butadiene'''
! '''Ethene'''
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Butadiene lumo yhw14.png|center|150px]]
|[[File:Ethene lumo yhw14.png|center|150px]]
|-
|Corresponding to the s orbital (symmetric)
|Corresponding to the a orbital (asymmetric)
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Butadiene homo yhw14.png|center|150px]]
|[[File:Ethene homo yhw14.png|center|150px]]
|-
|Corresponding to the a orbital (antisymmetric)
|Corresponding to the s orbital (symmetric)
|}

The transition state was first optimised to its minimum, followed by a transition state calculation at semi-empirical method PM6 level. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #01FCEF; color: #ffffff;" |'''Molecule'''
! '''Transition State'''
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Ts lumo+1 yhw14.png|center|150px]]
|-
|Corresponding to the 5 orbital (asymmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Ts lumo 1 yhw14.png|center|150px]]
|-
|Corresponding to the 4 orbital (symmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Ts homo yhw14.png|center|150px]]
|-
|Corresponding to the 3 orbital (symmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Ts homo-1 yhw14.png|center|150px]]
|-
|Corresponding to the 2 orbital (asymmetrical)
|}

Based on the MO diagram and the computed MOs shown above, a reaction is only allowed when the MOs with the same symmetry labels interact with each other, i.e. symmetric-symmetric and asymmetric-asymmetric interactions; and a reaction is forbidden when the MOs with different symmetry labels interact with each other, i.e. symmetric-asymmetric interactions.
In the reaction between butadiene and ethene, the butadiene asymmetric MO interacts with the ethene asymmetric MO to give the 2 and 5 MOs of the transition state, and the butadiene symmetric MO interacts with the ethene symmetric MO to give the 3 and 4 MOs of the transition state. Therefore, a reaction is allowed when the symmetry labels of the MOs of the reactants are the same; and forbidden when the symmetry labels are different.

The orbital overlap integral is zero in a symmetric-asymmetric interaction and non-zero in symmetric-symmetric and asymmetric-asymmetric interactions.

=== Bond Length Analysis ===

The changes in bond lengths between carbons in reactant, transition state and product as the reaction progresses were studied by comparing the bond lengths between carbons before and after the reaction. The summary of bond lengths is shown below.
[[File:Ex1 bondlength yhw14.png|470px|center|thumb|Diagram 3: Labelled carbons]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #0000FF; color: #ffffff" | State
! style="background: #0000FF; color: #ffffff" | C1-C2
! style="background: #0000FF; color: #ffffff" | C2-C3
! style="background: #0000FF; color: #ffffff" | C3-C4
! style="background: #0000FF; color: #ffffff" | C4-C5
! style="background: #0000FF; color: #ffffff" | C5-C6
! style="background: #0000FF; color: #ffffff" | C6-C1
|-
|Reactants
|1.335
|1.468
|1.335
|/
|1.327
|/
|-
|Transition State
|1.380
|1.411
|1.380
|2.115
|1.382
|2.114
|-
|Product
|1.500
|1.338
|1.500
|1.540
|1.540
|1.540
|+Table 1: Measurements of the C-C bond lengths of the reactants, transition state and products (Å)
|}
As the reaction progresses, the bond lengths between C1-C2, C3-C4 and C5-C6 increase from ~1.3 Å to ~1.5 Å as the bond order decrease to one, whereas bond length of C2-C3 decreases from ~1.5 Å to ~1.3 Å as the bond order increases from one to two.
This could be explained as the increase in bond length suggest a change from sp2-sp2 (C-C double bond) with typical bond length of 1.33 Å <ref name="C-C bond lengths"/> to sp3-sp3 (C-C single bond) with typical bond length of 1.54 Å <ref name="C-C bond lengths"/>, and vice versa for the decrease in bond length. Based on the calculated bond lengths above in Table 1, it is clear that bond lengths and bond orders of the reactants changed during the reaction and the new bonds formed at C4-C5 and C6-C1 are single bonds as they have bond lengths of 1.54 Å.
The typical Van der Waals radius of the C atom is 1.7 Å <ref name="Van der Waals radius of C"/>. As the bond lengths between C4-C5 and C6-C1 of the transition state are shorter than 2 x Van der Waals radii of C, this reflects that C-C bonds are forming at the transition state.

=== Vibration Analysis ===

The imaginary frequency at -948.32 cm-1 corresponds to the reaction path at the transition state, which shows a synchronous bond formation, which agrees with the concerted mechanism of [4+2] cycloaddition, where both reaction centres converge at the same time to form bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 15;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Reaction Path at the Transition State
|}

The lowest positive frequency at 145.14 cm-1 is asynchronous as shown below, where one of the C from the ethene moves towards the butadiene reaction centre and the other C moves away. This suggests that bonds are formed one at a time.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 16;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Lowest positive frequency
|}

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

[[File:Ex2 reactionscheme.png|550px|center|thumb|Diagram 4: Reaction Scheme of Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

Cyclohexadiene and 1,3-dioxole were optimised to their minima at DFT-B3LYP 631-G level. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #9A03FE; color: #ffffff;" |'''Molecule'''
! '''Cyclohexadiene'''
! '''1,3-Dioxole'''
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Cyclo lumo 631g yhw14.png|center|150px]]
|[[File:Dioxole lumo 631g yhw14.png|center|150px]]
|-
|Corresponding to the s orbital
|Corresponding to the a orbital
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Cyclo homo 631g yhw14.png|center|150px]]
|[[File:Dioxole homo 631g yhw14.png|center|150px]]
|-
|Corresponding to the a orbital
|Corresponding to the s orbital
|}

The transition state was first optimised to its minimum, followed by a transition state calculation at DFT-B3LYP 631-G level. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #BD5CFE; color: #ffffff;" |'''Molecule'''
! '''Endo Transition State'''
! '''Exo Transition State'''
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Endo ts lumo+1 yhw14.png|center|150px]]
|[[File:Exo ts lumo+1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 5 orbital (asymmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Endo ts lumo yhw14.png|center|150px]]
|[[File:Exo ts lumo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 4 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Endo ts homo yhw14.png|center|150px]]
|[[File:Exo ts homo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 3 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Endo ts homo-1 yhw14.png|center|150px]]
|[[File:Exo ts homo-1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 2 orbital (asymmetric)
|}

The diagram below illustrates the π molecular orbitals of cyclohexadiene and 1,3-dioxole involved in the formation of the transition state.

[[File:Ex2 mo diagram yhw14.png|550px|center|thumb|Diagram 5: MO diagram of Reaction of Cyclohexadiene and 1,3-dioxole]]

=== Normal Demand vs Inverse Demand Diels-Alder Reaction ===

A normal electron demand Diels-Alder reaction can be defined as a reaction between electron rich diene and electron poor dienophile. An inverse electron demand is the reaction between electron poor diene and electron rich dienophile.

The LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are very close in energy, which results in strong bonding interaction between the two to form the HOMO and LUMO of both endo and exo TS. Since the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole have the correct symmetry (symmetric) to interact, they interact to form the symmetric HOMO and LUMO of both TS.

The presence of electron rich O on 1,3-dioxole raise the energy of both its HOMO and LUMO, making the overlap between the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole much better than the HOMO of cyclohexadiene and the LUMO of 1,3-dioxole. Thus, the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are now the frontier orbitals that interact the most, hence this is an inverse demand Diels-Alder reaction.

=== Reaction Energies and Secondary Orbital Interaction ===

The energies of reactants were taken using the sum of the energies of cyclohexadiene and 1,3-dioxole optimised to their minima at DFT-B3LYP 631-G. The calculations were done using DFT-B3LYP 631-G.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FF4AFF; color: #ffffff" |
! style="background: #FF4AFF; color: #ffffff" | Reactants
! style="background: #FF4AFF; color: #ffffff" | Transition State
! style="background: #FF4AFF; color: #ffffff" | Product
! style="background: #FF4AFF; color: #ffffff" | Activation Energy
! style="background: #FF4AFF; color: #ffffff" | Gibbs Free Energy
|-
|Endo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313622</nowiki>
|<nowiki>-1313849</nowiki>
|160
|<nowiki>-67</nowiki>
|-
|Exo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313614</nowiki>
|<nowiki>-1313846</nowiki>
|168
|<nowiki>-64</nowiki>
|+Table 2: Energies of Reactants, Transition States and Products of both Endo and Exo Pathways in Diels-Alder Reaction of Cyclohexadiene and 1,3-Dioxole (kJ mol-1)
|}

Kinetically favourable product of a reaction is the one that has the lowest activation energy; Thermodynamically favourable product is the product with lowest energy conformer, hence the more stabilised product.

The endo transition state is the kinetic product of this reaction as it has lower activation energy. This could be explained using the secondary orbital interaction between the lone pair orbital on the oxygen atom and the empty π* orbital of diene. This favourable effect stabilises the endo transition state.

As the oxygen atom lone pair is oriented away from the diene π system in the exo transition state, the secondary orbital effect is not present, hence the activation energy of exo reaction is higher.

However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, i.e. increasing temperature, formation of the exo product would be more favourable.

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

Xylylene can react with sulfur dioxide through Diels-Alder reaction via either endo or exo pathways to form a 6-membered ring, or through cheletropic reaction to form a 5-membered ring. The reaction scheme is shown below. Reaction barriers and reaction energies for each pathway are compared to determine the reaction that is most favourable.

[[File:Ex3 reactionscheme yhw14.png|550px|center|thumb|Diagram 6: Reaction Scheme of Xylylene and Sulfur Dioxide]]

=== Intrinsic Reaction Coordinate ===
The following files show the intrinsic reaction coordinates of the three different reaction pathways of xylylene and SO2. Please click to see animation.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Endo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Exo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Cheletropic TS
|-
|[[File:DA endo irc animation yhw14.gif|center]]
|[[File:DA exo irc animation yhw14.gif|center]]
|[[File:Cheletropic irc animation yhw14.gif|center]]
|-
|[[File:DA endo irc plot yhw14.png|center|500px]]
|[[File:DA exo irc plot yhw14.png|center|500px]]
|[[File:Cheletropic irc plot yhw14.png|center|650px]]
|}

=== Reaction Energies and Reaction Barriers ===

[[File:Ex3 reactionprofile yhw14.png|550px|center|thumb|Diagram 7: Reaction Profile of Xylylene and Sulfur Dioxide]]

The energies of reactants were taken using the sum of the energies of xylylene and SO2 optimised to their minima at semi-empirical PM6 level. The calculations were done using semi-empirical PM6.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FFD1C3; color: #ffffff" |
! style="background: #FFD1C3; color: #ffffff" | Reactants
! style="background: #FFD1C3; color: #ffffff" | Transition State
! style="background: #FFD1C3; color: #ffffff" | Product
! style="background: #FFD1C3; color: #ffffff" | Activation Energy
! style="background: #FFD1C3; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|237.767824
|56.9576013
|83.391038
|<nowiki>-97.4191847</nowiki>
|-
|Exo
|154.376786
|241.753433
|56.3196048
|87.406647
|<nowiki>-98.0571812</nowiki>
|-
|Cheletropic
|154.376786
|260.08205
|0.013127501
|105.705264
|<nowiki>-154.3636585</nowiki>
|+Table 3: Energies of Reactants, Transition States and Products of Reactions between Xylylene and Sulfur Dioxide (kJ mol-1)
|}

With reference to the reaction profile and Table 3, the Diels-Alder reaction via the endo pathway has the lowest activation energy, making it a more kinetically favourable product, i.e. the kinetic product; the Diels-Alder exo product has a lower energy than endo, however with a higher activation energy hence it will not form under low temperature condition; the cheletropic product is the most stabilised product out of the three and it has the lowest reaction energy, therefore is the thermodynamic product.

=== Side Reaction between cis-diene in Xylylene 6-membered ring and SO2===

o-Xylylene contains another cis-butadiene fragment located in the 6-membered ring that can undergo a Diels-Alder reaction with SO2. The reaction energies and reaction barriers between endo and exo pathways are compared in the table below.

The energies of reactants were taken using the sum of the energies of xylylene and SO2 optimised to their minima at semi-empirical PM6 level. The calculations were done using semi-empirical PM6.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #4EBEBA; color: #ffffff" |
! style="background: #4EBEBA; color: #ffffff" | Reactants
! style="background: #4EBEBA; color: #ffffff" | Transition State
! style="background: #4EBEBA; color: #ffffff" | Product
! style="background: #4EBEBA; color: #ffffff" | Activation Energy
! style="background: #4EBEBA; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|267.984805
|172.272196
|113.608019
|17.89541
|-
|Exo
|154.376786
|275.821924
|176.711916
|121.445138
|22.33513
|+Table 4: Energies of Reactants, Transition States and Products of the Side Reaction in Xylylene 6-membered ring and Sulfur Dioxide (kJ mol-1)
|}

It is clear that both endo and exo Diels-Alder side reactions are kinetically and thermodynamically unfavourable at this site as the activation energies are much higher than the previous reactions mentioned above in Table 3 and the reaction energies show that the reactions are endothermic.

== Conclusion ==

The transition states of three pericyclic reactions were investigated in this computational lab, using Gaussian to optimise the reactants, transition states and products respectively, and the vibrational frequencies and intrinsic reaction coordinates were computed.

In the reaction between butadiene and ethene, the importance of molecular orbital symmetry in the interaction of molecular orbitals was illustrated, such that a reaction is only allowed when the molecular orbitals with the same symmetry labels interact with each other and forbidden when symmetric molecular orbital interact with asymmetric orbitals. Furthermore, the vibration frequency calculation proved that this [4+2] Diels-Alder reaction proceeds via a concerted mechanism as synchronous bond formation was demonstrated. Bonding interaction can be further confirmed as the bond distance between the two termini carbon atoms in the transition state is shorter than the sum of two Van der Waals radii of carbon.

In the reaction of cyclohexadiene and 1,3-dioxole, both the endo and exo transition states were investigated. In general, the endo transition state is kinetically more favourable as it has lower activation barrier, possibly due to the secondary orbital interaction between the lone pair in p orbital on the oxygen atom and the empty pi* orbital in the diene, which stabilises the transition state. However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, formation of the exo product could be possible.

The final reaction between xylylene and SO2 again proved that the endo Diels-Alder transition state has the lowest activation energy, making it kinetically favourable at low temperature. However, the cheletropic product is the most stabilised and thermodynamically favourable product. Therefore the reaction would yield the cheletropic product under thermodynamic control instead of the exo Diels-Alder product.

==References==
<references>
<ref name="C-C bond lengths">L. Pauling and L. O. Brockway, ''Journal of the American Chemical Society'', '''1937''', Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref>
<ref name="Van der Waals radius of C">S. S. Batsanov, ''Inorganic Materials'', '''2001''', Volume 37, Number 9, pp. 871-885, https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf.</ref>
</references>

Rep:Mod:yhw14cts

2017-02-09T20:55:43Z

Yhw14:

''' Transition States and Reactivity '''

'' Yi Hang Cherie WONG (yhw14) ''
'' CID: 00933828 ''

== Introduction ==
A potential energy surface is a mathematical function that gives the energy of a molecule as a function of its geometry with the relative positions of the atoms participating in the reaction. The stationary points may be classified according to the first and second derivatives of the energy with respect to position. At the minimum of a reaction profile, the gradient is represented by the first derivative of the reaction coordinate, which is zero, while curvature is represented by the second derivative, is positive in this case; hence energy rises in all directions. Energy minima correspond to physically stable chemical species, which could be reactants and products. The transition state is defined as the maximum in a reaction profile, where the gradient is again, zero, while curvature is negative; hence energy decreases in one direction, which indicates the reaction pathway of the chemical reaction. The potential energy surface can be computed using Gaussview 09, where structure and energy of reactants or products can be modelled to illustrate the transition states, which can rarely be obtained experimentally. The intrinsic reaction coordinate can then be calculated and compared to predict the reaction path at a transition state and follow it to the correct minima.

In this computational lab, all of the reactants and products were optimised to their minima, and the transition states were also optimised. The calculations were done by Gaussian 09, using mainly semi-empirical method PM6 and DFT-B3LYP. Frequency calculations were performed to show molecular vibrations to confirm the position on the potential energy surface. If all the vibrational frequencies are real, this confirms the structure is a minimum, and vice versa, the presence of imaginary frequency may suggest that the structure is at its transition state. Intrinsic reaction coordinate method was carried out using calculated force constants to predict which conformer a reaction path from the transition state would lead to.

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

The reaction between butadiene and ethene is a typical pericyclic [4+2] Diels-Alder reaction that proceeds via a concerted mechanism through a cyclic transition state. The reaction scheme is shown below.

[[File:Ex1 reactionscheme revised yhw14.png|550px|center|thumb|Diagram 1: Reaction Scheme of Butadiene and Ethene]]

=== Molecular Orbital Analysis ===

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of butadiene and ethene.

[[File:Ex1 mo diagram yhw14 revised v3.png|550px|center|thumb|Diagram 2: MO diagram of Reaction of Butadiene and Ethene]]

Butadiene and ethene were optimised to their minima at semi-empirical method PM6 level. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #06DCFB; color: #ffffff;" |'''Molecule'''
! '''Butadiene'''
! '''Ethene'''
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Butadiene lumo yhw14.png|center|150px]]
|[[File:Ethene lumo yhw14.png|center|150px]]
|-
|Corresponding to the s orbital (symmetric)
|Corresponding to the a orbital (asymmetric)
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Butadiene homo yhw14.png|center|150px]]
|[[File:Ethene homo yhw14.png|center|150px]]
|-
|Corresponding to the a orbital (antisymmetric)
|Corresponding to the s orbital (symmetric)
|}

The transition state was first optimised to its minimum, followed by a transition state calculation at semi-empirical method PM6 level. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #01FCEF; color: #ffffff;" |'''Molecule'''
! '''Transition State'''
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Ts lumo+1 yhw14.png|center|150px]]
|-
|Corresponding to the 5 orbital (asymmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Ts lumo 1 yhw14.png|center|150px]]
|-
|Corresponding to the 4 orbital (symmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Ts homo yhw14.png|center|150px]]
|-
|Corresponding to the 3 orbital (symmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Ts homo-1 yhw14.png|center|150px]]
|-
|Corresponding to the 2 orbital (asymmetrical)
|}

Based on the MO diagram and the computed MOs shown above, a reaction is only allowed when the MOs with the same symmetry labels interact with each other, i.e. symmetric-symmetric and asymmetric-asymmetric interactions; and a reaction is forbidden when the MOs with different symmetry labels interact with each other, i.e. symmetric-asymmetric interactions.
In the reaction between butadiene and ethene, the butadiene asymmetric MO interacts with the ethene asymmetric MO to give the 2 and 5 MOs of the transition state, and the butadiene symmetric MO interacts with the ethene symmetric MO to give the 3 and 4 MOs of the transition state. Therefore, a reaction is allowed when the symmetry labels of the MOs of the reactants are the same; and forbidden when the symmetry labels are different.

The orbital overlap integral is zero in a symmetric-asymmetric interaction and non-zero in symmetric-symmetric and asymmetric-asymmetric interactions.

=== Bond Length Analysis ===

The changes in bond lengths between carbons in reactant, transition state and product as the reaction progresses were studied by comparing the bond lengths between carbons before and after the reaction. The summary of bond lengths is shown below.
[[File:Ex1 bondlength yhw14.png|470px|center|thumb|Diagram 3: Labelled carbons]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #0000FF; color: #ffffff" | State
! style="background: #0000FF; color: #ffffff" | C1-C2
! style="background: #0000FF; color: #ffffff" | C2-C3
! style="background: #0000FF; color: #ffffff" | C3-C4
! style="background: #0000FF; color: #ffffff" | C4-C5
! style="background: #0000FF; color: #ffffff" | C5-C6
! style="background: #0000FF; color: #ffffff" | C6-C1
|-
|Reactants
|1.335
|1.468
|1.335
|/
|1.327
|/
|-
|Transition State
|1.380
|1.411
|1.380
|2.115
|1.382
|2.114
|-
|Product
|1.500
|1.338
|1.500
|1.540
|1.540
|1.540
|+Table 1: Measurements of the C-C bond lengths of the reactants, transition state and products (Å)
|}
As the reaction progresses, the bond lengths between C1-C2, C3-C4 and C5-C6 increase from ~1.3 Å to ~1.5 Å as the bond order decrease to one, whereas bond length of C2-C3 decreases from ~1.5 Å to ~1.3 Å as the bond order increases from one to two.
This could be explained as the increase in bond length suggest a change from sp2-sp2 (C-C double bond) with typical bond length of 1.33 Å <ref name="C-C bond lengths"/> to sp3-sp3 (C-C single bond) with typical bond length of 1.54 Å <ref name="C-C bond lengths"/>, and vice versa for the decrease in bond length. Based on the calculated bond lengths above in Table 1, it is clear that bond lengths and bond orders of the reactants changed during the reaction and the new bonds formed at C4-C5 and C6-C1 are single bonds as they have bond lengths of 1.54 Å.
The typical Van der Waals radius of the C atom is 1.7 Å <ref name="Van der Waals radius of C"/>. As the bond lengths between C4-C5 and C6-C1 of the transition state are shorter than 2 x Van der Waals radii of C, this reflects that C-C bonds are forming at the transition state.

=== Vibration Analysis ===

The imaginary frequency at -948.32 cm-1 corresponds to the reaction path at the transition state, which shows a synchronous bond formation, which agrees with the concerted mechanism of [4+2] cycloaddition, where both reaction centres converge at the same time to form bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 15;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Reaction Path at the Transition State
|}

The lowest positive frequency at 145.14 cm-1 is asynchronous as shown below, where one of the C from the ethene moves towards the butadiene reaction centre and the other C moves away. This suggests that bonds are formed one at a time.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 16;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Lowest positive frequency
|}

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

[[File:Ex2 reactionscheme.png|550px|center|thumb|Diagram 4: Reaction Scheme of Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

Cyclohexadiene and 1,3-dioxole were optimised to their minima at DFT-B3LYP 631-G level. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #9A03FE; color: #ffffff;" |'''Molecule'''
! '''Cyclohexadiene'''
! '''1,3-Dioxole'''
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Cyclo lumo 631g yhw14.png|center|150px]]
|[[File:Dioxole lumo 631g yhw14.png|center|150px]]
|-
|Corresponding to the s orbital
|Corresponding to the a orbital
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Cyclo homo 631g yhw14.png|center|150px]]
|[[File:Dioxole homo 631g yhw14.png|center|150px]]
|-
|Corresponding to the a orbital
|Corresponding to the s orbital
|}

The transition state was first optimised to its minimum, followed by a transition state calculation at DFT-B3LYP 631-G level. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #BD5CFE; color: #ffffff;" |'''Molecule'''
! '''Endo Transition State'''
! '''Exo Transition State'''
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Endo ts lumo+1 yhw14.png|center|150px]]
|[[File:Exo ts lumo+1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 5 orbital (asymmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Endo ts lumo yhw14.png|center|150px]]
|[[File:Exo ts lumo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 4 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Endo ts homo yhw14.png|center|150px]]
|[[File:Exo ts homo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 3 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Endo ts homo-1 yhw14.png|center|150px]]
|[[File:Exo ts homo-1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 2 orbital (asymmetric)
|}

The diagram below illustrates the π molecular orbitals of cyclohexadiene and 1,3-dioxole involved in the formation of the transition state.

[[File:Ex2 mo diagram yhw14.png|550px|center|thumb|Diagram 5: MO diagram of Reaction of Cyclohexadiene and 1,3-dioxole]]

=== Normal Demand vs Inverse Demand Diels-Alder Reaction ===

A normal electron demand Diels-Alder reaction can be defined as a reaction between electron rich diene and electron poor dienophile. An inverse electron demand is the reaction between electron poor diene and electron rich dienophile.

The LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are very close in energy, which results in strong bonding interaction between the two to form the HOMO and LUMO of both endo and exo TS. Since the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole have the correct symmetry (symmetric) to interact, they interact to form the symmetric HOMO and LUMO of both TS.

The presence of electron rich O on 1,3-dioxole raise the energy of both its HOMO and LUMO, making the overlap between the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole much better than the HOMO of cyclohexadiene and the LUMO of 1,3-dioxole. Thus, the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are now the frontier orbitals that interact the most, hence this is an inverse demand Diels-Alder reaction.

=== Reaction Energies and Secondary Orbital Interaction ===

The energies of reactants were taken using the sum of the energies of cyclohexadiene and 1,3-dioxole optimised to their minima at DFT-B3LYP 631-G. The calculations were done using DFT-B3LYP 631-G.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FF4AFF; color: #ffffff" |
! style="background: #FF4AFF; color: #ffffff" | Reactants
! style="background: #FF4AFF; color: #ffffff" | Transition State
! style="background: #FF4AFF; color: #ffffff" | Product
! style="background: #FF4AFF; color: #ffffff" | Activation Energy
! style="background: #FF4AFF; color: #ffffff" | Gibbs Free Energy
|-
|Endo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313622</nowiki>
|<nowiki>-1313849</nowiki>
|160
|<nowiki>-67</nowiki>
|-
|Exo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313614</nowiki>
|<nowiki>-1313846</nowiki>
|168
|<nowiki>-64</nowiki>
|+Table 2: Energies of Reactants, Transition States and Products of both Endo and Exo Pathways in Diels-Alder Reaction of Cyclohexadiene and 1,3-Dioxole (kJ mol-1)
|}

Kinetically favourable product of a reaction is the one that has the lowest activation energy; Thermodynamically favourable product is the product with lowest energy conformer, hence the more stabilised product.

The endo transition state is the kinetic product of this reaction as it has lower activation energy. This could be explained using the secondary orbital interaction between the lone pair orbital on the oxygen atom and the empty π* orbital of diene. This favourable effect stabilises the endo transition state.

As the oxygen atom lone pair is oriented away from the diene π system in the exo transition state, the secondary orbital effect is not present, hence the activation energy of exo reaction is higher.

However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, i.e. increasing temperature, formation of the exo product would be more favourable.

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

Xylylene can react with sulfur dioxide through Diels-Alder reaction via either endo or exo pathways to form a 6-membered ring, or through cheletropic reaction to form a 5-membered ring. The reaction scheme is shown below. Reaction barriers and reaction energies for each pathway are compared to determine the reaction that is most favourable.

[[File:Ex3 reactionscheme yhw14.png|550px|center|thumb|Diagram 6: Reaction Scheme of Xylylene and Sulfur Dioxide]]

=== Intrinsic Reaction Coordinate ===
The following files show the intrinsic reaction coordinates of the three different reaction pathways of xylylene and SO2. Please click to see animation.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Endo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Exo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Cheletropic TS
|-
|[[File:DA endo irc animation yhw14.gif|center]]
|[[File:DA exo irc animation yhw14.gif|center]]
|[[File:Cheletropic irc animation yhw14.gif|center]]
|-
|[[File:DA endo irc plot yhw14.png|center|500px]]
|[[File:DA exo irc plot yhw14.png|center|500px]]
|[[File:Cheletropic irc plot yhw14.png|center|650px]]
|}

=== Reaction Energies and Reaction Barriers ===

[[File:Ex3 reactionprofile yhw14.png|550px|center|thumb|Diagram 7: Reaction Profile of Xylylene and Sulfur Dioxide]]

The energies of reactants were taken using the sum of the energies of xylylene and SO2 optimised to their minima at semi-empirical PM6 level. The calculations were done using semi-empirical PM6.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FFD1C3; color: #ffffff" |
! style="background: #FFD1C3; color: #ffffff" | Reactants
! style="background: #FFD1C3; color: #ffffff" | Transition State
! style="background: #FFD1C3; color: #ffffff" | Product
! style="background: #FFD1C3; color: #ffffff" | Activation Energy
! style="background: #FFD1C3; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|237.767824
|56.9576013
|83.391038
|<nowiki>-97.4191847</nowiki>
|-
|Exo
|154.376786
|241.753433
|56.3196048
|87.406647
|<nowiki>-98.0571812</nowiki>
|-
|Cheletropic
|154.376786
|260.08205
|0.013127501
|105.705264
|<nowiki>-154.3636585</nowiki>
|+Table 3: Energies of Reactants, Transition States and Products of Reactions between Xylylene and Sulfur Dioxide (kJ mol-1)
|}

With reference to the reaction profile and Table 3, the Diels-Alder reaction via the endo pathway has the lowest activation energy, making it a more kinetically favourable product, i.e. the kinetic product; the Diels-Alder exo product has a lower energy than endo, however with a higher activation energy hence it will not form under low temperature condition; the cheletropic product is the most stabilised product out of the three and it has the lowest reaction energy, therefore is the thermodynamic product.

=== Side Reaction between cis-diene in Xylylene 6-membered ring and SO2===

o-Xylylene contains another cis-butadiene fragment located in the 6-membered ring that can undergo a Diels-Alder reaction with SO2. The reaction energies and reaction barriers between endo and exo pathways are compared in the table below.

The energies of reactants were taken using the sum of the energies of xylylene and SO2 optimised to their minima at semi-empirical PM6 level. The calculations were done using semi-empirical PM6.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #4EBEBA; color: #ffffff" |
! style="background: #4EBEBA; color: #ffffff" | Reactants
! style="background: #4EBEBA; color: #ffffff" | Transition State
! style="background: #4EBEBA; color: #ffffff" | Product
! style="background: #4EBEBA; color: #ffffff" | Activation Energy
! style="background: #4EBEBA; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|267.984805
|172.272196
|113.608019
|17.89541
|-
|Exo
|154.376786
|275.821924
|176.711916
|121.445138
|22.33513
|+Table 4: Energies of Reactants, Transition States and Products of the Side Reaction in Xylylene 6-membered ring and Sulfur Dioxide (kJ mol-1)
|}

It is clear that both endo and exo Diels-Alder side reactions are kinetically and thermodynamically unfavourable at this site as the activation energies are much higher than the previous reactions mentioned above in Table 4 and the reaction energies show that the reactions are endothermic.

== Conclusion ==

The transition states of three pericyclic reactions were investigated in this computational lab, using Gaussian to optimise the reactants, transition states and products respectively, and the vibrational frequencies and intrinsic reaction coordinates were computed.

In the reaction between butadiene and ethene, the importance of molecular orbital symmetry in the interaction of molecular orbitals was illustrated, such that a reaction is only allowed when the molecular orbitals with the same symmetry labels interact with each other and forbidden when symmetric molecular orbital interact with asymmetric orbitals. Furthermore, the vibration frequency calculation proved that this [4+2] Diels-Alder reaction proceeds via a concerted mechanism as synchronous bond formation was demonstrated. Bonding interaction can be further confirmed as the bond distance between the two termini carbon atoms in the transition state is shorter than the sum of two Van der Waals radii of carbon.

In the reaction of cyclohexadiene and 1,3-dioxole, both the endo and exo transition states were investigated. In general, the endo transition state is kinetically more favourable as it has lower activation barrier, possibly due to the secondary orbital interaction between the lone pair in p orbital on the oxygen atom and the empty pi* orbital in the diene, which stabilises the transition state. However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, formation of the exo product could be possible.

The final reaction between xylylene and SO2 again proved that the endo Diels-Alder transition state has the lowest activation energy, making it kinetically favourable at low temperature. However, the cheletropic product is the most stabilised and thermodynamically favourable product. Therefore the reaction would yield the cheletropic product under thermodynamic control instead of the exo Diels-Alder product.

==References==
<references>
<ref name="C-C bond lengths">L. Pauling and L. O. Brockway, ''Journal of the American Chemical Society'', '''1937''', Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref>
<ref name="Van der Waals radius of C">S. S. Batsanov, ''Inorganic Materials'', '''2001''', Volume 37, Number 9, pp. 871-885, https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf.</ref>
</references>

Rep:Mod:yhw14cts

2017-02-09T20:39:55Z

Yhw14:

''' Transition States and Reactivity '''

'' Yi Hang Cherie WONG (yhw14) ''
'' CID: 00933828 ''

== Introduction ==
A potential energy surface is a mathematical function that gives the energy of a molecule as a function of its geometry with the relative positions of the atoms participating in the reaction. The stationary points may be classified according to the first and second derivatives of the energy with respect to position. At the minimum of a reaction profile, the gradient is represented by the first derivative of the reaction coordinate, which is zero, while curvature is represented by the second derivative, is positive in this case; hence energy rises in all directions. Energy minima correspond to physically stable chemical species, which could be reactants and products. The transition state is defined as the maximum in a reaction profile, where the gradient is again, zero, while curvature is negative; hence energy decreases in one direction, which indicates the reaction pathway of the chemical reaction. The potential energy surface can be computed using Gaussview 09, where structure and energy of reactants or products can be modelled to illustrate the transition states, which can rarely be obtained experimentally. The intrinsic reaction coordinate can then be calculated and compared to predict the reaction path at a transition state and follow it to the correct minima.

In this computational lab, all of the reactants and products were optimised to their minima, and the transition states were also optimised. The calculations were done by Gaussian 09, using mainly semi-empirical method PM6 and DFT-B3LYP. Frequency calculations were performed to show molecular vibrations to confirm the position on the potential energy surface. If all the vibrational frequencies are real, this confirms the structure is a minimum, and vice versa, the presence of imaginary frequency may suggest that the structure is at its transition state. Intrinsic reaction coordinate method was carried out using calculated force constants to predict which conformer a reaction path from the transition state would lead to.

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

The reaction between butadiene and ethene is a typical pericyclic [4+2] Diels-Alder reaction that proceeds via a concerted mechanism through a cyclic transition state. The reaction scheme is shown below.

[[File:Ex1 reactionscheme revised yhw14.png|550px|center|thumb|Diagram 1: Reaction Scheme of Butadiene and Ethene]]

=== Molecular Orbital Analysis ===

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of butadiene and ethene.

[[File:Ex1 mo diagram yhw14 revised v3.png|550px|center|thumb|Diagram 2: MO diagram of Reaction of Butadiene and Ethene]]

Butadiene and ethene were optimised to their minima. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #06DCFB; color: #ffffff;" |'''Molecule'''
! '''Butadiene'''
! '''Ethene'''
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Butadiene lumo yhw14.png|center|150px]]
|[[File:Ethene lumo yhw14.png|center|150px]]
|-
|Corresponding to the s orbital (symmetric)
|Corresponding to the a orbital (asymmetric)
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Butadiene homo yhw14.png|center|150px]]
|[[File:Ethene homo yhw14.png|center|150px]]
|-
|Corresponding to the a orbital (antisymmetric)
|Corresponding to the s orbital (symmetric)
|}

The transition state was first optimised to its minimum, followed by a transition state calculation. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #01FCEF; color: #ffffff;" |'''Molecule'''
! '''Transition State'''
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Ts lumo+1 yhw14.png|center|150px]]
|-
|Corresponding to the 5 orbital (asymmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Ts lumo 1 yhw14.png|center|150px]]
|-
|Corresponding to the 4 orbital (symmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Ts homo yhw14.png|center|150px]]
|-
|Corresponding to the 3 orbital (symmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Ts homo-1 yhw14.png|center|150px]]
|-
|Corresponding to the 2 orbital (asymmetrical)
|}

Based on the MO diagram and the computed MOs shown above, a reaction is only allowed when the MOs with the same symmetry labels interact with each other, i.e. symmetric-symmetric and asymmetric-asymmetric interactions; and a reaction is forbidden when the MOs with different symmetry labels interact with each other, i.e. symmetric-asymmetric interactions.
In the reaction between butadiene and ethene, the butadiene asymmetric MO interacts with the ethene asymmetric MO to give the 2 and 5 MOs of the transition state, and the butadiene symmetric MO interacts with the ethene symmetric MO to give the 3 and 4 MOs of the transition state. Therefore, a reaction is allowed when the symmetry labels of the MOs of the reactants are the same; and forbidden when the symmetry labels are different.

The orbital overlap integral is zero in a symmetric-asymmetric interaction and non-zero in symmetric-symmetric and asymmetric-asymmetric interactions.

=== Bond Length Analysis ===

The changes in bond lengths between carbons in reactant, transition state and product as the reaction progresses were studied by comparing the bond lengths between carbons before and after the reaction. The summary of bond lengths is shown below.
[[File:Ex1 bondlength yhw14.png|470px|center|thumb|Diagram 3: Labelled carbons]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #0000FF; color: #ffffff" | State
! style="background: #0000FF; color: #ffffff" | C1-C2
! style="background: #0000FF; color: #ffffff" | C2-C3
! style="background: #0000FF; color: #ffffff" | C3-C4
! style="background: #0000FF; color: #ffffff" | C4-C5
! style="background: #0000FF; color: #ffffff" | C5-C6
! style="background: #0000FF; color: #ffffff" | C6-C1
|-
|Reactants
|1.335
|1.468
|1.335
|/
|1.327
|/
|-
|Transition State
|1.380
|1.411
|1.380
|2.115
|1.382
|2.114
|-
|Product
|1.500
|1.338
|1.500
|1.540
|1.540
|1.540
|+Table 1: Measurements of the C-C bond lengths of the reactants, transition state and products (Å)
|}
As the reaction progresses, the bond lengths between C1-C2, C3-C4 and C5-C6 increase from ~1.3 Å to ~1.5 Å as the bond order decrease to one, whereas bond length of C2-C3 decreases from ~1.5 Å to ~1.3 Å as the bond order increases from one to two.
This could be explained as the increase in bond length suggest a change from sp2-sp2 (C-C double bond) with typical bond length of 1.33 Å <ref name="C-C bond lengths"/> to sp3-sp3 (C-C single bond) with typical bond length of 1.54 Å <ref name="C-C bond lengths"/>, and vice versa for the decrease in bond length. Based on the calculated bond lengths above in Table 1, it is clear that bond lengths and bond orders of the reactants changed during the reaction and the new bonds formed at C4-C5 and C6-C1 are single bonds as they have bond lengths of 1.54 Å.
The typical Van der Waals radius of the C atom is 1.7 Å <ref name="Van der Waals radius of C"/>. As the bond lengths between C4-C5 and C6-C1 of the transition state are shorter than 2 x Van der Waals radii of C, this reflects that C-C bonds are forming at the transition state.

=== Vibration Analysis ===

The imaginary frequency at -948.32 cm-1 corresponds to the reaction path at the transition state, which shows a synchronous bond formation, which agrees with the concerted mechanism of [4+2] cycloaddition, where both reaction centres converge at the same time to form bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 15;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Reaction Path at the Transition State
|}

The lowest positive frequency at 145.14 cm-1 is asynchronous as shown below, where one of the C from the ethene moves towards the butadiene reaction centre and the other C moves away. This suggests that bonds are formed one at a time.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 16;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Lowest positive frequency
|}

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

[[File:Ex2 reactionscheme.png|550px|center|thumb|Diagram 4: Reaction Scheme of Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

Cyclohexadiene and 1,3-dioxole were optimised to their minima. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #9A03FE; color: #ffffff;" |'''Molecule'''
! '''Cyclohexadiene'''
! '''1,3-Dioxole'''
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Cyclo lumo 631g yhw14.png|center|150px]]
|[[File:Dioxole lumo 631g yhw14.png|center|150px]]
|-
|Corresponding to the s orbital
|Corresponding to the a orbital
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Cyclo homo 631g yhw14.png|center|150px]]
|[[File:Dioxole homo 631g yhw14.png|center|150px]]
|-
|Corresponding to the a orbital
|Corresponding to the s orbital
|}

The transition state was first optimised to its minimum, followed by a transition state calculation. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #BD5CFE; color: #ffffff;" |'''Molecule'''
! '''Endo Transition State'''
! '''Exo Transition State'''
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Endo ts lumo+1 yhw14.png|center|150px]]
|[[File:Exo ts lumo+1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 5 orbital (asymmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Endo ts lumo yhw14.png|center|150px]]
|[[File:Exo ts lumo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 4 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Endo ts homo yhw14.png|center|150px]]
|[[File:Exo ts homo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 3 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Endo ts homo-1 yhw14.png|center|150px]]
|[[File:Exo ts homo-1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 2 orbital (asymmetric)
|}

The diagram below illustrates the π molecular orbitals of cyclohexadiene and 1,3-dioxole involved in the formation of the transition state.

[[File:Ex2 mo diagram yhw14.png|550px|center|thumb|Diagram 5: MO diagram of Reaction of Cyclohexadiene and 1,3-dioxole]]

=== Normal Demand vs Inverse Demand Diels-Alder Reaction ===

A normal electron demand Diels-Alder reaction can be defined as a reaction between electron rich diene and electron poor dienophile. An inverse electron demand is the reaction between electron poor diene and electron rich dienophile.

The LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are very close in energy, which results in strong bonding interaction between the two to form the HOMO and LUMO of both endo and exo TS. Since the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole have the correct symmetry (symmetric) to interact, they interact to form the symmetric HOMO and LUMO of both TS.

The presence of electron rich O on 1,3-dioxole raise the energy of both its HOMO and LUMO, making the overlap between the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole much better than the HOMO of cyclohexadiene and the LUMO of 1,3-dioxole. Thus, the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are now the frontier orbitals that interact the most, hence this is an inverse demand Diels-Alder reaction.

=== Reaction Energies and Secondary Orbital Interaction ===

The energies of reactants were taken using the sum of the energies of cyclohexadiene and 1,3-dioxole optimised to their minima at DFT-B3LYP 631G.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FF4AFF; color: #ffffff" |
! style="background: #FF4AFF; color: #ffffff" | Reactants
! style="background: #FF4AFF; color: #ffffff" | Transition State
! style="background: #FF4AFF; color: #ffffff" | Product
! style="background: #FF4AFF; color: #ffffff" | Activation Energy
! style="background: #FF4AFF; color: #ffffff" | Gibbs Free Energy
|-
|Endo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313622</nowiki>
|<nowiki>-1313849</nowiki>
|160
|<nowiki>-67</nowiki>
|-
|Exo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313614</nowiki>
|<nowiki>-1313846</nowiki>
|168
|<nowiki>-64</nowiki>
|+Table 2: Energies of Reactants, Transition States and Products of both Endo and Exo Pathways in Diels-Alder Reaction of Cyclohexadiene and 1,3-Dioxole (kJ mol-1)
|}

Kinetically favourable product of a reaction is the one that has the lowest activation energy; Thermodynamically favourable product is the product with lowest energy conformer, hence the more stabilised product.

The endo transition state is the kinetic product of this reaction as it has lower activation energy. This could be explained using the secondary orbital interaction between the lone pair orbital on the oxygen atom and the empty π* orbital of diene. This favourable effect stabilises the endo transition state.

As the oxygen atom lone pair is oriented away from the diene π system in the exo transition state, the secondary orbital effect is not present, hence the activation energy of exo reaction is higher.

However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, i.e. increasing temperature, formation of the exo product would be more favourable.

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

Xylylene can react with sulfur dioxide through Diels-Alder reaction via either endo or exo pathways to form a 6-membered ring, or through cheletropic reaction to form a 5-membered ring. The reaction scheme is shown below. Reaction barriers and reaction energies for each pathway are compared to determine the reaction that is most favourable.

[[File:Ex3 reactionscheme yhw14.png|550px|center|thumb|Diagram 6: Reaction Scheme of Xylylene and Sulfur Dioxide]]

=== Intrinsic Reaction Coordinate ===
The following files show the intrinsic reaction coordinates of the three different reaction pathways of xylylene and SO2. Please click to see animation.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Endo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Exo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Cheletropic TS
|-
|[[File:DA endo irc animation yhw14.gif|center]]
|[[File:DA exo irc animation yhw14.gif|center]]
|[[File:Cheletropic irc animation yhw14.gif|center]]
|-
|[[File:DA endo irc plot yhw14.png|center|500px]]
|[[File:DA exo irc plot yhw14.png|center|500px]]
|[[File:Cheletropic irc plot yhw14.png|center|650px]]
|}

=== Reaction Energies and Reaction Barriers ===

[[File:Ex3 reactionprofile yhw14.png|550px|center|thumb|Diagram 7: Reaction Profile of Xylylene and Sulfur Dioxide]]

The energies of reactants were taken using the sum of the energies of xylylene and SO2 optimised to their minima at semi-empirical PM6 level.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FFD1C3; color: #ffffff" |
! style="background: #FFD1C3; color: #ffffff" | Reactants
! style="background: #FFD1C3; color: #ffffff" | Transition State
! style="background: #FFD1C3; color: #ffffff" | Product
! style="background: #FFD1C3; color: #ffffff" | Activation Energy
! style="background: #FFD1C3; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|237.767824
|56.9576013
|83.391038
|<nowiki>-97.4191847</nowiki>
|-
|Exo
|154.376786
|241.753433
|56.3196048
|87.406647
|<nowiki>-98.0571812</nowiki>
|-
|Cheletropic
|154.376786
|260.08205
|0.013127501
|105.705264
|<nowiki>-154.3636585</nowiki>
|+Table 3: Energies of Reactants, Transition States and Products of Reactions between Xylylene and Sulfur Dioxide (kJ mol-1)
|}

With reference to the reaction profile and Table 3, the Diels-Alder reaction via the endo pathway has the lowest activation energy, making it a more kinetically favourable product, i.e. the kinetic product; the Diels-Alder exo product has a lower energy than endo, however with a higher activation energy hence it will not form under low temperature condition; the cheletropic product is the most stabilised product out of the three and it has the lowest reaction energy, therefore is the thermodynamic product.

=== Side Reaction between cis-diene in Xylylene 6-membered ring and SO2===

o-Xylylene contains another cis-butadiene fragment located in the 6-membered ring that can undergo a Diels-Alder reaction with SO2. The reaction energies and reaction barriers between endo and exo pathways are compared in the table below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #4EBEBA; color: #ffffff" |
! style="background: #4EBEBA; color: #ffffff" | Reactants
! style="background: #4EBEBA; color: #ffffff" | Transition State
! style="background: #4EBEBA; color: #ffffff" | Product
! style="background: #4EBEBA; color: #ffffff" | Activation Energy
! style="background: #4EBEBA; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|267.984805
|172.272196
|113.608019
|17.89541
|-
|Exo
|154.376786
|275.821924
|176.711916
|121.445138
|22.33513
|+Table 4: Energies of Reactants, Transition States and Products of the Side Reaction in Xylylene 6-membered ring and Sulfur Dioxide (kJ mol-1)
|}

It is clear that both endo and exo Diels-Alder side reactions are kinetically and thermodynamically unfavourable at this site as the activation energies are much higher than the previous reactions mentioned above in Table 4 and the reaction energies show that the reactions are endothermic.

== Conclusion ==

The transition states of three pericyclic reactions were investigated in this computational lab, using Gaussian to optimise the reactants, transition states and products respectively, and the vibrational frequencies and intrinsic reaction coordinates were computed.

In the reaction between butadiene and ethene, the importance of molecular orbital symmetry in the interaction of molecular orbitals was illustrated, such that a reaction is only allowed when the molecular orbitals with the same symmetry labels interact with each other and forbidden when symmetric molecular orbital interact with asymmetric orbitals. Furthermore, the vibration frequency calculation proved that this [4+2] Diels-Alder reaction proceeds via a concerted mechanism as synchronous bond formation was demonstrated. Bonding interaction can be further confirmed as the bond distance between the two termini carbon atoms in the transition state is shorter than the sum of two Van der Waals radii of carbon.

In the reaction of cyclohexadiene and 1,3-dioxole, both the endo and exo transition states were investigated. In general, the endo transition state is kinetically more favourable as it has lower activation barrier, possibly due to the secondary orbital interaction between the lone pair in p orbital on the oxygen atom and the empty pi* orbital in the diene, which stabilises the transition state. However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, formation of the exo product could be possible.

The final reaction between xylylene and SO2 again proved that the endo Diels-Alder transition state has the lowest activation energy, making it kinetically favourable at low temperature. However, the cheletropic product is the most stabilised and thermodynamically favourable product. Therefore the reaction would yield the cheletropic product under thermodynamic control instead of the exo Diels-Alder product.

==References==
<references>
<ref name="C-C bond lengths">L. Pauling and L. O. Brockway, ''Journal of the American Chemical Society'', '''1937''', Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref>
<ref name="Van der Waals radius of C">S. S. Batsanov, ''Inorganic Materials'', '''2001''', Volume 37, Number 9, pp. 871-885, https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf.</ref>
</references>

Rep:Mod:yhw14cts

2017-02-09T20:37:54Z

Yhw14: /* Molecular Orbital Analysis */

''' Transition States and Reactivity '''

'' Yi Hang Cherie WONG (yhw14) ''
'' CID: 00933828 ''

== Introduction ==
A potential energy surface is a mathematical function that gives the energy of a molecule as a function of its geometry with the relative positions of the atoms participating in the reaction. The stationary points may be classified according to the first and second derivatives of the energy with respect to position. At the minimum of a reaction profile, the gradient is represented by the first derivative of the reaction coordinate, which is zero, while curvature is represented by the second derivative, is positive in this case; hence energy rises in all directions. Energy minima correspond to physically stable chemical species, which could be reactants and products. The transition state is defined as the maximum in a reaction profile, where the gradient is again, zero, while curvature is negative; hence energy decreases in one direction, which indicates the reaction pathway of the chemical reaction. The potential energy surface can be computed using Gaussview 09, where structure and energy of reactants or products can be modelled to illustrate the transition states, which can rarely be obtained experimentally. The intrinsic reaction coordinate can then be calculated and compared to predict the reaction path at a transition state and follow it to the correct minima.

In this computational lab, all of the reactants and products were optimised to their minima, and the transition states were also optimised. The calculations were done by Gaussian 09, using mainly semi-empirical method PM6 and DFT-B3LYP. Frequency calculations were performed to show molecular vibrations to confirm the position on the potential energy surface. If all the vibrational frequencies are real, this confirms the structure is a minimum, and vice versa, the presence of imaginary frequency may suggest that the structure is at its transition state. Intrinsic reaction coordinate method was carried out using calculated force constants to predict which conformer a reaction path from the transition state would lead to.

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

The reaction between butadiene and ethene is a typical pericyclic [4+2] Diels-Alder reaction that proceeds via a concerted mechanism through a cyclic transition state. The reaction scheme is shown below.

[[File:Ex1 reactionscheme revised yhw14.png|550px|center|thumb|Diagram 1: Reaction Scheme of Butadiene and Ethene]]

=== Molecular Orbital Analysis ===

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of butadiene and ethene.

[[File:Ex1 mo diagram yhw14 revised v3.png|550px|center|thumb|Diagram 2: MO diagram of Reaction of Butadiene and Ethene]]

Butadiene and ethene were optimised to their minima. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #06DCFB; color: #ffffff;" |'''Molecule'''
! '''Butadiene'''
! '''Ethene'''
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Butadiene lumo yhw14.png|center|150px]]
|[[File:Ethene lumo yhw14.png|center|150px]]
|-
|Corresponding to the s orbital (symmetric)
|Corresponding to the a orbital (asymmetric)
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Butadiene homo yhw14.png|center|150px]]
|[[File:Ethene homo yhw14.png|center|150px]]
|-
|Corresponding to the a orbital (antisymmetric)
|Corresponding to the s orbital (symmetric)
|}

The transition state was first optimised to its minimum, followed by a transition state calculation. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #01FCEF; color: #ffffff;" |'''Molecule'''
! '''Transition State'''
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Ts lumo+1 yhw14.png|center|150px]]
|-
|Corresponding to the 5 orbital (asymmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Ts lumo 1 yhw14.png|center|150px]]
|-
|Corresponding to the 4 orbital (symmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Ts homo yhw14.png|center|150px]]
|-
|Corresponding to the 3 orbital (symmetrical)
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Ts homo-1 yhw14.png|center|150px]]
|-
|Corresponding to the 2 orbital (asymmetrical)
|}

Based on the MO diagram and the computed MOs shown above, a reaction is only allowed when the MOs with the same symmetry labels interact with each other, i.e. symmetric-symmetric and asymmetric-asymmetric interactions; and a reaction is forbidden when the MOs with different symmetry labels interact with each other, i.e. symmetric-asymmetric interactions.
In the reaction between butadiene and ethene, the butadiene asymmetric MO interacts with the ethene asymmetric MO to give the 2 and 5 MOs of the transition state, and the butadiene symmetric MO interacts with the ethene symmetric MO to give the 3 and 4 MOs of the transition state. Therefore, a reaction is allowed when the symmetry labels of the MOs of the reactants are the same; and forbidden when the symmetry labels are different.

The orbital overlap integral is zero in a symmetric-asymmetric interaction and non-zero in symmetric-symmetric and asymmetric-asymmetric interactions.

=== Bond Length Analysis ===

The changes in bond lengths between carbons in reactant, transition state and product as the reaction progresses were studied by comparing the bond lengths between carbons before and after the reaction. The summary of bond lengths is shown below.
[[File:Ex1 bondlength yhw14.png|470px|center|thumb|Diagram 3: Labelled carbons]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #0000FF; color: #ffffff" | State
! style="background: #0000FF; color: #ffffff" | C1-C2
! style="background: #0000FF; color: #ffffff" | C2-C3
! style="background: #0000FF; color: #ffffff" | C3-C4
! style="background: #0000FF; color: #ffffff" | C4-C5
! style="background: #0000FF; color: #ffffff" | C5-C6
! style="background: #0000FF; color: #ffffff" | C6-C1
|-
|Reactants
|1.335
|1.468
|1.335
|/
|1.327
|/
|-
|Transition State
|1.380
|1.411
|1.380
|2.115
|1.382
|2.114
|-
|Product
|1.500
|1.338
|1.500
|1.540
|1.540
|1.540
|+Table 1: Measurements of the C-C bond lengths of the reactants, transition state and products (Å)
|}
As the reaction progresses, the bond lengths between C1-C2, C3-C4 and C5-C6 increase from ~1.3 Å to ~1.5 Å as the bond order decrease to one, whereas bond length of C2-C3 decreases from ~1.5 Å to ~1.3 Å as the bond order increases from one to two.
This could be explained as the increase in bond length suggest a change from sp2-sp2 (C-C double bond) with typical bond length of 1.33 Å <ref name="C-C bond lengths"/> to sp3-sp3 (C-C single bond) with typical bond length of 1.54 Å <ref name="C-C bond lengths"/>, and vice versa for the decrease in bond length. Based on the calculated bond lengths above in Table 1, it is clear that bond lengths and bond orders of the reactants changed during the reaction and the new bonds formed at C4-C5 and C6-C1 are single bonds as they have bond lengths of 1.54 Å.
The typical Van der Waals radius of the C atom is 1.7 Å <ref name="Van der Waals radius of C"/>. As the bond lengths between C4-C5 and C6-C1 of the transition state are shorter than 2 x Van der Waals radii of C, this reflects that C-C bonds are forming at the transition state.

=== Vibration Analysis ===

The imaginary frequency at -948.32 cm-1 corresponds to the reaction path at the transition state, which shows a synchronous bond formation, which agrees with the concerted mechanism of [4+2] cycloaddition, where both reaction centres converge at the same time to form bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 15;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Reaction Path at the Transition State
|}

The lowest positive frequency at 145.14 cm-1 is asynchronous as shown below, where one of the C from the ethene moves towards the butadiene reaction centre and the other C moves away. This suggests that bonds are formed one at a time.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 16;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Lowest positive frequency
|}

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

[[File:Ex2 reactionscheme.png|550px|center|thumb|Diagram 4: Reaction Scheme of Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

Cyclohexadiene and 1,3-dioxole were optimised to their minima. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #9A03FE; color: #ffffff;" |'''Molecule'''
! '''Cyclohexadiene'''
! '''1,3-Dioxole'''
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Cyclo lumo 631g yhw14.png|center|150px]]
|[[File:Dioxole lumo 631g yhw14.png|center|150px]]
|-
|Corresponding to the s orbital
|Corresponding to the a orbital
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Cyclo homo 631g yhw14.png|center|150px]]
|[[File:Dioxole homo 631g yhw14.png|center|150px]]
|-
|Corresponding to the a orbital
|Corresponding to the s orbital
|}

The transition state was first optimised to its minimum, followed by a transition state calculation. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #BD5CFE; color: #ffffff;" |'''Molecule'''
! '''Endo Transition State'''
! '''Exo Transition State'''
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Endo ts lumo+1 yhw14.png|center|150px]]
|[[File:Exo ts lumo+1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 5 orbital (asymmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Endo ts lumo yhw14.png|center|150px]]
|[[File:Exo ts lumo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 4 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Endo ts homo yhw14.png|center|150px]]
|[[File:Exo ts homo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 3 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Endo ts homo-1 yhw14.png|center|150px]]
|[[File:Exo ts homo-1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 2 orbital (asymmetric)
|}

The diagram below illustrates the π molecular orbitals of cyclohexadiene and 1,3-dioxole involved in the formation of the transition state.

[[File:Ex2 mo diagram yhw14.png|550px|center|thumb|Diagram 5: MO diagram of Reaction of Cyclohexadiene and 1,3-dioxole]]

=== Normal Demand vs Inverse Demand Diels-Alder Reaction ===

A normal electron demand Diels-Alder reaction can be defined as a reaction between electron rich diene and electron poor dienophile. An inverse electron demand is the reaction between electron poor diene and electron rich dienophile.

The LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are very close in energy, which results in strong bonding interaction between the two to form the HOMO and LUMO of both endo and exo TS. Since the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole have the correct symmetry (symmetric) to interact, they interact to form the symmetric HOMO and LUMO of both TS.

The presence of electron rich O on 1,3-dioxole raise the energy of both its HOMO and LUMO, making the overlap between the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole much better than the HOMO of cyclohexadiene and the LUMO of 1,3-dioxole. Thus, the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are now the frontier orbitals that interact the most, hence this is an inverse demand Diels-Alder reaction.

=== Reaction Energies and Secondary Orbital Interaction ===

The energies of reactants were taken using the sum of the energies of cyclohexadiene and 1,3-dioxole optimised to their minima at DFT-B3LYP 631G.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FF4AFF; color: #ffffff" |
! style="background: #FF4AFF; color: #ffffff" | Reactants
! style="background: #FF4AFF; color: #ffffff" | Transition State
! style="background: #FF4AFF; color: #ffffff" | Product
! style="background: #FF4AFF; color: #ffffff" | Activation Energy
! style="background: #FF4AFF; color: #ffffff" | Gibbs Free Energy
|-
|Endo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313622</nowiki>
|<nowiki>-1313849</nowiki>
|160
|<nowiki>-67</nowiki>
|-
|Exo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313614</nowiki>
|<nowiki>-1313846</nowiki>
|168
|<nowiki>-64</nowiki>
|+Table 2: Energies of Reactants, Transition States and Products of both Endo and Exo Pathways in Diels-Alder Reaction of Cyclohexadiene and 1,3-Dioxole (kJ mol-1)
|}

Kinetically favourable product of a reaction is the one that has the lowest activation energy; Thermodynamically favourable product is the product with lowest energy conformer, hence the more stabilised product.

The endo transition state is the kinetic product of this reaction as it has lower activation energy. This could be explained using the secondary orbital interaction between the lone pair orbital on the oxygen atom and the empty π* orbital of diene. This favourable effect stabilises the endo transition state.

As the oxygen atom lone pair is oriented away from the diene π system in the exo transition state, the secondary orbital effect is not present, hence the activation energy of exo reaction is higher.

However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, i.e. increasing temperature, formation of the exo product would be more favourable.

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

Xylylene can react with sulfur dioxide through Diels-Alder reaction via either endo or exo pathways to form a 6-membered ring, or through cheletropic reaction to form a 5-membered ring. The reaction scheme is shown below. Reaction barriers and reaction energies for each pathway are compared to determine the reaction that is most favourable.

[[File:Ex3 reactionscheme yhw14.png|550px|center|thumb|Diagram 6: Reaction Scheme of Xylylene and Sulfur Dioxide]]

=== Intrinsic Reaction Coordinate ===
The following files show the intrinsic reaction coordinates of the three different reaction pathways of xylylene and SO2. Please click to see animation.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Endo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Exo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Cheletropic TS
|-
|[[File:DA endo irc animation yhw14.gif|center]]
|[[File:DA exo irc animation yhw14.gif|center]]
|[[File:Cheletropic irc animation yhw14.gif|center]]
|-
|[[File:DA endo irc plot yhw14.png|center|500px]]
|[[File:DA exo irc plot yhw14.png|center|500px]]
|[[File:Cheletropic irc plot yhw14.png|center|650px]]
|}

=== Reaction Energies and Reaction Barriers ===

[[File:Ex3 reactionprofile yhw14.png|550px|center|thumb|Diagram 7: Reaction Profile of Xylylene and Sulfur Dioxide]]

The energies of reactants were taken using the sum of the energies of xylylene and SO2 optimised to their minima at semi-empirical PM6 level.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FFD1C3; color: #ffffff" |
! style="background: #FFD1C3; color: #ffffff" | Reactants
! style="background: #FFD1C3; color: #ffffff" | Transition State
! style="background: #FFD1C3; color: #ffffff" | Product
! style="background: #FFD1C3; color: #ffffff" | Activation Energy
! style="background: #FFD1C3; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|237.767824
|56.9576013
|83.391038
|<nowiki>-97.4191847</nowiki>
|-
|Exo
|154.376786
|241.753433
|56.3196048
|87.406647
|<nowiki>-98.0571812</nowiki>
|-
|Cheletropic
|154.376786
|260.08205
|0.013127501
|105.705264
|<nowiki>-154.3636585</nowiki>
|+Table 3: Energies of Reactants, Transition States and Products of Reactions between Xylylene and Sulfur Dioxide (kJ mol-1)
|}

With reference to the reaction profile and table 3, the Diels-Alder reaction via the endo pathway has the lowest activation energy, making it a more kinetically favourable product, i.e. the kinetic product; the Diels-Alder exo product has a lower energy than endo, however with a higher activation energy hence it will not form under low temperature condition; the cheletropic product is the most stabilised product out of the three and it has the lowest reaction energy, therefore is the thermodynamic product.

=== Side Reaction between cis-diene in Xylylene 6-membered ring and SO2===

o-Xylylene contains another cis-butadiene fragment located in the 6-membered ring that can undergo a Diels-Alder reaction with SO2. The reaction energies and reaction barriers between endo and exo pathways are compared in the table below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #4EBEBA; color: #ffffff" |
! style="background: #4EBEBA; color: #ffffff" | Reactants
! style="background: #4EBEBA; color: #ffffff" | Transition State
! style="background: #4EBEBA; color: #ffffff" | Product
! style="background: #4EBEBA; color: #ffffff" | Activation Energy
! style="background: #4EBEBA; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|267.984805
|172.272196
|113.608019
|17.89541
|-
|Exo
|154.376786
|275.821924
|176.711916
|121.445138
|22.33513
|+Table 4: Energies of Reactants, Transition States and Products of the Side Reaction in Xylylene 6-membered ring and Sulfur Dioxide (kJ mol-1)
|}

It is clear that both endo and exo Diels-Alder side reactions are kinetically and thermodynamically unfavourable at this site as the activation energies are much higher than the previous reactions mentioned above in table 4 and the reaction energies show that the reactions are endothermic.

== Conclusion ==

The transition states of three pericyclic reactions were investigated in this computational lab, using Gaussian to optimise the reactants, transition states and products respectively, and the vibrational frequencies and intrinsic reaction coordinates were computed.

In the reaction between butadiene and ethene, the importance of molecular orbital symmetry in the interaction of molecular orbitals was illustrated, such that a reaction is only allowed when the molecular orbitals with the same symmetry labels interact with each other and forbidden when symmetric molecular orbital interact with asymmetric orbitals. Furthermore, the vibration frequency calculation proved that this [4+2] Diels-Alder reaction proceeds via a concerted mechanism as synchronous bond formation was demonstrated. Bonding interaction can be further confirmed as the bond distance between the two termini carbon atoms in the transition state is shorter than the sum of two Van der Waals radii of carbon.

In the reaction of cyclohexadiene and 1,3-dioxole, both the endo and exo transition states were investigated. In general, the endo transition state is kinetically more favourable as it has lower activation barrier, possibly due to the secondary orbital interaction between the lone pair in p orbital on the oxygen atom and the empty pi* orbital in the diene, which stabilises the transition state. However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, formation of the exo product could be possible.

The final reaction between xylylene and SO2 again proved that the endo Diels-Alder transition state has the lowest activation energy, making it kinetically favourable at low temperature. However, the cheletropic product is the most stabilised and thermodynamically favourable product. Therefore the reaction would yield the cheletropic product under thermodynamic control instead of the exo Diels-Alder product.

==References==
<references>
<ref name="C-C bond lengths">L. Pauling and L. O. Brockway, ''Journal of the American Chemical Society'', '''1937''', Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref>
<ref name="Van der Waals radius of C">S. S. Batsanov, ''Inorganic Materials'', '''2001''', Volume 37, Number 9, pp. 871-885, https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf.</ref>
</references>

Rep:Mod:yhw14cts

2017-02-09T20:36:48Z

Yhw14: /* Exercise 3: Diels-Alder vs Cheletropic */

''' Transition States and Reactivity '''

'' Yi Hang Cherie WONG (yhw14) ''
'' CID: 00933828 ''

== Introduction ==
A potential energy surface is a mathematical function that gives the energy of a molecule as a function of its geometry with the relative positions of the atoms participating in the reaction. The stationary points may be classified according to the first and second derivatives of the energy with respect to position. At the minimum of a reaction profile, the gradient is represented by the first derivative of the reaction coordinate, which is zero, while curvature is represented by the second derivative, is positive in this case; hence energy rises in all directions. Energy minima correspond to physically stable chemical species, which could be reactants and products. The transition state is defined as the maximum in a reaction profile, where the gradient is again, zero, while curvature is negative; hence energy decreases in one direction, which indicates the reaction pathway of the chemical reaction. The potential energy surface can be computed using Gaussview 09, where structure and energy of reactants or products can be modelled to illustrate the transition states, which can rarely be obtained experimentally. The intrinsic reaction coordinate can then be calculated and compared to predict the reaction path at a transition state and follow it to the correct minima.

In this computational lab, all of the reactants and products were optimised to their minima, and the transition states were also optimised. The calculations were done by Gaussian 09, using mainly semi-empirical method PM6 and DFT-B3LYP. Frequency calculations were performed to show molecular vibrations to confirm the position on the potential energy surface. If all the vibrational frequencies are real, this confirms the structure is a minimum, and vice versa, the presence of imaginary frequency may suggest that the structure is at its transition state. Intrinsic reaction coordinate method was carried out using calculated force constants to predict which conformer a reaction path from the transition state would lead to.

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

The reaction between butadiene and ethene is a typical pericyclic [4+2] Diels-Alder reaction that proceeds via a concerted mechanism through a cyclic transition state. The reaction scheme is shown below.

[[File:Ex1 reactionscheme revised yhw14.png|550px|center|thumb|Diagram 1: Reaction Scheme of Butadiene and Ethene]]

=== Molecular Orbital Analysis ===

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of butadiene and ethene.

[[File:Ex1 mo diagram yhw14 revised v3.png|550px|center|thumb|Diagram 2: MO diagram of Reaction of Butadiene and Ethene]]

Butadiene and ethene were optimised to their minima. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #06DCFB; color: #ffffff;" |'''Molecule'''
! '''Butadiene'''
! '''Ethene'''
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Butadiene lumo yhw14.png|center|150px]]
|[[File:Ethene lumo yhw14.png|center|150px]]
|-
|Corresponding to the s orbital (symmetric)
|Corresponding to the a orbital (asymmetric)
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Butadiene homo yhw14.png|center|150px]]
|[[File:Ethene homo yhw14.png|center|150px]]
|-
|Corresponding to the a orbital (antisymmetric)
|Corresponding to the s orbital (symmetric)
|}

The transition state was first optimised to its minimum, followed by a transition state calculation. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #01FCEF; color: #ffffff;" |'''Molecule'''
! '''Transition State'''
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Ts lumo+1 yhw14.png|center|150px]]
|-
|Corresponding to the 5 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Ts lumo 1 yhw14.png|center|150px]]
|-
|Corresponding to the 4 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Ts homo yhw14.png|center|150px]]
|-
|Corresponding to the 3 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Ts homo-1 yhw14.png|center|150px]]
|-
|Corresponding to the 2 orbital
|}

Based on the MO diagram and the computed MOs shown above, a reaction is only allowed when the MOs with the same symmetry labels interact with each other, i.e. symmetric-symmetric and asymmetric-asymmetric interactions; and a reaction is forbidden when the MOs with different symmetry labels interact with each other, i.e. symmetric-asymmetric interactions.
In the reaction between butadiene and ethene, the butadiene asymmetric MO interacts with the ethene asymmetric MO to give the 2 and 5 MOs of the transition state, and the butadiene symmetric MO interacts with the ethene symmetric MO to give the 3 and 4 MOs of the transition state. Therefore, a reaction is allowed when the symmetry labels of the MOs of the reactants are the same; and forbidden when the symmetry labels are different.

The orbital overlap integral is zero in a symmetric-asymmetric interaction and non-zero in symmetric-symmetric and asymmetric-asymmetric interactions.

=== Bond Length Analysis ===

The changes in bond lengths between carbons in reactant, transition state and product as the reaction progresses were studied by comparing the bond lengths between carbons before and after the reaction. The summary of bond lengths is shown below.
[[File:Ex1 bondlength yhw14.png|470px|center|thumb|Diagram 3: Labelled carbons]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #0000FF; color: #ffffff" | State
! style="background: #0000FF; color: #ffffff" | C1-C2
! style="background: #0000FF; color: #ffffff" | C2-C3
! style="background: #0000FF; color: #ffffff" | C3-C4
! style="background: #0000FF; color: #ffffff" | C4-C5
! style="background: #0000FF; color: #ffffff" | C5-C6
! style="background: #0000FF; color: #ffffff" | C6-C1
|-
|Reactants
|1.335
|1.468
|1.335
|/
|1.327
|/
|-
|Transition State
|1.380
|1.411
|1.380
|2.115
|1.382
|2.114
|-
|Product
|1.500
|1.338
|1.500
|1.540
|1.540
|1.540
|+Table 1: Measurements of the C-C bond lengths of the reactants, transition state and products (Å)
|}
As the reaction progresses, the bond lengths between C1-C2, C3-C4 and C5-C6 increase from ~1.3 Å to ~1.5 Å as the bond order decrease to one, whereas bond length of C2-C3 decreases from ~1.5 Å to ~1.3 Å as the bond order increases from one to two.
This could be explained as the increase in bond length suggest a change from sp2-sp2 (C-C double bond) with typical bond length of 1.33 Å <ref name="C-C bond lengths"/> to sp3-sp3 (C-C single bond) with typical bond length of 1.54 Å <ref name="C-C bond lengths"/>, and vice versa for the decrease in bond length. Based on the calculated bond lengths above in Table 1, it is clear that bond lengths and bond orders of the reactants changed during the reaction and the new bonds formed at C4-C5 and C6-C1 are single bonds as they have bond lengths of 1.54 Å.
The typical Van der Waals radius of the C atom is 1.7 Å <ref name="Van der Waals radius of C"/>. As the bond lengths between C4-C5 and C6-C1 of the transition state are shorter than 2 x Van der Waals radii of C, this reflects that C-C bonds are forming at the transition state.

=== Vibration Analysis ===

The imaginary frequency at -948.32 cm-1 corresponds to the reaction path at the transition state, which shows a synchronous bond formation, which agrees with the concerted mechanism of [4+2] cycloaddition, where both reaction centres converge at the same time to form bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 15;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Reaction Path at the Transition State
|}

The lowest positive frequency at 145.14 cm-1 is asynchronous as shown below, where one of the C from the ethene moves towards the butadiene reaction centre and the other C moves away. This suggests that bonds are formed one at a time.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 16;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Lowest positive frequency
|}

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

[[File:Ex2 reactionscheme.png|550px|center|thumb|Diagram 4: Reaction Scheme of Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

Cyclohexadiene and 1,3-dioxole were optimised to their minima. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #9A03FE; color: #ffffff;" |'''Molecule'''
! '''Cyclohexadiene'''
! '''1,3-Dioxole'''
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Cyclo lumo 631g yhw14.png|center|150px]]
|[[File:Dioxole lumo 631g yhw14.png|center|150px]]
|-
|Corresponding to the s orbital
|Corresponding to the a orbital
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Cyclo homo 631g yhw14.png|center|150px]]
|[[File:Dioxole homo 631g yhw14.png|center|150px]]
|-
|Corresponding to the a orbital
|Corresponding to the s orbital
|}

The transition state was first optimised to its minimum, followed by a transition state calculation. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #BD5CFE; color: #ffffff;" |'''Molecule'''
! '''Endo Transition State'''
! '''Exo Transition State'''
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Endo ts lumo+1 yhw14.png|center|150px]]
|[[File:Exo ts lumo+1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 5 orbital (asymmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Endo ts lumo yhw14.png|center|150px]]
|[[File:Exo ts lumo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 4 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Endo ts homo yhw14.png|center|150px]]
|[[File:Exo ts homo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 3 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Endo ts homo-1 yhw14.png|center|150px]]
|[[File:Exo ts homo-1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 2 orbital (asymmetric)
|}

The diagram below illustrates the π molecular orbitals of cyclohexadiene and 1,3-dioxole involved in the formation of the transition state.

[[File:Ex2 mo diagram yhw14.png|550px|center|thumb|Diagram 5: MO diagram of Reaction of Cyclohexadiene and 1,3-dioxole]]

=== Normal Demand vs Inverse Demand Diels-Alder Reaction ===

A normal electron demand Diels-Alder reaction can be defined as a reaction between electron rich diene and electron poor dienophile. An inverse electron demand is the reaction between electron poor diene and electron rich dienophile.

The LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are very close in energy, which results in strong bonding interaction between the two to form the HOMO and LUMO of both endo and exo TS. Since the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole have the correct symmetry (symmetric) to interact, they interact to form the symmetric HOMO and LUMO of both TS.

The presence of electron rich O on 1,3-dioxole raise the energy of both its HOMO and LUMO, making the overlap between the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole much better than the HOMO of cyclohexadiene and the LUMO of 1,3-dioxole. Thus, the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are now the frontier orbitals that interact the most, hence this is an inverse demand Diels-Alder reaction.

=== Reaction Energies and Secondary Orbital Interaction ===

The energies of reactants were taken using the sum of the energies of cyclohexadiene and 1,3-dioxole optimised to their minima at DFT-B3LYP 631G.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FF4AFF; color: #ffffff" |
! style="background: #FF4AFF; color: #ffffff" | Reactants
! style="background: #FF4AFF; color: #ffffff" | Transition State
! style="background: #FF4AFF; color: #ffffff" | Product
! style="background: #FF4AFF; color: #ffffff" | Activation Energy
! style="background: #FF4AFF; color: #ffffff" | Gibbs Free Energy
|-
|Endo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313622</nowiki>
|<nowiki>-1313849</nowiki>
|160
|<nowiki>-67</nowiki>
|-
|Exo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313614</nowiki>
|<nowiki>-1313846</nowiki>
|168
|<nowiki>-64</nowiki>
|+Table 2: Energies of Reactants, Transition States and Products of both Endo and Exo Pathways in Diels-Alder Reaction of Cyclohexadiene and 1,3-Dioxole (kJ mol-1)
|}

Kinetically favourable product of a reaction is the one that has the lowest activation energy; Thermodynamically favourable product is the product with lowest energy conformer, hence the more stabilised product.

The endo transition state is the kinetic product of this reaction as it has lower activation energy. This could be explained using the secondary orbital interaction between the lone pair orbital on the oxygen atom and the empty π* orbital of diene. This favourable effect stabilises the endo transition state.

As the oxygen atom lone pair is oriented away from the diene π system in the exo transition state, the secondary orbital effect is not present, hence the activation energy of exo reaction is higher.

However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, i.e. increasing temperature, formation of the exo product would be more favourable.

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

Xylylene can react with sulfur dioxide through Diels-Alder reaction via either endo or exo pathways to form a 6-membered ring, or through cheletropic reaction to form a 5-membered ring. The reaction scheme is shown below. Reaction barriers and reaction energies for each pathway are compared to determine the reaction that is most favourable.

[[File:Ex3 reactionscheme yhw14.png|550px|center|thumb|Diagram 6: Reaction Scheme of Xylylene and Sulfur Dioxide]]

=== Intrinsic Reaction Coordinate ===
The following files show the intrinsic reaction coordinates of the three different reaction pathways of xylylene and SO2. Please click to see animation.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Endo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Exo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Cheletropic TS
|-
|[[File:DA endo irc animation yhw14.gif|center]]
|[[File:DA exo irc animation yhw14.gif|center]]
|[[File:Cheletropic irc animation yhw14.gif|center]]
|-
|[[File:DA endo irc plot yhw14.png|center|500px]]
|[[File:DA exo irc plot yhw14.png|center|500px]]
|[[File:Cheletropic irc plot yhw14.png|center|650px]]
|}

=== Reaction Energies and Reaction Barriers ===

[[File:Ex3 reactionprofile yhw14.png|550px|center|thumb|Diagram 7: Reaction Profile of Xylylene and Sulfur Dioxide]]

The energies of reactants were taken using the sum of the energies of xylylene and SO2 optimised to their minima at semi-empirical PM6 level.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FFD1C3; color: #ffffff" |
! style="background: #FFD1C3; color: #ffffff" | Reactants
! style="background: #FFD1C3; color: #ffffff" | Transition State
! style="background: #FFD1C3; color: #ffffff" | Product
! style="background: #FFD1C3; color: #ffffff" | Activation Energy
! style="background: #FFD1C3; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|237.767824
|56.9576013
|83.391038
|<nowiki>-97.4191847</nowiki>
|-
|Exo
|154.376786
|241.753433
|56.3196048
|87.406647
|<nowiki>-98.0571812</nowiki>
|-
|Cheletropic
|154.376786
|260.08205
|0.013127501
|105.705264
|<nowiki>-154.3636585</nowiki>
|+Table 3: Energies of Reactants, Transition States and Products of Reactions between Xylylene and Sulfur Dioxide (kJ mol-1)
|}

With reference to the reaction profile and table 3, the Diels-Alder reaction via the endo pathway has the lowest activation energy, making it a more kinetically favourable product, i.e. the kinetic product; the Diels-Alder exo product has a lower energy than endo, however with a higher activation energy hence it will not form under low temperature condition; the cheletropic product is the most stabilised product out of the three and it has the lowest reaction energy, therefore is the thermodynamic product.

=== Side Reaction between cis-diene in Xylylene 6-membered ring and SO2===

o-Xylylene contains another cis-butadiene fragment located in the 6-membered ring that can undergo a Diels-Alder reaction with SO2. The reaction energies and reaction barriers between endo and exo pathways are compared in the table below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #4EBEBA; color: #ffffff" |
! style="background: #4EBEBA; color: #ffffff" | Reactants
! style="background: #4EBEBA; color: #ffffff" | Transition State
! style="background: #4EBEBA; color: #ffffff" | Product
! style="background: #4EBEBA; color: #ffffff" | Activation Energy
! style="background: #4EBEBA; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|267.984805
|172.272196
|113.608019
|17.89541
|-
|Exo
|154.376786
|275.821924
|176.711916
|121.445138
|22.33513
|+Table 4: Energies of Reactants, Transition States and Products of the Side Reaction in Xylylene 6-membered ring and Sulfur Dioxide (kJ mol-1)
|}

It is clear that both endo and exo Diels-Alder side reactions are kinetically and thermodynamically unfavourable at this site as the activation energies are much higher than the previous reactions mentioned above in table 4 and the reaction energies show that the reactions are endothermic.

== Conclusion ==

The transition states of three pericyclic reactions were investigated in this computational lab, using Gaussian to optimise the reactants, transition states and products respectively, and the vibrational frequencies and intrinsic reaction coordinates were computed.

In the reaction between butadiene and ethene, the importance of molecular orbital symmetry in the interaction of molecular orbitals was illustrated, such that a reaction is only allowed when the molecular orbitals with the same symmetry labels interact with each other and forbidden when symmetric molecular orbital interact with asymmetric orbitals. Furthermore, the vibration frequency calculation proved that this [4+2] Diels-Alder reaction proceeds via a concerted mechanism as synchronous bond formation was demonstrated. Bonding interaction can be further confirmed as the bond distance between the two termini carbon atoms in the transition state is shorter than the sum of two Van der Waals radii of carbon.

In the reaction of cyclohexadiene and 1,3-dioxole, both the endo and exo transition states were investigated. In general, the endo transition state is kinetically more favourable as it has lower activation barrier, possibly due to the secondary orbital interaction between the lone pair in p orbital on the oxygen atom and the empty pi* orbital in the diene, which stabilises the transition state. However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, formation of the exo product could be possible.

The final reaction between xylylene and SO2 again proved that the endo Diels-Alder transition state has the lowest activation energy, making it kinetically favourable at low temperature. However, the cheletropic product is the most stabilised and thermodynamically favourable product. Therefore the reaction would yield the cheletropic product under thermodynamic control instead of the exo Diels-Alder product.

==References==
<references>
<ref name="C-C bond lengths">L. Pauling and L. O. Brockway, ''Journal of the American Chemical Society'', '''1937''', Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref>
<ref name="Van der Waals radius of C">S. S. Batsanov, ''Inorganic Materials'', '''2001''', Volume 37, Number 9, pp. 871-885, https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf.</ref>
</references>

Rep:Mod:yhw14cts

2017-02-09T20:35:05Z

Yhw14: /* Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole */

''' Transition States and Reactivity '''

'' Yi Hang Cherie WONG (yhw14) ''
'' CID: 00933828 ''

== Introduction ==
A potential energy surface is a mathematical function that gives the energy of a molecule as a function of its geometry with the relative positions of the atoms participating in the reaction. The stationary points may be classified according to the first and second derivatives of the energy with respect to position. At the minimum of a reaction profile, the gradient is represented by the first derivative of the reaction coordinate, which is zero, while curvature is represented by the second derivative, is positive in this case; hence energy rises in all directions. Energy minima correspond to physically stable chemical species, which could be reactants and products. The transition state is defined as the maximum in a reaction profile, where the gradient is again, zero, while curvature is negative; hence energy decreases in one direction, which indicates the reaction pathway of the chemical reaction. The potential energy surface can be computed using Gaussview 09, where structure and energy of reactants or products can be modelled to illustrate the transition states, which can rarely be obtained experimentally. The intrinsic reaction coordinate can then be calculated and compared to predict the reaction path at a transition state and follow it to the correct minima.

In this computational lab, all of the reactants and products were optimised to their minima, and the transition states were also optimised. The calculations were done by Gaussian 09, using mainly semi-empirical method PM6 and DFT-B3LYP. Frequency calculations were performed to show molecular vibrations to confirm the position on the potential energy surface. If all the vibrational frequencies are real, this confirms the structure is a minimum, and vice versa, the presence of imaginary frequency may suggest that the structure is at its transition state. Intrinsic reaction coordinate method was carried out using calculated force constants to predict which conformer a reaction path from the transition state would lead to.

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

The reaction between butadiene and ethene is a typical pericyclic [4+2] Diels-Alder reaction that proceeds via a concerted mechanism through a cyclic transition state. The reaction scheme is shown below.

[[File:Ex1 reactionscheme revised yhw14.png|550px|center|thumb|Diagram 1: Reaction Scheme of Butadiene and Ethene]]

=== Molecular Orbital Analysis ===

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of butadiene and ethene.

[[File:Ex1 mo diagram yhw14 revised v3.png|550px|center|thumb|Diagram 2: MO diagram of Reaction of Butadiene and Ethene]]

Butadiene and ethene were optimised to their minima. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #06DCFB; color: #ffffff;" |'''Molecule'''
! '''Butadiene'''
! '''Ethene'''
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Butadiene lumo yhw14.png|center|150px]]
|[[File:Ethene lumo yhw14.png|center|150px]]
|-
|Corresponding to the s orbital (symmetric)
|Corresponding to the a orbital (asymmetric)
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Butadiene homo yhw14.png|center|150px]]
|[[File:Ethene homo yhw14.png|center|150px]]
|-
|Corresponding to the a orbital (antisymmetric)
|Corresponding to the s orbital (symmetric)
|}

The transition state was first optimised to its minimum, followed by a transition state calculation. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #01FCEF; color: #ffffff;" |'''Molecule'''
! '''Transition State'''
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Ts lumo+1 yhw14.png|center|150px]]
|-
|Corresponding to the 5 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Ts lumo 1 yhw14.png|center|150px]]
|-
|Corresponding to the 4 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Ts homo yhw14.png|center|150px]]
|-
|Corresponding to the 3 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Ts homo-1 yhw14.png|center|150px]]
|-
|Corresponding to the 2 orbital
|}

Based on the MO diagram and the computed MOs shown above, a reaction is only allowed when the MOs with the same symmetry labels interact with each other, i.e. symmetric-symmetric and asymmetric-asymmetric interactions; and a reaction is forbidden when the MOs with different symmetry labels interact with each other, i.e. symmetric-asymmetric interactions.
In the reaction between butadiene and ethene, the butadiene asymmetric MO interacts with the ethene asymmetric MO to give the 2 and 5 MOs of the transition state, and the butadiene symmetric MO interacts with the ethene symmetric MO to give the 3 and 4 MOs of the transition state. Therefore, a reaction is allowed when the symmetry labels of the MOs of the reactants are the same; and forbidden when the symmetry labels are different.

The orbital overlap integral is zero in a symmetric-asymmetric interaction and non-zero in symmetric-symmetric and asymmetric-asymmetric interactions.

=== Bond Length Analysis ===

The changes in bond lengths between carbons in reactant, transition state and product as the reaction progresses were studied by comparing the bond lengths between carbons before and after the reaction. The summary of bond lengths is shown below.
[[File:Ex1 bondlength yhw14.png|470px|center|thumb|Diagram 3: Labelled carbons]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #0000FF; color: #ffffff" | State
! style="background: #0000FF; color: #ffffff" | C1-C2
! style="background: #0000FF; color: #ffffff" | C2-C3
! style="background: #0000FF; color: #ffffff" | C3-C4
! style="background: #0000FF; color: #ffffff" | C4-C5
! style="background: #0000FF; color: #ffffff" | C5-C6
! style="background: #0000FF; color: #ffffff" | C6-C1
|-
|Reactants
|1.335
|1.468
|1.335
|/
|1.327
|/
|-
|Transition State
|1.380
|1.411
|1.380
|2.115
|1.382
|2.114
|-
|Product
|1.500
|1.338
|1.500
|1.540
|1.540
|1.540
|+Table 1: Measurements of the C-C bond lengths of the reactants, transition state and products (Å)
|}
As the reaction progresses, the bond lengths between C1-C2, C3-C4 and C5-C6 increase from ~1.3 Å to ~1.5 Å as the bond order decrease to one, whereas bond length of C2-C3 decreases from ~1.5 Å to ~1.3 Å as the bond order increases from one to two.
This could be explained as the increase in bond length suggest a change from sp2-sp2 (C-C double bond) with typical bond length of 1.33 Å <ref name="C-C bond lengths"/> to sp3-sp3 (C-C single bond) with typical bond length of 1.54 Å <ref name="C-C bond lengths"/>, and vice versa for the decrease in bond length. Based on the calculated bond lengths above in Table 1, it is clear that bond lengths and bond orders of the reactants changed during the reaction and the new bonds formed at C4-C5 and C6-C1 are single bonds as they have bond lengths of 1.54 Å.
The typical Van der Waals radius of the C atom is 1.7 Å <ref name="Van der Waals radius of C"/>. As the bond lengths between C4-C5 and C6-C1 of the transition state are shorter than 2 x Van der Waals radii of C, this reflects that C-C bonds are forming at the transition state.

=== Vibration Analysis ===

The imaginary frequency at -948.32 cm-1 corresponds to the reaction path at the transition state, which shows a synchronous bond formation, which agrees with the concerted mechanism of [4+2] cycloaddition, where both reaction centres converge at the same time to form bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 15;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Reaction Path at the Transition State
|}

The lowest positive frequency at 145.14 cm-1 is asynchronous as shown below, where one of the C from the ethene moves towards the butadiene reaction centre and the other C moves away. This suggests that bonds are formed one at a time.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 16;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Lowest positive frequency
|}

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

[[File:Ex2 reactionscheme.png|550px|center|thumb|Diagram 4: Reaction Scheme of Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

Cyclohexadiene and 1,3-dioxole were optimised to their minima. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #9A03FE; color: #ffffff;" |'''Molecule'''
! '''Cyclohexadiene'''
! '''1,3-Dioxole'''
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Cyclo lumo 631g yhw14.png|center|150px]]
|[[File:Dioxole lumo 631g yhw14.png|center|150px]]
|-
|Corresponding to the s orbital
|Corresponding to the a orbital
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Cyclo homo 631g yhw14.png|center|150px]]
|[[File:Dioxole homo 631g yhw14.png|center|150px]]
|-
|Corresponding to the a orbital
|Corresponding to the s orbital
|}

The transition state was first optimised to its minimum, followed by a transition state calculation. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #BD5CFE; color: #ffffff;" |'''Molecule'''
! '''Endo Transition State'''
! '''Exo Transition State'''
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Endo ts lumo+1 yhw14.png|center|150px]]
|[[File:Exo ts lumo+1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 5 orbital (asymmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Endo ts lumo yhw14.png|center|150px]]
|[[File:Exo ts lumo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 4 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Endo ts homo yhw14.png|center|150px]]
|[[File:Exo ts homo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 3 orbital (symmetric)
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Endo ts homo-1 yhw14.png|center|150px]]
|[[File:Exo ts homo-1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 2 orbital (asymmetric)
|}

The diagram below illustrates the π molecular orbitals of cyclohexadiene and 1,3-dioxole involved in the formation of the transition state.

[[File:Ex2 mo diagram yhw14.png|550px|center|thumb|Diagram 5: MO diagram of Reaction of Cyclohexadiene and 1,3-dioxole]]

=== Normal Demand vs Inverse Demand Diels-Alder Reaction ===

A normal electron demand Diels-Alder reaction can be defined as a reaction between electron rich diene and electron poor dienophile. An inverse electron demand is the reaction between electron poor diene and electron rich dienophile.

The LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are very close in energy, which results in strong bonding interaction between the two to form the HOMO and LUMO of both endo and exo TS. Since the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole have the correct symmetry (symmetric) to interact, they interact to form the symmetric HOMO and LUMO of both TS.

The presence of electron rich O on 1,3-dioxole raise the energy of both its HOMO and LUMO, making the overlap between the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole much better than the HOMO of cyclohexadiene and the LUMO of 1,3-dioxole. Thus, the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are now the frontier orbitals that interact the most, hence this is an inverse demand Diels-Alder reaction.

=== Reaction Energies and Secondary Orbital Interaction ===

The energies of reactants were taken using the sum of the energies of cyclohexadiene and 1,3-dioxole optimised to their minima at DFT-B3LYP 631G.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FF4AFF; color: #ffffff" |
! style="background: #FF4AFF; color: #ffffff" | Reactants
! style="background: #FF4AFF; color: #ffffff" | Transition State
! style="background: #FF4AFF; color: #ffffff" | Product
! style="background: #FF4AFF; color: #ffffff" | Activation Energy
! style="background: #FF4AFF; color: #ffffff" | Gibbs Free Energy
|-
|Endo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313622</nowiki>
|<nowiki>-1313849</nowiki>
|160
|<nowiki>-67</nowiki>
|-
|Exo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313614</nowiki>
|<nowiki>-1313846</nowiki>
|168
|<nowiki>-64</nowiki>
|+Table 2: Energies of Reactants, Transition States and Products of both Endo and Exo Pathways in Diels-Alder Reaction of Cyclohexadiene and 1,3-Dioxole (kJ mol-1)
|}

Kinetically favourable product of a reaction is the one that has the lowest activation energy; Thermodynamically favourable product is the product with lowest energy conformer, hence the more stabilised product.

The endo transition state is the kinetic product of this reaction as it has lower activation energy. This could be explained using the secondary orbital interaction between the lone pair orbital on the oxygen atom and the empty π* orbital of diene. This favourable effect stabilises the endo transition state.

As the oxygen atom lone pair is oriented away from the diene π system in the exo transition state, the secondary orbital effect is not present, hence the activation energy of exo reaction is higher.

However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, i.e. increasing temperature, formation of the exo product would be more favourable.

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

Xylylene can react with sulfur dioxide through Diels-Alder reaction via either endo or exo pathways to form a 6-membered ring, or through cheletropic reaction to form a 5-membered ring. The reaction scheme is shown below. Reaction barriers and reaction energies for each pathway are compared to determine the reaction that is most favourable.

[[File:Ex3 reactionscheme yhw14.png|550px|center|thumb|Diagram 6: Reaction Scheme of Xylylene and Sulfur Dioxide]]

=== Intrinsic Reaction Coordinate ===
The following files show the intrinsic reaction coordinates of the three different reaction pathways of xylylene and SO2. Please click to see animation.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Endo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Exo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Cheletropic TS
|-
|[[File:DA endo irc animation yhw14.gif|center]]
|[[File:DA exo irc animation yhw14.gif|center]]
|[[File:Cheletropic irc animation yhw14.gif|center]]
|-
|[[File:DA endo irc plot yhw14.png|center|500px]]
|[[File:DA exo irc plot yhw14.png|center|500px]]
|[[File:Cheletropic irc plot yhw14.png|center|650px]]
|}

=== Reaction Energies and Reaction Barriers ===

[[File:Ex3 reactionprofile yhw14.png|550px|center|thumb|Diagram 7: Reaction Profile of Xylylene and Sulfur Dioxide]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FFD1C3; color: #ffffff" |
! style="background: #FFD1C3; color: #ffffff" | Reactants
! style="background: #FFD1C3; color: #ffffff" | Transition State
! style="background: #FFD1C3; color: #ffffff" | Product
! style="background: #FFD1C3; color: #ffffff" | Activation Energy
! style="background: #FFD1C3; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|237.767824
|56.9576013
|83.391038
|<nowiki>-97.4191847</nowiki>
|-
|Exo
|154.376786
|241.753433
|56.3196048
|87.406647
|<nowiki>-98.0571812</nowiki>
|-
|Cheletropic
|154.376786
|260.08205
|0.013127501
|105.705264
|<nowiki>-154.3636585</nowiki>
|+Table 3: Energies of Reactants, Transition States and Products of Reactions between Xylylene and Sulfur Dioxide (kJ mol-1)
|}

With reference to the reaction profile and table __, the Diels-Alder reaction via the endo pathway has the lowest activation energy, making it a more kinetically favourable product, i.e. the kinetic product; the Diels-Alder exo product has a lower energy than endo, however with a higher activation energy hence it will not form under low temperature condition; the cheletropic product is the most stabilised product out of the three and it has the lowest reaction energy, therefore is the thermodynamic product.

=== Side Reaction between cis-diene in Xylylene 6-membered ring and SO2===

o-Xylylene contains another cis-butadiene fragment located in the 6-membered ring that can undergo a Diels-Alder reaction with SO2. The reaction energies and reaction barriers between endo and exo pathways are compared in the table below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #4EBEBA; color: #ffffff" |
! style="background: #4EBEBA; color: #ffffff" | Reactants
! style="background: #4EBEBA; color: #ffffff" | Transition State
! style="background: #4EBEBA; color: #ffffff" | Product
! style="background: #4EBEBA; color: #ffffff" | Activation Energy
! style="background: #4EBEBA; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|267.984805
|172.272196
|113.608019
|17.89541
|-
|Exo
|154.376786
|275.821924
|176.711916
|121.445138
|22.33513
|+Table 4: Energies of Reactants, Transition States and Products of the Side Reaction in Xylylene 6-membered ring and Sulfur Dioxide (kJ mol-1)
|}

It is clear that both endo and exo Diels-Alder side reactions are kinetically and thermodynamically unfavourable at this site as the activation energies are much higher than the previous reactions mentioned above in table __ and the reaction energies show that the reactions are endothermic.

== Conclusion ==

The transition states of three pericyclic reactions were investigated in this computational lab, using Gaussian to optimise the reactants, transition states and products respectively, and the vibrational frequencies and intrinsic reaction coordinates were computed.

In the reaction between butadiene and ethene, the importance of molecular orbital symmetry in the interaction of molecular orbitals was illustrated, such that a reaction is only allowed when the molecular orbitals with the same symmetry labels interact with each other and forbidden when symmetric molecular orbital interact with asymmetric orbitals. Furthermore, the vibration frequency calculation proved that this [4+2] Diels-Alder reaction proceeds via a concerted mechanism as synchronous bond formation was demonstrated. Bonding interaction can be further confirmed as the bond distance between the two termini carbon atoms in the transition state is shorter than the sum of two Van der Waals radii of carbon.

In the reaction of cyclohexadiene and 1,3-dioxole, both the endo and exo transition states were investigated. In general, the endo transition state is kinetically more favourable as it has lower activation barrier, possibly due to the secondary orbital interaction between the lone pair in p orbital on the oxygen atom and the empty pi* orbital in the diene, which stabilises the transition state. However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, formation of the exo product could be possible.

The final reaction between xylylene and SO2 again proved that the endo Diels-Alder transition state has the lowest activation energy, making it kinetically favourable at low temperature. However, the cheletropic product is the most stabilised and thermodynamically favourable product. Therefore the reaction would yield the cheletropic product under thermodynamic control instead of the exo Diels-Alder product.

==References==
<references>
<ref name="C-C bond lengths">L. Pauling and L. O. Brockway, ''Journal of the American Chemical Society'', '''1937''', Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref>
<ref name="Van der Waals radius of C">S. S. Batsanov, ''Inorganic Materials'', '''2001''', Volume 37, Number 9, pp. 871-885, https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf.</ref>
</references>

Rep:Mod:yhw14cts

2017-02-09T20:25:47Z

Yhw14: /* Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole */

''' Transition States and Reactivity '''

'' Yi Hang Cherie WONG (yhw14) ''
'' CID: 00933828 ''

== Introduction ==
A potential energy surface is a mathematical function that gives the energy of a molecule as a function of its geometry with the relative positions of the atoms participating in the reaction. The stationary points may be classified according to the first and second derivatives of the energy with respect to position. At the minimum of a reaction profile, the gradient is represented by the first derivative of the reaction coordinate, which is zero, while curvature is represented by the second derivative, is positive in this case; hence energy rises in all directions. Energy minima correspond to physically stable chemical species, which could be reactants and products. The transition state is defined as the maximum in a reaction profile, where the gradient is again, zero, while curvature is negative; hence energy decreases in one direction, which indicates the reaction pathway of the chemical reaction. The potential energy surface can be computed using Gaussview 09, where structure and energy of reactants or products can be modelled to illustrate the transition states, which can rarely be obtained experimentally. The intrinsic reaction coordinate can then be calculated and compared to predict the reaction path at a transition state and follow it to the correct minima.

In this computational lab, all of the reactants and products were optimised to their minima, and the transition states were also optimised. The calculations were done by Gaussian 09, using mainly semi-empirical method PM6 and DFT-B3LYP. Frequency calculations were performed to show molecular vibrations to confirm the position on the potential energy surface. If all the vibrational frequencies are real, this confirms the structure is a minimum, and vice versa, the presence of imaginary frequency may suggest that the structure is at its transition state. Intrinsic reaction coordinate method was carried out using calculated force constants to predict which conformer a reaction path from the transition state would lead to.

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

The reaction between butadiene and ethene is a typical pericyclic [4+2] Diels-Alder reaction that proceeds via a concerted mechanism through a cyclic transition state. The reaction scheme is shown below.

[[File:Ex1 reactionscheme revised yhw14.png|550px|center|thumb|Diagram 1: Reaction Scheme of Butadiene and Ethene]]

=== Molecular Orbital Analysis ===

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of butadiene and ethene.

[[File:Ex1 mo diagram yhw14 revised v3.png|550px|center|thumb|Diagram 2: MO diagram of Reaction of Butadiene and Ethene]]

Butadiene and ethene were optimised to their minima. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #06DCFB; color: #ffffff;" |'''Molecule'''
! '''Butadiene'''
! '''Ethene'''
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Butadiene lumo yhw14.png|center|150px]]
|[[File:Ethene lumo yhw14.png|center|150px]]
|-
|Corresponding to the s orbital (symmetric)
|Corresponding to the a orbital (asymmetric)
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Butadiene homo yhw14.png|center|150px]]
|[[File:Ethene homo yhw14.png|center|150px]]
|-
|Corresponding to the a orbital (antisymmetric)
|Corresponding to the s orbital (symmetric)
|}

The transition state was first optimised to its minimum, followed by a transition state calculation. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #01FCEF; color: #ffffff;" |'''Molecule'''
! '''Transition State'''
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Ts lumo+1 yhw14.png|center|150px]]
|-
|Corresponding to the 5 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Ts lumo 1 yhw14.png|center|150px]]
|-
|Corresponding to the 4 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Ts homo yhw14.png|center|150px]]
|-
|Corresponding to the 3 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Ts homo-1 yhw14.png|center|150px]]
|-
|Corresponding to the 2 orbital
|}

Based on the MO diagram and the computed MOs shown above, a reaction is only allowed when the MOs with the same symmetry labels interact with each other, i.e. symmetric-symmetric and asymmetric-asymmetric interactions; and a reaction is forbidden when the MOs with different symmetry labels interact with each other, i.e. symmetric-asymmetric interactions.
In the reaction between butadiene and ethene, the butadiene asymmetric MO interacts with the ethene asymmetric MO to give the 2 and 5 MOs of the transition state, and the butadiene symmetric MO interacts with the ethene symmetric MO to give the 3 and 4 MOs of the transition state. Therefore, a reaction is allowed when the symmetry labels of the MOs of the reactants are the same; and forbidden when the symmetry labels are different.

The orbital overlap integral is zero in a symmetric-asymmetric interaction and non-zero in symmetric-symmetric and asymmetric-asymmetric interactions.

=== Bond Length Analysis ===

The changes in bond lengths between carbons in reactant, transition state and product as the reaction progresses were studied by comparing the bond lengths between carbons before and after the reaction. The summary of bond lengths is shown below.
[[File:Ex1 bondlength yhw14.png|470px|center|thumb|Diagram 3: Labelled carbons]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #0000FF; color: #ffffff" | State
! style="background: #0000FF; color: #ffffff" | C1-C2
! style="background: #0000FF; color: #ffffff" | C2-C3
! style="background: #0000FF; color: #ffffff" | C3-C4
! style="background: #0000FF; color: #ffffff" | C4-C5
! style="background: #0000FF; color: #ffffff" | C5-C6
! style="background: #0000FF; color: #ffffff" | C6-C1
|-
|Reactants
|1.335
|1.468
|1.335
|/
|1.327
|/
|-
|Transition State
|1.380
|1.411
|1.380
|2.115
|1.382
|2.114
|-
|Product
|1.500
|1.338
|1.500
|1.540
|1.540
|1.540
|+Table 1: Measurements of the C-C bond lengths of the reactants, transition state and products (Å)
|}
As the reaction progresses, the bond lengths between C1-C2, C3-C4 and C5-C6 increase from ~1.3 Å to ~1.5 Å as the bond order decrease to one, whereas bond length of C2-C3 decreases from ~1.5 Å to ~1.3 Å as the bond order increases from one to two.
This could be explained as the increase in bond length suggest a change from sp2-sp2 (C-C double bond) with typical bond length of 1.33 Å <ref name="C-C bond lengths"/> to sp3-sp3 (C-C single bond) with typical bond length of 1.54 Å <ref name="C-C bond lengths"/>, and vice versa for the decrease in bond length. Based on the calculated bond lengths above in Table 1, it is clear that bond lengths and bond orders of the reactants changed during the reaction and the new bonds formed at C4-C5 and C6-C1 are single bonds as they have bond lengths of 1.54 Å.
The typical Van der Waals radius of the C atom is 1.7 Å <ref name="Van der Waals radius of C"/>. As the bond lengths between C4-C5 and C6-C1 of the transition state are shorter than 2 x Van der Waals radii of C, this reflects that C-C bonds are forming at the transition state.

=== Vibration Analysis ===

The imaginary frequency at -948.32 cm-1 corresponds to the reaction path at the transition state, which shows a synchronous bond formation, which agrees with the concerted mechanism of [4+2] cycloaddition, where both reaction centres converge at the same time to form bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 15;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Reaction Path at the Transition State
|}

The lowest positive frequency at 145.14 cm-1 is asynchronous as shown below, where one of the C from the ethene moves towards the butadiene reaction centre and the other C moves away. This suggests that bonds are formed one at a time.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 16;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Lowest positive frequency
|}

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

[[File:Ex2 reactionscheme.png|550px|center|thumb|Diagram 4: Reaction Scheme of Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

Cyclohexadiene and 1,3-dioxole were optimised to their minima. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #9A03FE; color: #ffffff;" |'''Molecule'''
! '''Cyclohexadiene'''
! '''1,3-Dioxole'''
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Cyclo lumo 631g yhw14.png|center|150px]]
|[[File:Dioxole lumo 631g yhw14.png|center|150px]]
|-
|Corresponding to the s orbital
|Corresponding to the a orbital
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Cyclo homo 631g yhw14.png|center|150px]]
|[[File:Dioxole homo 631g yhw14.png|center|150px]]
|-
|Corresponding to the a orbital
|Corresponding to the s orbital
|}

The transition state was first optimised to its minimum, followed by a transition state calculation. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #BD5CFE; color: #ffffff;" |'''Molecule'''
! '''Endo Transition State'''
! '''Exo Transition State'''
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Endo ts lumo+1 yhw14.png|center|150px]]
|[[File:Exo ts lumo+1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 5 orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Endo ts lumo yhw14.png|center|150px]]
|[[File:Exo ts lumo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 4 orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Endo ts homo yhw14.png|center|150px]]
|[[File:Exo ts homo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 3 orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Endo ts homo-1 yhw14.png|center|150px]]
|[[File:Exo ts homo-1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the 2 orbital
|}

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of cyclohexadiene and 1,3-dioxole.

[[File:Ex2 mo diagram yhw14.png|550px|center|thumb|Diagram 5: MO diagram of Reaction of Cyclohexadiene and 1,3-dioxole]]

=== Normal Demand vs Inverse Demand Diels-Alder Reaction ===

A normal electron demand Diels-Alder reaction can be defined as a reaction between electron rich diene and electron poor dienophile. An inverse electron demand is the reaction between electron poor diene and electron rich dienophile.

The LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are very close in energy, which results in strong bonding interaction between the two to form the HOMO and LUMO of both endo and exo TS. Since only the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole have the correct symmetry () to interact, they interact to form the __(symmetry) HOMO and LUMO of both TS.

This could be explained by the presence of electron rich O on 1,3-dioxole which raises the energy of both its HOMO and LUMO, making the overlap between the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole much better than the HOMO of cyclohexadiene and the LUMO of 1,3-dioxole. Thus, the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are now the frontier orbitals that interact the most, hence this is an inverse demand Diels-Alder reaction.

=== Reaction Energies and Secondary Orbital Interaction ===

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FF4AFF; color: #ffffff" |
! style="background: #FF4AFF; color: #ffffff" | Reactants
! style="background: #FF4AFF; color: #ffffff" | Transition State
! style="background: #FF4AFF; color: #ffffff" | Product
! style="background: #FF4AFF; color: #ffffff" | Activation Energy
! style="background: #FF4AFF; color: #ffffff" | Gibbs Free Energy
|-
|Endo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313622</nowiki>
|<nowiki>-1313849</nowiki>
|160
|<nowiki>-67</nowiki>
|-
|Exo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313614</nowiki>
|<nowiki>-1313846</nowiki>
|168
|<nowiki>-64</nowiki>
|+Table 2: Energies of Reactants, Transition States and Products of both Endo and Exo Pathways in Diels-Alder Reaction of Cyclohexadiene and 1,3-Dioxole (kJ mol-1)
|}

Kinetically favourable product of a reaction is the one that has the lowest activation energy; Thermodynamically favourable product is the product with lowest energy conformer, hence the more stabilised product.

The endo transition state is the kinetic product of this reaction as it has lower activation energy. This could be explained using the secondary orbital interaction between the lone pair orbital on the oxygen atom and the empty π* orbital of diene. This favourable effect stabilises the endo transition state.

As the oxygen atom lone pair is oriented away from the diene π system in the exo transition state, the secondary orbital effect is not present, hence the activation energy of exo reaction is higher.

However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, i.e. increasing temperature, formation of the exo product would be more favourable.

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

Xylylene can react with sulfur dioxide through Diels-Alder reaction via either endo or exo pathways to form a 6-membered ring, or through cheletropic reaction to form a 5-membered ring. The reaction scheme is shown below. Reaction barriers and reaction energies for each pathway are compared to determine the reaction that is most favourable.

[[File:Ex3 reactionscheme yhw14.png|550px|center|thumb|Diagram 6: Reaction Scheme of Xylylene and Sulfur Dioxide]]

=== Intrinsic Reaction Coordinate ===
The following files show the intrinsic reaction coordinates of the three different reaction pathways of xylylene and SO2. Please click to see animation.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Endo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Exo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Cheletropic TS
|-
|[[File:DA endo irc animation yhw14.gif|center]]
|[[File:DA exo irc animation yhw14.gif|center]]
|[[File:Cheletropic irc animation yhw14.gif|center]]
|-
|[[File:DA endo irc plot yhw14.png|center|500px]]
|[[File:DA exo irc plot yhw14.png|center|500px]]
|[[File:Cheletropic irc plot yhw14.png|center|650px]]
|}

=== Reaction Energies and Reaction Barriers ===

[[File:Ex3 reactionprofile yhw14.png|550px|center|thumb|Diagram 7: Reaction Profile of Xylylene and Sulfur Dioxide]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FFD1C3; color: #ffffff" |
! style="background: #FFD1C3; color: #ffffff" | Reactants
! style="background: #FFD1C3; color: #ffffff" | Transition State
! style="background: #FFD1C3; color: #ffffff" | Product
! style="background: #FFD1C3; color: #ffffff" | Activation Energy
! style="background: #FFD1C3; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|237.767824
|56.9576013
|83.391038
|<nowiki>-97.4191847</nowiki>
|-
|Exo
|154.376786
|241.753433
|56.3196048
|87.406647
|<nowiki>-98.0571812</nowiki>
|-
|Cheletropic
|154.376786
|260.08205
|0.013127501
|105.705264
|<nowiki>-154.3636585</nowiki>
|+Table 3: Energies of Reactants, Transition States and Products of Reactions between Xylylene and Sulfur Dioxide (kJ mol-1)
|}

With reference to the reaction profile and table __, the Diels-Alder reaction via the endo pathway has the lowest activation energy, making it a more kinetically favourable product, i.e. the kinetic product; the Diels-Alder exo product has a lower energy than endo, however with a higher activation energy hence it will not form under low temperature condition; the cheletropic product is the most stabilised product out of the three and it has the lowest reaction energy, therefore is the thermodynamic product.

=== Side Reaction between cis-diene in Xylylene 6-membered ring and SO2===

o-Xylylene contains another cis-butadiene fragment located in the 6-membered ring that can undergo a Diels-Alder reaction with SO2. The reaction energies and reaction barriers between endo and exo pathways are compared in the table below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #4EBEBA; color: #ffffff" |
! style="background: #4EBEBA; color: #ffffff" | Reactants
! style="background: #4EBEBA; color: #ffffff" | Transition State
! style="background: #4EBEBA; color: #ffffff" | Product
! style="background: #4EBEBA; color: #ffffff" | Activation Energy
! style="background: #4EBEBA; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|267.984805
|172.272196
|113.608019
|17.89541
|-
|Exo
|154.376786
|275.821924
|176.711916
|121.445138
|22.33513
|+Table 4: Energies of Reactants, Transition States and Products of the Side Reaction in Xylylene 6-membered ring and Sulfur Dioxide (kJ mol-1)
|}

It is clear that both endo and exo Diels-Alder side reactions are kinetically and thermodynamically unfavourable at this site as the activation energies are much higher than the previous reactions mentioned above in table __ and the reaction energies show that the reactions are endothermic.

== Conclusion ==

The transition states of three pericyclic reactions were investigated in this computational lab, using Gaussian to optimise the reactants, transition states and products respectively, and the vibrational frequencies and intrinsic reaction coordinates were computed.

In the reaction between butadiene and ethene, the importance of molecular orbital symmetry in the interaction of molecular orbitals was illustrated, such that a reaction is only allowed when the molecular orbitals with the same symmetry labels interact with each other and forbidden when symmetric molecular orbital interact with asymmetric orbitals. Furthermore, the vibration frequency calculation proved that this [4+2] Diels-Alder reaction proceeds via a concerted mechanism as synchronous bond formation was demonstrated. Bonding interaction can be further confirmed as the bond distance between the two termini carbon atoms in the transition state is shorter than the sum of two Van der Waals radii of carbon.

In the reaction of cyclohexadiene and 1,3-dioxole, both the endo and exo transition states were investigated. In general, the endo transition state is kinetically more favourable as it has lower activation barrier, possibly due to the secondary orbital interaction between the lone pair in p orbital on the oxygen atom and the empty pi* orbital in the diene, which stabilises the transition state. However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, formation of the exo product could be possible.

The final reaction between xylylene and SO2 again proved that the endo Diels-Alder transition state has the lowest activation energy, making it kinetically favourable at low temperature. However, the cheletropic product is the most stabilised and thermodynamically favourable product. Therefore the reaction would yield the cheletropic product under thermodynamic control instead of the exo Diels-Alder product.

==References==
<references>
<ref name="C-C bond lengths">L. Pauling and L. O. Brockway, ''Journal of the American Chemical Society'', '''1937''', Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref>
<ref name="Van der Waals radius of C">S. S. Batsanov, ''Inorganic Materials'', '''2001''', Volume 37, Number 9, pp. 871-885, https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf.</ref>
</references>

Rep:Mod:yhw14cts

2017-02-09T19:58:51Z

Yhw14: /* Intrinsic Reaction Coordinate */

''' Transition States and Reactivity '''

'' Yi Hang Cherie WONG (yhw14) ''
'' CID: 00933828 ''

== Introduction ==
A potential energy surface is a mathematical function that gives the energy of a molecule as a function of its geometry with the relative positions of the atoms participating in the reaction. The stationary points may be classified according to the first and second derivatives of the energy with respect to position. At the minimum of a reaction profile, the gradient is represented by the first derivative of the reaction coordinate, which is zero, while curvature is represented by the second derivative, is positive in this case; hence energy rises in all directions. Energy minima correspond to physically stable chemical species, which could be reactants and products. The transition state is defined as the maximum in a reaction profile, where the gradient is again, zero, while curvature is negative; hence energy decreases in one direction, which indicates the reaction pathway of the chemical reaction. The potential energy surface can be computed using Gaussview 09, where structure and energy of reactants or products can be modelled to illustrate the transition states, which can rarely be obtained experimentally. The intrinsic reaction coordinate can then be calculated and compared to predict the reaction path at a transition state and follow it to the correct minima.

In this computational lab, all of the reactants and products were optimised to their minima, and the transition states were also optimised. The calculations were done by Gaussian 09, using mainly semi-empirical method PM6 and DFT-B3LYP. Frequency calculations were performed to show molecular vibrations to confirm the position on the potential energy surface. If all the vibrational frequencies are real, this confirms the structure is a minimum, and vice versa, the presence of imaginary frequency may suggest that the structure is at its transition state. Intrinsic reaction coordinate method was carried out using calculated force constants to predict which conformer a reaction path from the transition state would lead to.

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

The reaction between butadiene and ethene is a typical pericyclic [4+2] Diels-Alder reaction that proceeds via a concerted mechanism through a cyclic transition state. The reaction scheme is shown below.

[[File:Ex1 reactionscheme revised yhw14.png|550px|center|thumb|Diagram 1: Reaction Scheme of Butadiene and Ethene]]

=== Molecular Orbital Analysis ===

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of butadiene and ethene.

[[File:Ex1 mo diagram yhw14 revised v3.png|550px|center|thumb|Diagram 2: MO diagram of Reaction of Butadiene and Ethene]]

Butadiene and ethene were optimised to their minima. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #06DCFB; color: #ffffff;" |'''Molecule'''
! '''Butadiene'''
! '''Ethene'''
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Butadiene lumo yhw14.png|center|150px]]
|[[File:Ethene lumo yhw14.png|center|150px]]
|-
|Corresponding to the s orbital (symmetric)
|Corresponding to the a orbital (asymmetric)
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Butadiene homo yhw14.png|center|150px]]
|[[File:Ethene homo yhw14.png|center|150px]]
|-
|Corresponding to the a orbital (antisymmetric)
|Corresponding to the s orbital (symmetric)
|}

The transition state was first optimised to its minimum, followed by a transition state calculation. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #01FCEF; color: #ffffff;" |'''Molecule'''
! '''Transition State'''
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Ts lumo+1 yhw14.png|center|150px]]
|-
|Corresponding to the 5 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Ts lumo 1 yhw14.png|center|150px]]
|-
|Corresponding to the 4 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Ts homo yhw14.png|center|150px]]
|-
|Corresponding to the 3 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Ts homo-1 yhw14.png|center|150px]]
|-
|Corresponding to the 2 orbital
|}

Based on the MO diagram and the computed MOs shown above, a reaction is only allowed when the MOs with the same symmetry labels interact with each other, i.e. symmetric-symmetric and asymmetric-asymmetric interactions; and a reaction is forbidden when the MOs with different symmetry labels interact with each other, i.e. symmetric-asymmetric interactions.
In the reaction between butadiene and ethene, the butadiene asymmetric MO interacts with the ethene asymmetric MO to give the 2 and 5 MOs of the transition state, and the butadiene symmetric MO interacts with the ethene symmetric MO to give the 3 and 4 MOs of the transition state. Therefore, a reaction is allowed when the symmetry labels of the MOs of the reactants are the same; and forbidden when the symmetry labels are different.

The orbital overlap integral is zero in a symmetric-asymmetric interaction and non-zero in symmetric-symmetric and asymmetric-asymmetric interactions.

=== Bond Length Analysis ===

The changes in bond lengths between carbons in reactant, transition state and product as the reaction progresses were studied by comparing the bond lengths between carbons before and after the reaction. The summary of bond lengths is shown below.
[[File:Ex1 bondlength yhw14.png|470px|center|thumb|Diagram 3: Labelled carbons]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #0000FF; color: #ffffff" | State
! style="background: #0000FF; color: #ffffff" | C1-C2
! style="background: #0000FF; color: #ffffff" | C2-C3
! style="background: #0000FF; color: #ffffff" | C3-C4
! style="background: #0000FF; color: #ffffff" | C4-C5
! style="background: #0000FF; color: #ffffff" | C5-C6
! style="background: #0000FF; color: #ffffff" | C6-C1
|-
|Reactants
|1.335
|1.468
|1.335
|/
|1.327
|/
|-
|Transition State
|1.380
|1.411
|1.380
|2.115
|1.382
|2.114
|-
|Product
|1.500
|1.338
|1.500
|1.540
|1.540
|1.540
|+Table 1: Measurements of the C-C bond lengths of the reactants, transition state and products (Å)
|}
As the reaction progresses, the bond lengths between C1-C2, C3-C4 and C5-C6 increase from ~1.3 Å to ~1.5 Å as the bond order decrease to one, whereas bond length of C2-C3 decreases from ~1.5 Å to ~1.3 Å as the bond order increases from one to two.
This could be explained as the increase in bond length suggest a change from sp2-sp2 (C-C double bond) with typical bond length of 1.33 Å <ref name="C-C bond lengths"/> to sp3-sp3 (C-C single bond) with typical bond length of 1.54 Å <ref name="C-C bond lengths"/>, and vice versa for the decrease in bond length. Based on the calculated bond lengths above in Table 1, it is clear that bond lengths and bond orders of the reactants changed during the reaction and the new bonds formed at C4-C5 and C6-C1 are single bonds as they have bond lengths of 1.54 Å.
The typical Van der Waals radius of the C atom is 1.7 Å <ref name="Van der Waals radius of C"/>. As the bond lengths between C4-C5 and C6-C1 of the transition state are shorter than 2 x Van der Waals radii of C, this reflects that C-C bonds are forming at the transition state.

=== Vibration Analysis ===

The imaginary frequency at -948.32 cm-1 corresponds to the reaction path at the transition state, which shows a synchronous bond formation, which agrees with the concerted mechanism of [4+2] cycloaddition, where both reaction centres converge at the same time to form bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 15;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Reaction Path at the Transition State
|}

The lowest positive frequency at 145.14 cm-1 is asynchronous as shown below, where one of the C from the ethene moves towards the butadiene reaction centre and the other C moves away. This suggests that bonds are formed one at a time.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 16;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Lowest positive frequency
|}

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

[[File:Ex2 reactionscheme.png|550px|center|thumb|Diagram 4: Reaction Scheme of Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

Cyclohexadiene and 1,3-dioxole were optimised to their minima. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #9A03FE; color: #ffffff;" |'''Molecule'''
! '''Cyclohexadiene'''
! '''1,3-Dioxole'''
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Cyclo lumo 631g yhw14.png|center|150px]]
|[[File:Dioxole lumo 631g yhw14.png|center|150px]]
|-
|Corresponding to the orbital
|Corresponding to the orbital
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Cyclo homo 631g yhw14.png|center|150px]]
|[[File:Dioxole homo 631g yhw14.png|center|150px]]
|-
|Corresponding to the orbital
|Corresponding to the orbital
|}

The transition state was first optimised to its minimum, followed by a transition state calculation. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #BD5CFE; color: #ffffff;" |'''Molecule'''
! '''Endo Transition State'''
! '''Exo Transition State'''
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Endo ts lumo+1 yhw14.png|center|150px]]
|[[File:Exo ts lumo+1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Endo ts lumo yhw14.png|center|150px]]
|[[File:Exo ts lumo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Endo ts homo yhw14.png|center|150px]]
|[[File:Exo ts homo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Endo ts homo-1 yhw14.png|center|150px]]
|[[File:Exo ts homo-1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|}

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of cyclohexadiene and 1,3-dioxole.

[[File:Ex2 mo diagram yhw14.png|550px|center|thumb|Diagram 5: MO diagram of Reaction of Cyclohexadiene and 1,3-dioxole]]

=== Normal Demand vs Inverse Demand Diels-Alder Reaction ===

A normal electron demand Diels-Alder reaction can be defined as a reaction between electron rich diene and electron poor dienophile. An inverse electron demand is the reaction between electron poor diene and electron rich dienophile.

The LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are very close in energy, which results in strong bonding interaction between the two to form the HOMO and LUMO of both endo and exo TS. Since only the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole have the correct symmetry () to interact, they interact to form the __(symmetry) HOMO and LUMO of both TS.

This could be explained by the presence of electron rich O on 1,3-dioxole which raises the energy of both its HOMO and LUMO, making the overlap between the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole much better than the HOMO of cyclohexadiene and the LUMO of 1,3-dioxole. Thus, the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are now the frontier orbitals that interact the most, hence this is an inverse demand Diels-Alder reaction.

=== Reaction Energies and Secondary Orbital Interaction ===

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FF4AFF; color: #ffffff" |
! style="background: #FF4AFF; color: #ffffff" | Reactants
! style="background: #FF4AFF; color: #ffffff" | Transition State
! style="background: #FF4AFF; color: #ffffff" | Product
! style="background: #FF4AFF; color: #ffffff" | Activation Energy
! style="background: #FF4AFF; color: #ffffff" | Gibbs Free Energy
|-
|Endo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313622</nowiki>
|<nowiki>-1313849</nowiki>
|160
|<nowiki>-67</nowiki>
|-
|Exo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313614</nowiki>
|<nowiki>-1313846</nowiki>
|168
|<nowiki>-64</nowiki>
|+Table 2: Energies of Reactants, Transition States and Products of both Endo and Exo Pathways in Diels-Alder Reaction of Cyclohexadiene and 1,3-Dioxole (kJ mol-1)
|}

Kinetically favourable product of a reaction is the one that has the lowest activation energy; Thermodynamically favourable product is the product with lowest energy conformer, hence the more stabilised product.

The endo transition state is the kinetic product of this reaction as it has lower activation energy. This could be explained using the secondary orbital interaction between the lone pair orbital on the oxygen atom and the empty π* orbital of diene. This favourable effect stabilises the endo transition state.

As the oxygen atom lone pair is oriented away from the diene π system in the exo transition state, the secondary orbital effect is not present, hence the activation energy of exo reaction is higher.

However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, i.e. increasing temperature, formation of the exo product would be more favourable.

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

Xylylene can react with sulfur dioxide through Diels-Alder reaction via either endo or exo pathways to form a 6-membered ring, or through cheletropic reaction to form a 5-membered ring. The reaction scheme is shown below. Reaction barriers and reaction energies for each pathway are compared to determine the reaction that is most favourable.

[[File:Ex3 reactionscheme yhw14.png|550px|center|thumb|Diagram 6: Reaction Scheme of Xylylene and Sulfur Dioxide]]

=== Intrinsic Reaction Coordinate ===
The following files show the intrinsic reaction coordinates of the three different reaction pathways of xylylene and SO2. Please click to see animation.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Endo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Exo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Cheletropic TS
|-
|[[File:DA endo irc animation yhw14.gif|center]]
|[[File:DA exo irc animation yhw14.gif|center]]
|[[File:Cheletropic irc animation yhw14.gif|center]]
|-
|[[File:DA endo irc plot yhw14.png|center|500px]]
|[[File:DA exo irc plot yhw14.png|center|500px]]
|[[File:Cheletropic irc plot yhw14.png|center|650px]]
|}

=== Reaction Energies and Reaction Barriers ===

[[File:Ex3 reactionprofile yhw14.png|550px|center|thumb|Diagram 7: Reaction Profile of Xylylene and Sulfur Dioxide]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FFD1C3; color: #ffffff" |
! style="background: #FFD1C3; color: #ffffff" | Reactants
! style="background: #FFD1C3; color: #ffffff" | Transition State
! style="background: #FFD1C3; color: #ffffff" | Product
! style="background: #FFD1C3; color: #ffffff" | Activation Energy
! style="background: #FFD1C3; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|237.767824
|56.9576013
|83.391038
|<nowiki>-97.4191847</nowiki>
|-
|Exo
|154.376786
|241.753433
|56.3196048
|87.406647
|<nowiki>-98.0571812</nowiki>
|-
|Cheletropic
|154.376786
|260.08205
|0.013127501
|105.705264
|<nowiki>-154.3636585</nowiki>
|+Table 3: Energies of Reactants, Transition States and Products of Reactions between Xylylene and Sulfur Dioxide (kJ mol-1)
|}

With reference to the reaction profile and table __, the Diels-Alder reaction via the endo pathway has the lowest activation energy, making it a more kinetically favourable product, i.e. the kinetic product; the Diels-Alder exo product has a lower energy than endo, however with a higher activation energy hence it will not form under low temperature condition; the cheletropic product is the most stabilised product out of the three and it has the lowest reaction energy, therefore is the thermodynamic product.

=== Side Reaction between cis-diene in Xylylene 6-membered ring and SO2===

o-Xylylene contains another cis-butadiene fragment located in the 6-membered ring that can undergo a Diels-Alder reaction with SO2. The reaction energies and reaction barriers between endo and exo pathways are compared in the table below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #4EBEBA; color: #ffffff" |
! style="background: #4EBEBA; color: #ffffff" | Reactants
! style="background: #4EBEBA; color: #ffffff" | Transition State
! style="background: #4EBEBA; color: #ffffff" | Product
! style="background: #4EBEBA; color: #ffffff" | Activation Energy
! style="background: #4EBEBA; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|267.984805
|172.272196
|113.608019
|17.89541
|-
|Exo
|154.376786
|275.821924
|176.711916
|121.445138
|22.33513
|+Table 4: Energies of Reactants, Transition States and Products of the Side Reaction in Xylylene 6-membered ring and Sulfur Dioxide (kJ mol-1)
|}

It is clear that both endo and exo Diels-Alder side reactions are kinetically and thermodynamically unfavourable at this site as the activation energies are much higher than the previous reactions mentioned above in table __ and the reaction energies show that the reactions are endothermic.

== Conclusion ==

The transition states of three pericyclic reactions were investigated in this computational lab, using Gaussian to optimise the reactants, transition states and products respectively, and the vibrational frequencies and intrinsic reaction coordinates were computed.

In the reaction between butadiene and ethene, the importance of molecular orbital symmetry in the interaction of molecular orbitals was illustrated, such that a reaction is only allowed when the molecular orbitals with the same symmetry labels interact with each other and forbidden when symmetric molecular orbital interact with asymmetric orbitals. Furthermore, the vibration frequency calculation proved that this [4+2] Diels-Alder reaction proceeds via a concerted mechanism as synchronous bond formation was demonstrated. Bonding interaction can be further confirmed as the bond distance between the two termini carbon atoms in the transition state is shorter than the sum of two Van der Waals radii of carbon.

In the reaction of cyclohexadiene and 1,3-dioxole, both the endo and exo transition states were investigated. In general, the endo transition state is kinetically more favourable as it has lower activation barrier, possibly due to the secondary orbital interaction between the lone pair in p orbital on the oxygen atom and the empty pi* orbital in the diene, which stabilises the transition state. However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, formation of the exo product could be possible.

The final reaction between xylylene and SO2 again proved that the endo Diels-Alder transition state has the lowest activation energy, making it kinetically favourable at low temperature. However, the cheletropic product is the most stabilised and thermodynamically favourable product. Therefore the reaction would yield the cheletropic product under thermodynamic control instead of the exo Diels-Alder product.

==References==
<references>
<ref name="C-C bond lengths">L. Pauling and L. O. Brockway, ''Journal of the American Chemical Society'', '''1937''', Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref>
<ref name="Van der Waals radius of C">S. S. Batsanov, ''Inorganic Materials'', '''2001''', Volume 37, Number 9, pp. 871-885, https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf.</ref>
</references>

Rep:Mod:yhw14cts

2017-02-09T19:57:12Z

Yhw14: /* Vibration Analysis */

''' Transition States and Reactivity '''

'' Yi Hang Cherie WONG (yhw14) ''
'' CID: 00933828 ''

== Introduction ==
A potential energy surface is a mathematical function that gives the energy of a molecule as a function of its geometry with the relative positions of the atoms participating in the reaction. The stationary points may be classified according to the first and second derivatives of the energy with respect to position. At the minimum of a reaction profile, the gradient is represented by the first derivative of the reaction coordinate, which is zero, while curvature is represented by the second derivative, is positive in this case; hence energy rises in all directions. Energy minima correspond to physically stable chemical species, which could be reactants and products. The transition state is defined as the maximum in a reaction profile, where the gradient is again, zero, while curvature is negative; hence energy decreases in one direction, which indicates the reaction pathway of the chemical reaction. The potential energy surface can be computed using Gaussview 09, where structure and energy of reactants or products can be modelled to illustrate the transition states, which can rarely be obtained experimentally. The intrinsic reaction coordinate can then be calculated and compared to predict the reaction path at a transition state and follow it to the correct minima.

In this computational lab, all of the reactants and products were optimised to their minima, and the transition states were also optimised. The calculations were done by Gaussian 09, using mainly semi-empirical method PM6 and DFT-B3LYP. Frequency calculations were performed to show molecular vibrations to confirm the position on the potential energy surface. If all the vibrational frequencies are real, this confirms the structure is a minimum, and vice versa, the presence of imaginary frequency may suggest that the structure is at its transition state. Intrinsic reaction coordinate method was carried out using calculated force constants to predict which conformer a reaction path from the transition state would lead to.

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

The reaction between butadiene and ethene is a typical pericyclic [4+2] Diels-Alder reaction that proceeds via a concerted mechanism through a cyclic transition state. The reaction scheme is shown below.

[[File:Ex1 reactionscheme revised yhw14.png|550px|center|thumb|Diagram 1: Reaction Scheme of Butadiene and Ethene]]

=== Molecular Orbital Analysis ===

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of butadiene and ethene.

[[File:Ex1 mo diagram yhw14 revised v3.png|550px|center|thumb|Diagram 2: MO diagram of Reaction of Butadiene and Ethene]]

Butadiene and ethene were optimised to their minima. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #06DCFB; color: #ffffff;" |'''Molecule'''
! '''Butadiene'''
! '''Ethene'''
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Butadiene lumo yhw14.png|center|150px]]
|[[File:Ethene lumo yhw14.png|center|150px]]
|-
|Corresponding to the s orbital (symmetric)
|Corresponding to the a orbital (asymmetric)
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Butadiene homo yhw14.png|center|150px]]
|[[File:Ethene homo yhw14.png|center|150px]]
|-
|Corresponding to the a orbital (antisymmetric)
|Corresponding to the s orbital (symmetric)
|}

The transition state was first optimised to its minimum, followed by a transition state calculation. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #01FCEF; color: #ffffff;" |'''Molecule'''
! '''Transition State'''
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Ts lumo+1 yhw14.png|center|150px]]
|-
|Corresponding to the 5 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Ts lumo 1 yhw14.png|center|150px]]
|-
|Corresponding to the 4 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Ts homo yhw14.png|center|150px]]
|-
|Corresponding to the 3 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Ts homo-1 yhw14.png|center|150px]]
|-
|Corresponding to the 2 orbital
|}

Based on the MO diagram and the computed MOs shown above, a reaction is only allowed when the MOs with the same symmetry labels interact with each other, i.e. symmetric-symmetric and asymmetric-asymmetric interactions; and a reaction is forbidden when the MOs with different symmetry labels interact with each other, i.e. symmetric-asymmetric interactions.
In the reaction between butadiene and ethene, the butadiene asymmetric MO interacts with the ethene asymmetric MO to give the 2 and 5 MOs of the transition state, and the butadiene symmetric MO interacts with the ethene symmetric MO to give the 3 and 4 MOs of the transition state. Therefore, a reaction is allowed when the symmetry labels of the MOs of the reactants are the same; and forbidden when the symmetry labels are different.

The orbital overlap integral is zero in a symmetric-asymmetric interaction and non-zero in symmetric-symmetric and asymmetric-asymmetric interactions.

=== Bond Length Analysis ===

The changes in bond lengths between carbons in reactant, transition state and product as the reaction progresses were studied by comparing the bond lengths between carbons before and after the reaction. The summary of bond lengths is shown below.
[[File:Ex1 bondlength yhw14.png|470px|center|thumb|Diagram 3: Labelled carbons]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #0000FF; color: #ffffff" | State
! style="background: #0000FF; color: #ffffff" | C1-C2
! style="background: #0000FF; color: #ffffff" | C2-C3
! style="background: #0000FF; color: #ffffff" | C3-C4
! style="background: #0000FF; color: #ffffff" | C4-C5
! style="background: #0000FF; color: #ffffff" | C5-C6
! style="background: #0000FF; color: #ffffff" | C6-C1
|-
|Reactants
|1.335
|1.468
|1.335
|/
|1.327
|/
|-
|Transition State
|1.380
|1.411
|1.380
|2.115
|1.382
|2.114
|-
|Product
|1.500
|1.338
|1.500
|1.540
|1.540
|1.540
|+Table 1: Measurements of the C-C bond lengths of the reactants, transition state and products (Å)
|}
As the reaction progresses, the bond lengths between C1-C2, C3-C4 and C5-C6 increase from ~1.3 Å to ~1.5 Å as the bond order decrease to one, whereas bond length of C2-C3 decreases from ~1.5 Å to ~1.3 Å as the bond order increases from one to two.
This could be explained as the increase in bond length suggest a change from sp2-sp2 (C-C double bond) with typical bond length of 1.33 Å <ref name="C-C bond lengths"/> to sp3-sp3 (C-C single bond) with typical bond length of 1.54 Å <ref name="C-C bond lengths"/>, and vice versa for the decrease in bond length. Based on the calculated bond lengths above in Table 1, it is clear that bond lengths and bond orders of the reactants changed during the reaction and the new bonds formed at C4-C5 and C6-C1 are single bonds as they have bond lengths of 1.54 Å.
The typical Van der Waals radius of the C atom is 1.7 Å <ref name="Van der Waals radius of C"/>. As the bond lengths between C4-C5 and C6-C1 of the transition state are shorter than 2 x Van der Waals radii of C, this reflects that C-C bonds are forming at the transition state.

=== Vibration Analysis ===

The imaginary frequency at -948.32 cm-1 corresponds to the reaction path at the transition state, which shows a synchronous bond formation, which agrees with the concerted mechanism of [4+2] cycloaddition, where both reaction centres converge at the same time to form bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 15;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Reaction Path at the Transition State
|}

The lowest positive frequency at 145.14 cm-1 is asynchronous as shown below, where one of the C from the ethene moves towards the butadiene reaction centre and the other C moves away. This suggests that bonds are formed one at a time.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|<jmol><jmolApplet>
|<uploadedFileContents>TS OPT PM6 yhw14.LOG</uploadedFileContents>
|<color>white</color>
|<size>400</size>
|<script>frame 16;center {0 0 0};vibration 3;zoom 0</script></jmolApplet></jmol>
|-
|style="text-align: center;"|Lowest positive frequency
|}

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

[[File:Ex2 reactionscheme.png|550px|center|thumb|Diagram 4: Reaction Scheme of Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

Cyclohexadiene and 1,3-dioxole were optimised to their minima. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #9A03FE; color: #ffffff;" |'''Molecule'''
! '''Cyclohexadiene'''
! '''1,3-Dioxole'''
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Cyclo lumo 631g yhw14.png|center|150px]]
|[[File:Dioxole lumo 631g yhw14.png|center|150px]]
|-
|Corresponding to the orbital
|Corresponding to the orbital
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Cyclo homo 631g yhw14.png|center|150px]]
|[[File:Dioxole homo 631g yhw14.png|center|150px]]
|-
|Corresponding to the orbital
|Corresponding to the orbital
|}

The transition state was first optimised to its minimum, followed by a transition state calculation. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #BD5CFE; color: #ffffff;" |'''Molecule'''
! '''Endo Transition State'''
! '''Exo Transition State'''
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Endo ts lumo+1 yhw14.png|center|150px]]
|[[File:Exo ts lumo+1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Endo ts lumo yhw14.png|center|150px]]
|[[File:Exo ts lumo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Endo ts homo yhw14.png|center|150px]]
|[[File:Exo ts homo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Endo ts homo-1 yhw14.png|center|150px]]
|[[File:Exo ts homo-1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|}

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of cyclohexadiene and 1,3-dioxole.

[[File:Ex2 mo diagram yhw14.png|550px|center|thumb|Diagram 5: MO diagram of Reaction of Cyclohexadiene and 1,3-dioxole]]

=== Normal Demand vs Inverse Demand Diels-Alder Reaction ===

A normal electron demand Diels-Alder reaction can be defined as a reaction between electron rich diene and electron poor dienophile. An inverse electron demand is the reaction between electron poor diene and electron rich dienophile.

The LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are very close in energy, which results in strong bonding interaction between the two to form the HOMO and LUMO of both endo and exo TS. Since only the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole have the correct symmetry () to interact, they interact to form the __(symmetry) HOMO and LUMO of both TS.

This could be explained by the presence of electron rich O on 1,3-dioxole which raises the energy of both its HOMO and LUMO, making the overlap between the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole much better than the HOMO of cyclohexadiene and the LUMO of 1,3-dioxole. Thus, the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are now the frontier orbitals that interact the most, hence this is an inverse demand Diels-Alder reaction.

=== Reaction Energies and Secondary Orbital Interaction ===

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FF4AFF; color: #ffffff" |
! style="background: #FF4AFF; color: #ffffff" | Reactants
! style="background: #FF4AFF; color: #ffffff" | Transition State
! style="background: #FF4AFF; color: #ffffff" | Product
! style="background: #FF4AFF; color: #ffffff" | Activation Energy
! style="background: #FF4AFF; color: #ffffff" | Gibbs Free Energy
|-
|Endo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313622</nowiki>
|<nowiki>-1313849</nowiki>
|160
|<nowiki>-67</nowiki>
|-
|Exo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313614</nowiki>
|<nowiki>-1313846</nowiki>
|168
|<nowiki>-64</nowiki>
|+Table 2: Energies of Reactants, Transition States and Products of both Endo and Exo Pathways in Diels-Alder Reaction of Cyclohexadiene and 1,3-Dioxole (kJ mol-1)
|}

Kinetically favourable product of a reaction is the one that has the lowest activation energy; Thermodynamically favourable product is the product with lowest energy conformer, hence the more stabilised product.

The endo transition state is the kinetic product of this reaction as it has lower activation energy. This could be explained using the secondary orbital interaction between the lone pair orbital on the oxygen atom and the empty π* orbital of diene. This favourable effect stabilises the endo transition state.

As the oxygen atom lone pair is oriented away from the diene π system in the exo transition state, the secondary orbital effect is not present, hence the activation energy of exo reaction is higher.

However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, i.e. increasing temperature, formation of the exo product would be more favourable.

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

Xylylene can react with sulfur dioxide through Diels-Alder reaction via either endo or exo pathways to form a 6-membered ring, or through cheletropic reaction to form a 5-membered ring. The reaction scheme is shown below. Reaction barriers and reaction energies for each pathway are compared to determine the reaction that is most favourable.

[[File:Ex3 reactionscheme yhw14.png|550px|center|thumb|Diagram 6: Reaction Scheme of Xylylene and Sulfur Dioxide]]

=== Intrinsic Reaction Coordinate ===
The following files show the intrinsic reaction coordinates of the three different reaction pathways of xylylene and SO2. Please click to see animation.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Endo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Exo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Cheletropic TS
|-
|[[File:DA endo irc animation purple yhw14.gif|center]]
|[[File:DA exo irc animation purple yhw14.gif|center]]
|[[File: Ex3 Chele movie yhw14.gif|center]]
|-
|[[File:DA endo irc animation yhw14.gif|center]]
|[[File:DA exo irc animation yhw14.gif|center]]
|[[File:Cheletropic irc animation yhw14.gif|center]]
|-
|[[File:DA endo irc plot yhw14.png|center|500px]]
|[[File:DA exo irc plot yhw14.png|center|500px]]
|[[File:Cheletropic irc plot yhw14.png|center|650px]]
|}

=== Reaction Energies and Reaction Barriers ===

[[File:Ex3 reactionprofile yhw14.png|550px|center|thumb|Diagram 7: Reaction Profile of Xylylene and Sulfur Dioxide]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FFD1C3; color: #ffffff" |
! style="background: #FFD1C3; color: #ffffff" | Reactants
! style="background: #FFD1C3; color: #ffffff" | Transition State
! style="background: #FFD1C3; color: #ffffff" | Product
! style="background: #FFD1C3; color: #ffffff" | Activation Energy
! style="background: #FFD1C3; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|237.767824
|56.9576013
|83.391038
|<nowiki>-97.4191847</nowiki>
|-
|Exo
|154.376786
|241.753433
|56.3196048
|87.406647
|<nowiki>-98.0571812</nowiki>
|-
|Cheletropic
|154.376786
|260.08205
|0.013127501
|105.705264
|<nowiki>-154.3636585</nowiki>
|+Table 3: Energies of Reactants, Transition States and Products of Reactions between Xylylene and Sulfur Dioxide (kJ mol-1)
|}

With reference to the reaction profile and table __, the Diels-Alder reaction via the endo pathway has the lowest activation energy, making it a more kinetically favourable product, i.e. the kinetic product; the Diels-Alder exo product has a lower energy than endo, however with a higher activation energy hence it will not form under low temperature condition; the cheletropic product is the most stabilised product out of the three and it has the lowest reaction energy, therefore is the thermodynamic product.

=== Side Reaction between cis-diene in Xylylene 6-membered ring and SO2===

o-Xylylene contains another cis-butadiene fragment located in the 6-membered ring that can undergo a Diels-Alder reaction with SO2. The reaction energies and reaction barriers between endo and exo pathways are compared in the table below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #4EBEBA; color: #ffffff" |
! style="background: #4EBEBA; color: #ffffff" | Reactants
! style="background: #4EBEBA; color: #ffffff" | Transition State
! style="background: #4EBEBA; color: #ffffff" | Product
! style="background: #4EBEBA; color: #ffffff" | Activation Energy
! style="background: #4EBEBA; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|267.984805
|172.272196
|113.608019
|17.89541
|-
|Exo
|154.376786
|275.821924
|176.711916
|121.445138
|22.33513
|+Table 4: Energies of Reactants, Transition States and Products of the Side Reaction in Xylylene 6-membered ring and Sulfur Dioxide (kJ mol-1)
|}

It is clear that both endo and exo Diels-Alder side reactions are kinetically and thermodynamically unfavourable at this site as the activation energies are much higher than the previous reactions mentioned above in table __ and the reaction energies show that the reactions are endothermic.

== Conclusion ==

The transition states of three pericyclic reactions were investigated in this computational lab, using Gaussian to optimise the reactants, transition states and products respectively, and the vibrational frequencies and intrinsic reaction coordinates were computed.

In the reaction between butadiene and ethene, the importance of molecular orbital symmetry in the interaction of molecular orbitals was illustrated, such that a reaction is only allowed when the molecular orbitals with the same symmetry labels interact with each other and forbidden when symmetric molecular orbital interact with asymmetric orbitals. Furthermore, the vibration frequency calculation proved that this [4+2] Diels-Alder reaction proceeds via a concerted mechanism as synchronous bond formation was demonstrated. Bonding interaction can be further confirmed as the bond distance between the two termini carbon atoms in the transition state is shorter than the sum of two Van der Waals radii of carbon.

In the reaction of cyclohexadiene and 1,3-dioxole, both the endo and exo transition states were investigated. In general, the endo transition state is kinetically more favourable as it has lower activation barrier, possibly due to the secondary orbital interaction between the lone pair in p orbital on the oxygen atom and the empty pi* orbital in the diene, which stabilises the transition state. However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, formation of the exo product could be possible.

The final reaction between xylylene and SO2 again proved that the endo Diels-Alder transition state has the lowest activation energy, making it kinetically favourable at low temperature. However, the cheletropic product is the most stabilised and thermodynamically favourable product. Therefore the reaction would yield the cheletropic product under thermodynamic control instead of the exo Diels-Alder product.

==References==
<references>
<ref name="C-C bond lengths">L. Pauling and L. O. Brockway, ''Journal of the American Chemical Society'', '''1937''', Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref>
<ref name="Van der Waals radius of C">S. S. Batsanov, ''Inorganic Materials'', '''2001''', Volume 37, Number 9, pp. 871-885, https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf.</ref>
</references>

Rep:Mod:yhw14cts

2017-02-09T18:51:08Z

Yhw14: /* Introduction */

''' Transition States and Reactivity '''

'' Yi Hang Cherie WONG (yhw14) ''
'' CID: 00933828 ''

== Introduction ==
A potential energy surface is a mathematical function that gives the energy of a molecule as a function of its geometry with the relative positions of the atoms participating in the reaction. The stationary points may be classified according to the first and second derivatives of the energy with respect to position. At the minimum of a reaction profile, the gradient is represented by the first derivative of the reaction coordinate, which is zero, while curvature is represented by the second derivative, is positive in this case; hence energy rises in all directions. Energy minima correspond to physically stable chemical species, which could be reactants and products. The transition state is defined as the maximum in a reaction profile, where the gradient is again, zero, while curvature is negative; hence energy decreases in one direction, which indicates the reaction pathway of the chemical reaction. The potential energy surface can be computed using Gaussview 09, where structure and energy of reactants or products can be modelled to illustrate the transition states, which can rarely be obtained experimentally. The intrinsic reaction coordinate can then be calculated and compared to predict the reaction path at a transition state and follow it to the correct minima.

In this computational lab, all of the reactants and products were optimised to their minima, and the transition states were also optimised. The calculations were done by Gaussian 09, using mainly semi-empirical method PM6 and DFT-B3LYP. Frequency calculations were performed to show molecular vibrations to confirm the position on the potential energy surface. If all the vibrational frequencies are real, this confirms the structure is a minimum, and vice versa, the presence of imaginary frequency may suggest that the structure is at its transition state. Intrinsic reaction coordinate method was carried out using calculated force constants to predict which conformer a reaction path from the transition state would lead to.

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

The reaction between butadiene and ethene is a typical pericyclic [4+2] Diels-Alder reaction that proceeds via a concerted mechanism through a cyclic transition state. The reaction scheme is shown below.

[[File:Ex1 reactionscheme revised yhw14.png|550px|center|thumb|Diagram 1: Reaction Scheme of Butadiene and Ethene]]

=== Molecular Orbital Analysis ===

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of butadiene and ethene.

[[File:Ex1 mo diagram yhw14 revised v3.png|550px|center|thumb|Diagram 2: MO diagram of Reaction of Butadiene and Ethene]]

Butadiene and ethene were optimised to their minima. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #06DCFB; color: #ffffff;" |'''Molecule'''
! '''Butadiene'''
! '''Ethene'''
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Butadiene lumo yhw14.png|center|150px]]
|[[File:Ethene lumo yhw14.png|center|150px]]
|-
|Corresponding to the s orbital (symmetric)
|Corresponding to the a orbital (asymmetric)
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Butadiene homo yhw14.png|center|150px]]
|[[File:Ethene homo yhw14.png|center|150px]]
|-
|Corresponding to the a orbital (antisymmetric)
|Corresponding to the s orbital (symmetric)
|}

The transition state was first optimised to its minimum, followed by a transition state calculation. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #01FCEF; color: #ffffff;" |'''Molecule'''
! '''Transition State'''
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Ts lumo+1 yhw14.png|center|150px]]
|-
|Corresponding to the 5 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Ts lumo 1 yhw14.png|center|150px]]
|-
|Corresponding to the 4 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Ts homo yhw14.png|center|150px]]
|-
|Corresponding to the 3 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Ts homo-1 yhw14.png|center|150px]]
|-
|Corresponding to the 2 orbital
|}

Based on the MO diagram and the computed MOs shown above, a reaction is only allowed when the MOs with the same symmetry labels interact with each other, i.e. symmetric-symmetric and asymmetric-asymmetric interactions; and a reaction is forbidden when the MOs with different symmetry labels interact with each other, i.e. symmetric-asymmetric interactions.
In the reaction between butadiene and ethene, the butadiene asymmetric MO interacts with the ethene asymmetric MO to give the 2 and 5 MOs of the transition state, and the butadiene symmetric MO interacts with the ethene symmetric MO to give the 3 and 4 MOs of the transition state. Therefore, a reaction is allowed when the symmetry labels of the MOs of the reactants are the same; and forbidden when the symmetry labels are different.

The orbital overlap integral is zero in a symmetric-asymmetric interaction and non-zero in symmetric-symmetric and asymmetric-asymmetric interactions.

=== Bond Length Analysis ===

The changes in bond lengths between carbons in reactant, transition state and product as the reaction progresses were studied by comparing the bond lengths between carbons before and after the reaction. The summary of bond lengths is shown below.
[[File:Ex1 bondlength yhw14.png|470px|center|thumb|Diagram 3: Labelled carbons]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #0000FF; color: #ffffff" | State
! style="background: #0000FF; color: #ffffff" | C1-C2
! style="background: #0000FF; color: #ffffff" | C2-C3
! style="background: #0000FF; color: #ffffff" | C3-C4
! style="background: #0000FF; color: #ffffff" | C4-C5
! style="background: #0000FF; color: #ffffff" | C5-C6
! style="background: #0000FF; color: #ffffff" | C6-C1
|-
|Reactants
|1.335
|1.468
|1.335
|/
|1.327
|/
|-
|Transition State
|1.380
|1.411
|1.380
|2.115
|1.382
|2.114
|-
|Product
|1.500
|1.338
|1.500
|1.540
|1.540
|1.540
|+Table 1: Measurements of the C-C bond lengths of the reactants, transition state and products (Å)
|}
As the reaction progresses, the bond lengths between C1-C2, C3-C4 and C5-C6 increase from ~1.3 Å to ~1.5 Å as the bond order decrease to one, whereas bond length of C2-C3 decreases from ~1.5 Å to ~1.3 Å as the bond order increases from one to two.
This could be explained as the increase in bond length suggest a change from sp2-sp2 (C-C double bond) with typical bond length of 1.33 Å <ref name="C-C bond lengths"/> to sp3-sp3 (C-C single bond) with typical bond length of 1.54 Å <ref name="C-C bond lengths"/>, and vice versa for the decrease in bond length. Based on the calculated bond lengths above in Table 1, it is clear that bond lengths and bond orders of the reactants changed during the reaction and the new bonds formed at C4-C5 and C6-C1 are single bonds as they have bond lengths of 1.54 Å.
The typical Van der Waals radius of the C atom is 1.7 Å <ref name="Van der Waals radius of C"/>. As the bond lengths between C4-C5 and C6-C1 of the transition state are shorter than 2 x Van der Waals radii of C, this reflects that C-C bonds are forming at the transition state.

=== Vibration Analysis ===

The imaginary frequency at -948.32 cm-1 corresponds to the reaction path at the transition state, which shows a synchronous bond formation, which agrees with the concerted mechanism of [4+2] cycloaddition, where both reaction centres converge at the same time to form bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|[[File:Ex1 ts imaginary white yhw14.gif|center|500px]]
|-
|[[File:Ex1 ts imaginary yhw14.gif|center|500px]]
|-
|style="text-align: center;"|Reaction Path at the Transition State (Please double click to see animation)
|}

The lowest positive frequency at 145.14 cm-1 is asynchronous as shown below, where one of the C from the ethene moves towards the butadiene reaction centre and the other C moves away. This suggests that bonds are formed one at a time.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|[[File:Ex1 ts positive white yhw14.gif|center|500px]]
|-
|[[File:Ex1 ts positive yhw14.gif|center|500px]]
|-
|style="text-align: center;"|Lowest positive frequency (Please double click to see animation)
|}

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

[[File:Ex2 reactionscheme.png|550px|center|thumb|Diagram 4: Reaction Scheme of Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

Cyclohexadiene and 1,3-dioxole were optimised to their minima. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #9A03FE; color: #ffffff;" |'''Molecule'''
! '''Cyclohexadiene'''
! '''1,3-Dioxole'''
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Cyclo lumo 631g yhw14.png|center|150px]]
|[[File:Dioxole lumo 631g yhw14.png|center|150px]]
|-
|Corresponding to the orbital
|Corresponding to the orbital
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Cyclo homo 631g yhw14.png|center|150px]]
|[[File:Dioxole homo 631g yhw14.png|center|150px]]
|-
|Corresponding to the orbital
|Corresponding to the orbital
|}

The transition state was first optimised to its minimum, followed by a transition state calculation. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #BD5CFE; color: #ffffff;" |'''Molecule'''
! '''Endo Transition State'''
! '''Exo Transition State'''
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Endo ts lumo+1 yhw14.png|center|150px]]
|[[File:Exo ts lumo+1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Endo ts lumo yhw14.png|center|150px]]
|[[File:Exo ts lumo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Endo ts homo yhw14.png|center|150px]]
|[[File:Exo ts homo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Endo ts homo-1 yhw14.png|center|150px]]
|[[File:Exo ts homo-1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|}

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of cyclohexadiene and 1,3-dioxole.

[[File:Ex2 mo diagram yhw14.png|550px|center|thumb|Diagram 5: MO diagram of Reaction of Cyclohexadiene and 1,3-dioxole]]

=== Normal Demand vs Inverse Demand Diels-Alder Reaction ===

A normal electron demand Diels-Alder reaction can be defined as a reaction between electron rich diene and electron poor dienophile. An inverse electron demand is the reaction between electron poor diene and electron rich dienophile.

The LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are very close in energy, which results in strong bonding interaction between the two to form the HOMO and LUMO of both endo and exo TS. Since only the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole have the correct symmetry () to interact, they interact to form the __(symmetry) HOMO and LUMO of both TS.

This could be explained by the presence of electron rich O on 1,3-dioxole which raises the energy of both its HOMO and LUMO, making the overlap between the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole much better than the HOMO of cyclohexadiene and the LUMO of 1,3-dioxole. Thus, the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are now the frontier orbitals that interact the most, hence this is an inverse demand Diels-Alder reaction.

=== Reaction Energies and Secondary Orbital Interaction ===

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FF4AFF; color: #ffffff" |
! style="background: #FF4AFF; color: #ffffff" | Reactants
! style="background: #FF4AFF; color: #ffffff" | Transition State
! style="background: #FF4AFF; color: #ffffff" | Product
! style="background: #FF4AFF; color: #ffffff" | Activation Energy
! style="background: #FF4AFF; color: #ffffff" | Gibbs Free Energy
|-
|Endo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313622</nowiki>
|<nowiki>-1313849</nowiki>
|160
|<nowiki>-67</nowiki>
|-
|Exo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313614</nowiki>
|<nowiki>-1313846</nowiki>
|168
|<nowiki>-64</nowiki>
|+Table 2: Energies of Reactants, Transition States and Products of both Endo and Exo Pathways in Diels-Alder Reaction of Cyclohexadiene and 1,3-Dioxole (kJ mol-1)
|}

Kinetically favourable product of a reaction is the one that has the lowest activation energy; Thermodynamically favourable product is the product with lowest energy conformer, hence the more stabilised product.

The endo transition state is the kinetic product of this reaction as it has lower activation energy. This could be explained using the secondary orbital interaction between the lone pair orbital on the oxygen atom and the empty π* orbital of diene. This favourable effect stabilises the endo transition state.

As the oxygen atom lone pair is oriented away from the diene π system in the exo transition state, the secondary orbital effect is not present, hence the activation energy of exo reaction is higher.

However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, i.e. increasing temperature, formation of the exo product would be more favourable.

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

Xylylene can react with sulfur dioxide through Diels-Alder reaction via either endo or exo pathways to form a 6-membered ring, or through cheletropic reaction to form a 5-membered ring. The reaction scheme is shown below. Reaction barriers and reaction energies for each pathway are compared to determine the reaction that is most favourable.

[[File:Ex3 reactionscheme yhw14.png|550px|center|thumb|Diagram 6: Reaction Scheme of Xylylene and Sulfur Dioxide]]

=== Intrinsic Reaction Coordinate ===
The following files show the intrinsic reaction coordinates of the three different reaction pathways of xylylene and SO2. Please click to see animation.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Endo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Exo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Cheletropic TS
|-
|[[File:DA endo irc animation purple yhw14.gif|center]]
|[[File:DA exo irc animation purple yhw14.gif|center]]
|[[File: Ex3 Chele movie yhw14.gif|center]]
|-
|[[File:DA endo irc animation yhw14.gif|center]]
|[[File:DA exo irc animation yhw14.gif|center]]
|[[File:Cheletropic irc animation yhw14.gif|center]]
|-
|[[File:DA endo irc plot yhw14.png|center|500px]]
|[[File:DA exo irc plot yhw14.png|center|500px]]
|[[File:Cheletropic irc plot yhw14.png|center|650px]]
|}

=== Reaction Energies and Reaction Barriers ===

[[File:Ex3 reactionprofile yhw14.png|550px|center|thumb|Diagram 7: Reaction Profile of Xylylene and Sulfur Dioxide]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FFD1C3; color: #ffffff" |
! style="background: #FFD1C3; color: #ffffff" | Reactants
! style="background: #FFD1C3; color: #ffffff" | Transition State
! style="background: #FFD1C3; color: #ffffff" | Product
! style="background: #FFD1C3; color: #ffffff" | Activation Energy
! style="background: #FFD1C3; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|237.767824
|56.9576013
|83.391038
|<nowiki>-97.4191847</nowiki>
|-
|Exo
|154.376786
|241.753433
|56.3196048
|87.406647
|<nowiki>-98.0571812</nowiki>
|-
|Cheletropic
|154.376786
|260.08205
|0.013127501
|105.705264
|<nowiki>-154.3636585</nowiki>
|+Table 3: Energies of Reactants, Transition States and Products of Reactions between Xylylene and Sulfur Dioxide (kJ mol-1)
|}

With reference to the reaction profile and table __, the Diels-Alder reaction via the endo pathway has the lowest activation energy, making it a more kinetically favourable product, i.e. the kinetic product; the Diels-Alder exo product has a lower energy than endo, however with a higher activation energy hence it will not form under low temperature condition; the cheletropic product is the most stabilised product out of the three and it has the lowest reaction energy, therefore is the thermodynamic product.

=== Side Reaction between cis-diene in Xylylene 6-membered ring and SO2===

o-Xylylene contains another cis-butadiene fragment located in the 6-membered ring that can undergo a Diels-Alder reaction with SO2. The reaction energies and reaction barriers between endo and exo pathways are compared in the table below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #4EBEBA; color: #ffffff" |
! style="background: #4EBEBA; color: #ffffff" | Reactants
! style="background: #4EBEBA; color: #ffffff" | Transition State
! style="background: #4EBEBA; color: #ffffff" | Product
! style="background: #4EBEBA; color: #ffffff" | Activation Energy
! style="background: #4EBEBA; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|267.984805
|172.272196
|113.608019
|17.89541
|-
|Exo
|154.376786
|275.821924
|176.711916
|121.445138
|22.33513
|+Table 4: Energies of Reactants, Transition States and Products of the Side Reaction in Xylylene 6-membered ring and Sulfur Dioxide (kJ mol-1)
|}

It is clear that both endo and exo Diels-Alder side reactions are kinetically and thermodynamically unfavourable at this site as the activation energies are much higher than the previous reactions mentioned above in table __ and the reaction energies show that the reactions are endothermic.

== Conclusion ==

The transition states of three pericyclic reactions were investigated in this computational lab, using Gaussian to optimise the reactants, transition states and products respectively, and the vibrational frequencies and intrinsic reaction coordinates were computed.

In the reaction between butadiene and ethene, the importance of molecular orbital symmetry in the interaction of molecular orbitals was illustrated, such that a reaction is only allowed when the molecular orbitals with the same symmetry labels interact with each other and forbidden when symmetric molecular orbital interact with asymmetric orbitals. Furthermore, the vibration frequency calculation proved that this [4+2] Diels-Alder reaction proceeds via a concerted mechanism as synchronous bond formation was demonstrated. Bonding interaction can be further confirmed as the bond distance between the two termini carbon atoms in the transition state is shorter than the sum of two Van der Waals radii of carbon.

In the reaction of cyclohexadiene and 1,3-dioxole, both the endo and exo transition states were investigated. In general, the endo transition state is kinetically more favourable as it has lower activation barrier, possibly due to the secondary orbital interaction between the lone pair in p orbital on the oxygen atom and the empty pi* orbital in the diene, which stabilises the transition state. However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, formation of the exo product could be possible.

The final reaction between xylylene and SO2 again proved that the endo Diels-Alder transition state has the lowest activation energy, making it kinetically favourable at low temperature. However, the cheletropic product is the most stabilised and thermodynamically favourable product. Therefore the reaction would yield the cheletropic product under thermodynamic control instead of the exo Diels-Alder product.

==References==
<references>
<ref name="C-C bond lengths">L. Pauling and L. O. Brockway, ''Journal of the American Chemical Society'', '''1937''', Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref>
<ref name="Van der Waals radius of C">S. S. Batsanov, ''Inorganic Materials'', '''2001''', Volume 37, Number 9, pp. 871-885, https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf.</ref>
</references>

Rep:Mod:yhw14cts

2017-02-09T18:24:10Z

Yhw14: /* Molecular Orbital Analysis */

''' Transition States and Reactivity '''

'' Yi Hang Cherie WONG (yhw14) ''
'' CID: 00933828 ''

== Introduction ==
A potential energy surface is a mathematical function that gives the energy of a molecule as a function of its geometry with the relative positions of the atoms participating in the reaction. The stationary points may be classified according to the first and second derivatives of the energy with respect to position. At the minimum of a reaction profile, the first derivative of the reaction coordinate, which indicates the gradient, is zero, while the second derivative, which indicates curvature, is positive; hence energy rises in all directions. Energy minima correspond to physically stable chemical species, which could be reactants and products. The transition state is defined as the maximum in a reaction profile, where the gradient is again, zero, while curvature is negative, hence energy decreases in one direction, which indicates the reaction pathway of the chemical reaction. The potential energy surface can be computed using Gaussview 09, where structure and energy of reactants or products can be modelled to illustrate the transition states, which can rarely be obtained experimentally. The intrinsic reaction coordinate can then be calculated and compared to predict the reaction path at a transition state and follow it to the correct minima.

In this computational lab, all of the reactants and products were optimised to their minima, and the transition states were also optimised. The calculations were done by Gaussian 09, using mainly semi-empirical method PM6 and DFT-B3LYP. Frequency calculations were performed to show molecular vibrations to confirm the position on the potential energy surface. If all the vibrational frequencies are real, this confirms the structure is a minimum, and vice versa, the presence of imaginary frequency may suggest that the structure is at its transition state. Intrinsic reaction coordinate method was carried out using calculated force constants to predict which conformer a reaction path from the transition state would lead to.

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

The reaction between butadiene and ethene is a typical pericyclic [4+2] Diels-Alder reaction that proceeds via a concerted mechanism through a cyclic transition state. The reaction scheme is shown below.

[[File:Ex1 reactionscheme revised yhw14.png|550px|center|thumb|Diagram 1: Reaction Scheme of Butadiene and Ethene]]

=== Molecular Orbital Analysis ===

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of butadiene and ethene.

[[File:Ex1 mo diagram yhw14 revised v3.png|550px|center|thumb|Diagram 2: MO diagram of Reaction of Butadiene and Ethene]]

Butadiene and ethene were optimised to their minima. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #06DCFB; color: #ffffff;" |'''Molecule'''
! '''Butadiene'''
! '''Ethene'''
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Butadiene lumo yhw14.png|center|150px]]
|[[File:Ethene lumo yhw14.png|center|150px]]
|-
|Corresponding to the s orbital (symmetric)
|Corresponding to the a orbital (asymmetric)
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Butadiene homo yhw14.png|center|150px]]
|[[File:Ethene homo yhw14.png|center|150px]]
|-
|Corresponding to the a orbital (antisymmetric)
|Corresponding to the s orbital (symmetric)
|}

The transition state was first optimised to its minimum, followed by a transition state calculation. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #01FCEF; color: #ffffff;" |'''Molecule'''
! '''Transition State'''
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Ts lumo+1 yhw14.png|center|150px]]
|-
|Corresponding to the 5 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Ts lumo 1 yhw14.png|center|150px]]
|-
|Corresponding to the 4 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Ts homo yhw14.png|center|150px]]
|-
|Corresponding to the 3 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Ts homo-1 yhw14.png|center|150px]]
|-
|Corresponding to the 2 orbital
|}

Based on the MO diagram and the computed MOs shown above, a reaction is only allowed when the MOs with the same symmetry labels interact with each other, i.e. symmetric-symmetric and asymmetric-asymmetric interactions; and a reaction is forbidden when the MOs with different symmetry labels interact with each other, i.e. symmetric-asymmetric interactions.
In the reaction between butadiene and ethene, the butadiene asymmetric MO interacts with the ethene asymmetric MO to give the 2 and 5 MOs of the transition state, and the butadiene symmetric MO interacts with the ethene symmetric MO to give the 3 and 4 MOs of the transition state. Therefore, a reaction is allowed when the symmetry labels of the MOs of the reactants are the same; and forbidden when the symmetry labels are different.

The orbital overlap integral is zero in a symmetric-asymmetric interaction and non-zero in symmetric-symmetric and asymmetric-asymmetric interactions.

=== Bond Length Analysis ===

The changes in bond lengths between carbons in reactant, transition state and product as the reaction progresses were studied by comparing the bond lengths between carbons before and after the reaction. The summary of bond lengths is shown below.
[[File:Ex1 bondlength yhw14.png|470px|center|thumb|Diagram 3: Labelled carbons]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #0000FF; color: #ffffff" | State
! style="background: #0000FF; color: #ffffff" | C1-C2
! style="background: #0000FF; color: #ffffff" | C2-C3
! style="background: #0000FF; color: #ffffff" | C3-C4
! style="background: #0000FF; color: #ffffff" | C4-C5
! style="background: #0000FF; color: #ffffff" | C5-C6
! style="background: #0000FF; color: #ffffff" | C6-C1
|-
|Reactants
|1.335
|1.468
|1.335
|/
|1.327
|/
|-
|Transition State
|1.380
|1.411
|1.380
|2.115
|1.382
|2.114
|-
|Product
|1.500
|1.338
|1.500
|1.540
|1.540
|1.540
|+Table 1: Measurements of the C-C bond lengths of the reactants, transition state and products (Å)
|}
As the reaction progresses, the bond lengths between C1-C2, C3-C4 and C5-C6 increase from ~1.3 Å to ~1.5 Å as the bond order decrease to one, whereas bond length of C2-C3 decreases from ~1.5 Å to ~1.3 Å as the bond order increases from one to two.
This could be explained as the increase in bond length suggest a change from sp2-sp2 (C-C double bond) with typical bond length of 1.33 Å <ref name="C-C bond lengths"/> to sp3-sp3 (C-C single bond) with typical bond length of 1.54 Å <ref name="C-C bond lengths"/>, and vice versa for the decrease in bond length. Based on the calculated bond lengths above in Table 1, it is clear that bond lengths and bond orders of the reactants changed during the reaction and the new bonds formed at C4-C5 and C6-C1 are single bonds as they have bond lengths of 1.54 Å.
The typical Van der Waals radius of the C atom is 1.7 Å <ref name="Van der Waals radius of C"/>. As the bond lengths between C4-C5 and C6-C1 of the transition state are shorter than 2 x Van der Waals radii of C, this reflects that C-C bonds are forming at the transition state.

=== Vibration Analysis ===

The imaginary frequency at -948.32 cm-1 corresponds to the reaction path at the transition state, which shows a synchronous bond formation, which agrees with the concerted mechanism of [4+2] cycloaddition, where both reaction centres converge at the same time to form bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|[[File:Ex1 ts imaginary white yhw14.gif|center|500px]]
|-
|[[File:Ex1 ts imaginary yhw14.gif|center|500px]]
|-
|style="text-align: center;"|Reaction Path at the Transition State (Please double click to see animation)
|}

The lowest positive frequency at 145.14 cm-1 is asynchronous as shown below, where one of the C from the ethene moves towards the butadiene reaction centre and the other C moves away. This suggests that bonds are formed one at a time.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|[[File:Ex1 ts positive white yhw14.gif|center|500px]]
|-
|[[File:Ex1 ts positive yhw14.gif|center|500px]]
|-
|style="text-align: center;"|Lowest positive frequency (Please double click to see animation)
|}

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

[[File:Ex2 reactionscheme.png|550px|center|thumb|Diagram 4: Reaction Scheme of Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

Cyclohexadiene and 1,3-dioxole were optimised to their minima. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #9A03FE; color: #ffffff;" |'''Molecule'''
! '''Cyclohexadiene'''
! '''1,3-Dioxole'''
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Cyclo lumo 631g yhw14.png|center|150px]]
|[[File:Dioxole lumo 631g yhw14.png|center|150px]]
|-
|Corresponding to the orbital
|Corresponding to the orbital
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Cyclo homo 631g yhw14.png|center|150px]]
|[[File:Dioxole homo 631g yhw14.png|center|150px]]
|-
|Corresponding to the orbital
|Corresponding to the orbital
|}

The transition state was first optimised to its minimum, followed by a transition state calculation. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #BD5CFE; color: #ffffff;" |'''Molecule'''
! '''Endo Transition State'''
! '''Exo Transition State'''
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Endo ts lumo+1 yhw14.png|center|150px]]
|[[File:Exo ts lumo+1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Endo ts lumo yhw14.png|center|150px]]
|[[File:Exo ts lumo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Endo ts homo yhw14.png|center|150px]]
|[[File:Exo ts homo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Endo ts homo-1 yhw14.png|center|150px]]
|[[File:Exo ts homo-1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|}

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of cyclohexadiene and 1,3-dioxole.

[[File:Ex2 mo diagram yhw14.png|550px|center|thumb|Diagram 5: MO diagram of Reaction of Cyclohexadiene and 1,3-dioxole]]

=== Normal Demand vs Inverse Demand Diels-Alder Reaction ===

A normal electron demand Diels-Alder reaction can be defined as a reaction between electron rich diene and electron poor dienophile. An inverse electron demand is the reaction between electron poor diene and electron rich dienophile.

The LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are very close in energy, which results in strong bonding interaction between the two to form the HOMO and LUMO of both endo and exo TS. Since only the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole have the correct symmetry () to interact, they interact to form the __(symmetry) HOMO and LUMO of both TS.

This could be explained by the presence of electron rich O on 1,3-dioxole which raises the energy of both its HOMO and LUMO, making the overlap between the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole much better than the HOMO of cyclohexadiene and the LUMO of 1,3-dioxole. Thus, the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are now the frontier orbitals that interact the most, hence this is an inverse demand Diels-Alder reaction.

=== Reaction Energies and Secondary Orbital Interaction ===

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FF4AFF; color: #ffffff" |
! style="background: #FF4AFF; color: #ffffff" | Reactants
! style="background: #FF4AFF; color: #ffffff" | Transition State
! style="background: #FF4AFF; color: #ffffff" | Product
! style="background: #FF4AFF; color: #ffffff" | Activation Energy
! style="background: #FF4AFF; color: #ffffff" | Gibbs Free Energy
|-
|Endo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313622</nowiki>
|<nowiki>-1313849</nowiki>
|160
|<nowiki>-67</nowiki>
|-
|Exo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313614</nowiki>
|<nowiki>-1313846</nowiki>
|168
|<nowiki>-64</nowiki>
|+Table 2: Energies of Reactants, Transition States and Products of both Endo and Exo Pathways in Diels-Alder Reaction of Cyclohexadiene and 1,3-Dioxole (kJ mol-1)
|}

Kinetically favourable product of a reaction is the one that has the lowest activation energy; Thermodynamically favourable product is the product with lowest energy conformer, hence the more stabilised product.

The endo transition state is the kinetic product of this reaction as it has lower activation energy. This could be explained using the secondary orbital interaction between the lone pair orbital on the oxygen atom and the empty π* orbital of diene. This favourable effect stabilises the endo transition state.

As the oxygen atom lone pair is oriented away from the diene π system in the exo transition state, the secondary orbital effect is not present, hence the activation energy of exo reaction is higher.

However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, i.e. increasing temperature, formation of the exo product would be more favourable.

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

Xylylene can react with sulfur dioxide through Diels-Alder reaction via either endo or exo pathways to form a 6-membered ring, or through cheletropic reaction to form a 5-membered ring. The reaction scheme is shown below. Reaction barriers and reaction energies for each pathway are compared to determine the reaction that is most favourable.

[[File:Ex3 reactionscheme yhw14.png|550px|center|thumb|Diagram 6: Reaction Scheme of Xylylene and Sulfur Dioxide]]

=== Intrinsic Reaction Coordinate ===
The following files show the intrinsic reaction coordinates of the three different reaction pathways of xylylene and SO2. Please click to see animation.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Endo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Exo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Cheletropic TS
|-
|[[File:DA endo irc animation purple yhw14.gif|center]]
|[[File:DA exo irc animation purple yhw14.gif|center]]
|[[File: Ex3 Chele movie yhw14.gif|center]]
|-
|[[File:DA endo irc animation yhw14.gif|center]]
|[[File:DA exo irc animation yhw14.gif|center]]
|[[File:Cheletropic irc animation yhw14.gif|center]]
|-
|[[File:DA endo irc plot yhw14.png|center|500px]]
|[[File:DA exo irc plot yhw14.png|center|500px]]
|[[File:Cheletropic irc plot yhw14.png|center|650px]]
|}

=== Reaction Energies and Reaction Barriers ===

[[File:Ex3 reactionprofile yhw14.png|550px|center|thumb|Diagram 7: Reaction Profile of Xylylene and Sulfur Dioxide]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FFD1C3; color: #ffffff" |
! style="background: #FFD1C3; color: #ffffff" | Reactants
! style="background: #FFD1C3; color: #ffffff" | Transition State
! style="background: #FFD1C3; color: #ffffff" | Product
! style="background: #FFD1C3; color: #ffffff" | Activation Energy
! style="background: #FFD1C3; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|237.767824
|56.9576013
|83.391038
|<nowiki>-97.4191847</nowiki>
|-
|Exo
|154.376786
|241.753433
|56.3196048
|87.406647
|<nowiki>-98.0571812</nowiki>
|-
|Cheletropic
|154.376786
|260.08205
|0.013127501
|105.705264
|<nowiki>-154.3636585</nowiki>
|+Table 3: Energies of Reactants, Transition States and Products of Reactions between Xylylene and Sulfur Dioxide (kJ mol-1)
|}

With reference to the reaction profile and table __, the Diels-Alder reaction via the endo pathway has the lowest activation energy, making it a more kinetically favourable product, i.e. the kinetic product; the Diels-Alder exo product has a lower energy than endo, however with a higher activation energy hence it will not form under low temperature condition; the cheletropic product is the most stabilised product out of the three and it has the lowest reaction energy, therefore is the thermodynamic product.

=== Side Reaction between cis-diene in Xylylene 6-membered ring and SO2===

o-Xylylene contains another cis-butadiene fragment located in the 6-membered ring that can undergo a Diels-Alder reaction with SO2. The reaction energies and reaction barriers between endo and exo pathways are compared in the table below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #4EBEBA; color: #ffffff" |
! style="background: #4EBEBA; color: #ffffff" | Reactants
! style="background: #4EBEBA; color: #ffffff" | Transition State
! style="background: #4EBEBA; color: #ffffff" | Product
! style="background: #4EBEBA; color: #ffffff" | Activation Energy
! style="background: #4EBEBA; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|267.984805
|172.272196
|113.608019
|17.89541
|-
|Exo
|154.376786
|275.821924
|176.711916
|121.445138
|22.33513
|+Table 4: Energies of Reactants, Transition States and Products of the Side Reaction in Xylylene 6-membered ring and Sulfur Dioxide (kJ mol-1)
|}

It is clear that both endo and exo Diels-Alder side reactions are kinetically and thermodynamically unfavourable at this site as the activation energies are much higher than the previous reactions mentioned above in table __ and the reaction energies show that the reactions are endothermic.

== Conclusion ==

The transition states of three pericyclic reactions were investigated in this computational lab, using Gaussian to optimise the reactants, transition states and products respectively, and the vibrational frequencies and intrinsic reaction coordinates were computed.

In the reaction between butadiene and ethene, the importance of molecular orbital symmetry in the interaction of molecular orbitals was illustrated, such that a reaction is only allowed when the molecular orbitals with the same symmetry labels interact with each other and forbidden when symmetric molecular orbital interact with asymmetric orbitals. Furthermore, the vibration frequency calculation proved that this [4+2] Diels-Alder reaction proceeds via a concerted mechanism as synchronous bond formation was demonstrated. Bonding interaction can be further confirmed as the bond distance between the two termini carbon atoms in the transition state is shorter than the sum of two Van der Waals radii of carbon.

In the reaction of cyclohexadiene and 1,3-dioxole, both the endo and exo transition states were investigated. In general, the endo transition state is kinetically more favourable as it has lower activation barrier, possibly due to the secondary orbital interaction between the lone pair in p orbital on the oxygen atom and the empty pi* orbital in the diene, which stabilises the transition state. However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, formation of the exo product could be possible.

The final reaction between xylylene and SO2 again proved that the endo Diels-Alder transition state has the lowest activation energy, making it kinetically favourable at low temperature. However, the cheletropic product is the most stabilised and thermodynamically favourable product. Therefore the reaction would yield the cheletropic product under thermodynamic control instead of the exo Diels-Alder product.

==References==
<references>
<ref name="C-C bond lengths">L. Pauling and L. O. Brockway, ''Journal of the American Chemical Society'', '''1937''', Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref>
<ref name="Van der Waals radius of C">S. S. Batsanov, ''Inorganic Materials'', '''2001''', Volume 37, Number 9, pp. 871-885, https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf.</ref>
</references>

File:Ex2 mo diagram yhw14.png

2017-02-09T18:23:26Z

Yhw14:

Rep:Mod:yhw14cts

2017-02-09T18:09:12Z

Yhw14: /* Vibration Analysis */

''' Transition States and Reactivity '''

'' Yi Hang Cherie WONG (yhw14) ''
'' CID: 00933828 ''

== Introduction ==
A potential energy surface is a mathematical function that gives the energy of a molecule as a function of its geometry with the relative positions of the atoms participating in the reaction. The stationary points may be classified according to the first and second derivatives of the energy with respect to position. At the minimum of a reaction profile, the first derivative of the reaction coordinate, which indicates the gradient, is zero, while the second derivative, which indicates curvature, is positive; hence energy rises in all directions. Energy minima correspond to physically stable chemical species, which could be reactants and products. The transition state is defined as the maximum in a reaction profile, where the gradient is again, zero, while curvature is negative, hence energy decreases in one direction, which indicates the reaction pathway of the chemical reaction. The potential energy surface can be computed using Gaussview 09, where structure and energy of reactants or products can be modelled to illustrate the transition states, which can rarely be obtained experimentally. The intrinsic reaction coordinate can then be calculated and compared to predict the reaction path at a transition state and follow it to the correct minima.

In this computational lab, all of the reactants and products were optimised to their minima, and the transition states were also optimised. The calculations were done by Gaussian 09, using mainly semi-empirical method PM6 and DFT-B3LYP. Frequency calculations were performed to show molecular vibrations to confirm the position on the potential energy surface. If all the vibrational frequencies are real, this confirms the structure is a minimum, and vice versa, the presence of imaginary frequency may suggest that the structure is at its transition state. Intrinsic reaction coordinate method was carried out using calculated force constants to predict which conformer a reaction path from the transition state would lead to.

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

The reaction between butadiene and ethene is a typical pericyclic [4+2] Diels-Alder reaction that proceeds via a concerted mechanism through a cyclic transition state. The reaction scheme is shown below.

[[File:Ex1 reactionscheme revised yhw14.png|550px|center|thumb|Diagram 1: Reaction Scheme of Butadiene and Ethene]]

=== Molecular Orbital Analysis ===

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of butadiene and ethene.

[[File:Ex1 mo diagram yhw14 revised v3.png|550px|center|thumb|Diagram 2: MO diagram of Reaction of Butadiene and Ethene]]

Butadiene and ethene were optimised to their minima. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #06DCFB; color: #ffffff;" |'''Molecule'''
! '''Butadiene'''
! '''Ethene'''
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Butadiene lumo yhw14.png|center|150px]]
|[[File:Ethene lumo yhw14.png|center|150px]]
|-
|Corresponding to the s orbital (symmetric)
|Corresponding to the a orbital (asymmetric)
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Butadiene homo yhw14.png|center|150px]]
|[[File:Ethene homo yhw14.png|center|150px]]
|-
|Corresponding to the a orbital (antisymmetric)
|Corresponding to the s orbital (symmetric)
|}

The transition state was first optimised to its minimum, followed by a transition state calculation. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #01FCEF; color: #ffffff;" |'''Molecule'''
! '''Transition State'''
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Ts lumo+1 yhw14.png|center|150px]]
|-
|Corresponding to the 5 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Ts lumo 1 yhw14.png|center|150px]]
|-
|Corresponding to the 4 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Ts homo yhw14.png|center|150px]]
|-
|Corresponding to the 3 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Ts homo-1 yhw14.png|center|150px]]
|-
|Corresponding to the 2 orbital
|}

Based on the MO diagram and the computed MOs shown above, a reaction is only allowed when the MOs with the same symmetry labels interact with each other, i.e. symmetric-symmetric and asymmetric-asymmetric interactions; and a reaction is forbidden when the MOs with different symmetry labels interact with each other, i.e. symmetric-asymmetric interactions.
In the reaction between butadiene and ethene, the butadiene asymmetric MO interacts with the ethene asymmetric MO to give the 2 and 5 MOs of the transition state, and the butadiene symmetric MO interacts with the ethene symmetric MO to give the 3 and 4 MOs of the transition state. Therefore, a reaction is allowed when the symmetry labels of the MOs of the reactants are the same; and forbidden when the symmetry labels are different.

The orbital overlap integral is zero in a symmetric-asymmetric interaction and non-zero in symmetric-symmetric and asymmetric-asymmetric interactions.

=== Bond Length Analysis ===

The changes in bond lengths between carbons in reactant, transition state and product as the reaction progresses were studied by comparing the bond lengths between carbons before and after the reaction. The summary of bond lengths is shown below.
[[File:Ex1 bondlength yhw14.png|470px|center|thumb|Diagram 3: Labelled carbons]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #0000FF; color: #ffffff" | State
! style="background: #0000FF; color: #ffffff" | C1-C2
! style="background: #0000FF; color: #ffffff" | C2-C3
! style="background: #0000FF; color: #ffffff" | C3-C4
! style="background: #0000FF; color: #ffffff" | C4-C5
! style="background: #0000FF; color: #ffffff" | C5-C6
! style="background: #0000FF; color: #ffffff" | C6-C1
|-
|Reactants
|1.335
|1.468
|1.335
|/
|1.327
|/
|-
|Transition State
|1.380
|1.411
|1.380
|2.115
|1.382
|2.114
|-
|Product
|1.500
|1.338
|1.500
|1.540
|1.540
|1.540
|+Table 1: Measurements of the C-C bond lengths of the reactants, transition state and products (Å)
|}
As the reaction progresses, the bond lengths between C1-C2, C3-C4 and C5-C6 increase from ~1.3 Å to ~1.5 Å as the bond order decrease to one, whereas bond length of C2-C3 decreases from ~1.5 Å to ~1.3 Å as the bond order increases from one to two.
This could be explained as the increase in bond length suggest a change from sp2-sp2 (C-C double bond) with typical bond length of 1.33 Å <ref name="C-C bond lengths"/> to sp3-sp3 (C-C single bond) with typical bond length of 1.54 Å <ref name="C-C bond lengths"/>, and vice versa for the decrease in bond length. Based on the calculated bond lengths above in Table 1, it is clear that bond lengths and bond orders of the reactants changed during the reaction and the new bonds formed at C4-C5 and C6-C1 are single bonds as they have bond lengths of 1.54 Å.
The typical Van der Waals radius of the C atom is 1.7 Å <ref name="Van der Waals radius of C"/>. As the bond lengths between C4-C5 and C6-C1 of the transition state are shorter than 2 x Van der Waals radii of C, this reflects that C-C bonds are forming at the transition state.

=== Vibration Analysis ===

The imaginary frequency at -948.32 cm-1 corresponds to the reaction path at the transition state, which shows a synchronous bond formation, which agrees with the concerted mechanism of [4+2] cycloaddition, where both reaction centres converge at the same time to form bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|[[File:Ex1 ts imaginary white yhw14.gif|center|500px]]
|-
|[[File:Ex1 ts imaginary yhw14.gif|center|500px]]
|-
|style="text-align: center;"|Reaction Path at the Transition State (Please double click to see animation)
|}

The lowest positive frequency at 145.14 cm-1 is asynchronous as shown below, where one of the C from the ethene moves towards the butadiene reaction centre and the other C moves away. This suggests that bonds are formed one at a time.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|[[File:Ex1 ts positive white yhw14.gif|center|500px]]
|-
|[[File:Ex1 ts positive yhw14.gif|center|500px]]
|-
|style="text-align: center;"|Lowest positive frequency (Please double click to see animation)
|}

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

[[File:Ex2 reactionscheme.png|550px|center|thumb|Diagram 4: Reaction Scheme of Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

Cyclohexadiene and 1,3-dioxole were optimised to their minima. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #9A03FE; color: #ffffff;" |'''Molecule'''
! '''Cyclohexadiene'''
! '''1,3-Dioxole'''
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Cyclo lumo 631g yhw14.png|center|150px]]
|[[File:Dioxole lumo 631g yhw14.png|center|150px]]
|-
|Corresponding to the orbital
|Corresponding to the orbital
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Cyclo homo 631g yhw14.png|center|150px]]
|[[File:Dioxole homo 631g yhw14.png|center|150px]]
|-
|Corresponding to the orbital
|Corresponding to the orbital
|}

The transition state was first optimised to its minimum, followed by a transition state calculation. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #BD5CFE; color: #ffffff;" |'''Molecule'''
! '''Endo Transition State'''
! '''Exo Transition State'''
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Endo ts lumo+1 yhw14.png|center|150px]]
|[[File:Exo ts lumo+1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Endo ts lumo yhw14.png|center|150px]]
|[[File:Exo ts lumo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Endo ts homo yhw14.png|center|150px]]
|[[File:Exo ts homo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Endo ts homo-1 yhw14.png|center|150px]]
|[[File:Exo ts homo-1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|}

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of cyclohexadiene and 1,3-dioxole.

[[File:|550px|center|thumb|Diagram 5: MO diagram of Reaction of Cyclohexadiene and 1,3-dioxole]]

=== Normal Demand vs Inverse Demand Diels-Alder Reaction ===

A normal electron demand Diels-Alder reaction can be defined as a reaction between electron rich diene and electron poor dienophile. An inverse electron demand is the reaction between electron poor diene and electron rich dienophile.

The LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are very close in energy, which results in strong bonding interaction between the two to form the HOMO and LUMO of both endo and exo TS. Since only the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole have the correct symmetry () to interact, they interact to form the __(symmetry) HOMO and LUMO of both TS.

This could be explained by the presence of electron rich O on 1,3-dioxole which raises the energy of both its HOMO and LUMO, making the overlap between the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole much better than the HOMO of cyclohexadiene and the LUMO of 1,3-dioxole. Thus, the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are now the frontier orbitals that interact the most, hence this is an inverse demand Diels-Alder reaction.

=== Reaction Energies and Secondary Orbital Interaction ===

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FF4AFF; color: #ffffff" |
! style="background: #FF4AFF; color: #ffffff" | Reactants
! style="background: #FF4AFF; color: #ffffff" | Transition State
! style="background: #FF4AFF; color: #ffffff" | Product
! style="background: #FF4AFF; color: #ffffff" | Activation Energy
! style="background: #FF4AFF; color: #ffffff" | Gibbs Free Energy
|-
|Endo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313622</nowiki>
|<nowiki>-1313849</nowiki>
|160
|<nowiki>-67</nowiki>
|-
|Exo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313614</nowiki>
|<nowiki>-1313846</nowiki>
|168
|<nowiki>-64</nowiki>
|+Table 2: Energies of Reactants, Transition States and Products of both Endo and Exo Pathways in Diels-Alder Reaction of Cyclohexadiene and 1,3-Dioxole (kJ mol-1)
|}

Kinetically favourable product of a reaction is the one that has the lowest activation energy; Thermodynamically favourable product is the product with lowest energy conformer, hence the more stabilised product.

The endo transition state is the kinetic product of this reaction as it has lower activation energy. This could be explained using the secondary orbital interaction between the lone pair orbital on the oxygen atom and the empty π* orbital of diene. This favourable effect stabilises the endo transition state.

As the oxygen atom lone pair is oriented away from the diene π system in the exo transition state, the secondary orbital effect is not present, hence the activation energy of exo reaction is higher.

However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, i.e. increasing temperature, formation of the exo product would be more favourable.

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

Xylylene can react with sulfur dioxide through Diels-Alder reaction via either endo or exo pathways to form a 6-membered ring, or through cheletropic reaction to form a 5-membered ring. The reaction scheme is shown below. Reaction barriers and reaction energies for each pathway are compared to determine the reaction that is most favourable.

[[File:Ex3 reactionscheme yhw14.png|550px|center|thumb|Diagram 6: Reaction Scheme of Xylylene and Sulfur Dioxide]]

=== Intrinsic Reaction Coordinate ===
The following files show the intrinsic reaction coordinates of the three different reaction pathways of xylylene and SO2. Please click to see animation.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Endo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Exo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Cheletropic TS
|-
|[[File:DA endo irc animation purple yhw14.gif|center]]
|[[File:DA exo irc animation purple yhw14.gif|center]]
|[[File: Ex3 Chele movie yhw14.gif|center]]
|-
|[[File:DA endo irc animation yhw14.gif|center]]
|[[File:DA exo irc animation yhw14.gif|center]]
|[[File:Cheletropic irc animation yhw14.gif|center]]
|-
|[[File:DA endo irc plot yhw14.png|center|500px]]
|[[File:DA exo irc plot yhw14.png|center|500px]]
|[[File:Cheletropic irc plot yhw14.png|center|650px]]
|}

=== Reaction Energies and Reaction Barriers ===

[[File:Ex3 reactionprofile yhw14.png|550px|center|thumb|Diagram 7: Reaction Profile of Xylylene and Sulfur Dioxide]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FFD1C3; color: #ffffff" |
! style="background: #FFD1C3; color: #ffffff" | Reactants
! style="background: #FFD1C3; color: #ffffff" | Transition State
! style="background: #FFD1C3; color: #ffffff" | Product
! style="background: #FFD1C3; color: #ffffff" | Activation Energy
! style="background: #FFD1C3; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|237.767824
|56.9576013
|83.391038
|<nowiki>-97.4191847</nowiki>
|-
|Exo
|154.376786
|241.753433
|56.3196048
|87.406647
|<nowiki>-98.0571812</nowiki>
|-
|Cheletropic
|154.376786
|260.08205
|0.013127501
|105.705264
|<nowiki>-154.3636585</nowiki>
|+Table 3: Energies of Reactants, Transition States and Products of Reactions between Xylylene and Sulfur Dioxide (kJ mol-1)
|}

With reference to the reaction profile and table __, the Diels-Alder reaction via the endo pathway has the lowest activation energy, making it a more kinetically favourable product, i.e. the kinetic product; the Diels-Alder exo product has a lower energy than endo, however with a higher activation energy hence it will not form under low temperature condition; the cheletropic product is the most stabilised product out of the three and it has the lowest reaction energy, therefore is the thermodynamic product.

=== Side Reaction between cis-diene in Xylylene 6-membered ring and SO2===

o-Xylylene contains another cis-butadiene fragment located in the 6-membered ring that can undergo a Diels-Alder reaction with SO2. The reaction energies and reaction barriers between endo and exo pathways are compared in the table below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #4EBEBA; color: #ffffff" |
! style="background: #4EBEBA; color: #ffffff" | Reactants
! style="background: #4EBEBA; color: #ffffff" | Transition State
! style="background: #4EBEBA; color: #ffffff" | Product
! style="background: #4EBEBA; color: #ffffff" | Activation Energy
! style="background: #4EBEBA; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|267.984805
|172.272196
|113.608019
|17.89541
|-
|Exo
|154.376786
|275.821924
|176.711916
|121.445138
|22.33513
|+Table 4: Energies of Reactants, Transition States and Products of the Side Reaction in Xylylene 6-membered ring and Sulfur Dioxide (kJ mol-1)
|}

It is clear that both endo and exo Diels-Alder side reactions are kinetically and thermodynamically unfavourable at this site as the activation energies are much higher than the previous reactions mentioned above in table __ and the reaction energies show that the reactions are endothermic.

== Conclusion ==

The transition states of three pericyclic reactions were investigated in this computational lab, using Gaussian to optimise the reactants, transition states and products respectively, and the vibrational frequencies and intrinsic reaction coordinates were computed.

In the reaction between butadiene and ethene, the importance of molecular orbital symmetry in the interaction of molecular orbitals was illustrated, such that a reaction is only allowed when the molecular orbitals with the same symmetry labels interact with each other and forbidden when symmetric molecular orbital interact with asymmetric orbitals. Furthermore, the vibration frequency calculation proved that this [4+2] Diels-Alder reaction proceeds via a concerted mechanism as synchronous bond formation was demonstrated. Bonding interaction can be further confirmed as the bond distance between the two termini carbon atoms in the transition state is shorter than the sum of two Van der Waals radii of carbon.

In the reaction of cyclohexadiene and 1,3-dioxole, both the endo and exo transition states were investigated. In general, the endo transition state is kinetically more favourable as it has lower activation barrier, possibly due to the secondary orbital interaction between the lone pair in p orbital on the oxygen atom and the empty pi* orbital in the diene, which stabilises the transition state. However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, formation of the exo product could be possible.

The final reaction between xylylene and SO2 again proved that the endo Diels-Alder transition state has the lowest activation energy, making it kinetically favourable at low temperature. However, the cheletropic product is the most stabilised and thermodynamically favourable product. Therefore the reaction would yield the cheletropic product under thermodynamic control instead of the exo Diels-Alder product.

==References==
<references>
<ref name="C-C bond lengths">L. Pauling and L. O. Brockway, ''Journal of the American Chemical Society'', '''1937''', Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref>
<ref name="Van der Waals radius of C">S. S. Batsanov, ''Inorganic Materials'', '''2001''', Volume 37, Number 9, pp. 871-885, https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf.</ref>
</references>

Rep:Mod:yhw14cts

2017-02-09T18:08:20Z

Yhw14: /* Intrinsic Reaction Coordinate */

''' Transition States and Reactivity '''

'' Yi Hang Cherie WONG (yhw14) ''
'' CID: 00933828 ''

== Introduction ==
A potential energy surface is a mathematical function that gives the energy of a molecule as a function of its geometry with the relative positions of the atoms participating in the reaction. The stationary points may be classified according to the first and second derivatives of the energy with respect to position. At the minimum of a reaction profile, the first derivative of the reaction coordinate, which indicates the gradient, is zero, while the second derivative, which indicates curvature, is positive; hence energy rises in all directions. Energy minima correspond to physically stable chemical species, which could be reactants and products. The transition state is defined as the maximum in a reaction profile, where the gradient is again, zero, while curvature is negative, hence energy decreases in one direction, which indicates the reaction pathway of the chemical reaction. The potential energy surface can be computed using Gaussview 09, where structure and energy of reactants or products can be modelled to illustrate the transition states, which can rarely be obtained experimentally. The intrinsic reaction coordinate can then be calculated and compared to predict the reaction path at a transition state and follow it to the correct minima.

In this computational lab, all of the reactants and products were optimised to their minima, and the transition states were also optimised. The calculations were done by Gaussian 09, using mainly semi-empirical method PM6 and DFT-B3LYP. Frequency calculations were performed to show molecular vibrations to confirm the position on the potential energy surface. If all the vibrational frequencies are real, this confirms the structure is a minimum, and vice versa, the presence of imaginary frequency may suggest that the structure is at its transition state. Intrinsic reaction coordinate method was carried out using calculated force constants to predict which conformer a reaction path from the transition state would lead to.

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

The reaction between butadiene and ethene is a typical pericyclic [4+2] Diels-Alder reaction that proceeds via a concerted mechanism through a cyclic transition state. The reaction scheme is shown below.

[[File:Ex1 reactionscheme revised yhw14.png|550px|center|thumb|Diagram 1: Reaction Scheme of Butadiene and Ethene]]

=== Molecular Orbital Analysis ===

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of butadiene and ethene.

[[File:Ex1 mo diagram yhw14 revised v3.png|550px|center|thumb|Diagram 2: MO diagram of Reaction of Butadiene and Ethene]]

Butadiene and ethene were optimised to their minima. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #06DCFB; color: #ffffff;" |'''Molecule'''
! '''Butadiene'''
! '''Ethene'''
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Butadiene lumo yhw14.png|center|150px]]
|[[File:Ethene lumo yhw14.png|center|150px]]
|-
|Corresponding to the s orbital (symmetric)
|Corresponding to the a orbital (asymmetric)
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Butadiene homo yhw14.png|center|150px]]
|[[File:Ethene homo yhw14.png|center|150px]]
|-
|Corresponding to the a orbital (antisymmetric)
|Corresponding to the s orbital (symmetric)
|}

The transition state was first optimised to its minimum, followed by a transition state calculation. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #01FCEF; color: #ffffff;" |'''Molecule'''
! '''Transition State'''
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Ts lumo+1 yhw14.png|center|150px]]
|-
|Corresponding to the 5 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Ts lumo 1 yhw14.png|center|150px]]
|-
|Corresponding to the 4 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Ts homo yhw14.png|center|150px]]
|-
|Corresponding to the 3 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Ts homo-1 yhw14.png|center|150px]]
|-
|Corresponding to the 2 orbital
|}

Based on the MO diagram and the computed MOs shown above, a reaction is only allowed when the MOs with the same symmetry labels interact with each other, i.e. symmetric-symmetric and asymmetric-asymmetric interactions; and a reaction is forbidden when the MOs with different symmetry labels interact with each other, i.e. symmetric-asymmetric interactions.
In the reaction between butadiene and ethene, the butadiene asymmetric MO interacts with the ethene asymmetric MO to give the 2 and 5 MOs of the transition state, and the butadiene symmetric MO interacts with the ethene symmetric MO to give the 3 and 4 MOs of the transition state. Therefore, a reaction is allowed when the symmetry labels of the MOs of the reactants are the same; and forbidden when the symmetry labels are different.

The orbital overlap integral is zero in a symmetric-asymmetric interaction and non-zero in symmetric-symmetric and asymmetric-asymmetric interactions.

=== Bond Length Analysis ===

The changes in bond lengths between carbons in reactant, transition state and product as the reaction progresses were studied by comparing the bond lengths between carbons before and after the reaction. The summary of bond lengths is shown below.
[[File:Ex1 bondlength yhw14.png|470px|center|thumb|Diagram 3: Labelled carbons]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #0000FF; color: #ffffff" | State
! style="background: #0000FF; color: #ffffff" | C1-C2
! style="background: #0000FF; color: #ffffff" | C2-C3
! style="background: #0000FF; color: #ffffff" | C3-C4
! style="background: #0000FF; color: #ffffff" | C4-C5
! style="background: #0000FF; color: #ffffff" | C5-C6
! style="background: #0000FF; color: #ffffff" | C6-C1
|-
|Reactants
|1.335
|1.468
|1.335
|/
|1.327
|/
|-
|Transition State
|1.380
|1.411
|1.380
|2.115
|1.382
|2.114
|-
|Product
|1.500
|1.338
|1.500
|1.540
|1.540
|1.540
|+Table 1: Measurements of the C-C bond lengths of the reactants, transition state and products (Å)
|}
As the reaction progresses, the bond lengths between C1-C2, C3-C4 and C5-C6 increase from ~1.3 Å to ~1.5 Å as the bond order decrease to one, whereas bond length of C2-C3 decreases from ~1.5 Å to ~1.3 Å as the bond order increases from one to two.
This could be explained as the increase in bond length suggest a change from sp2-sp2 (C-C double bond) with typical bond length of 1.33 Å <ref name="C-C bond lengths"/> to sp3-sp3 (C-C single bond) with typical bond length of 1.54 Å <ref name="C-C bond lengths"/>, and vice versa for the decrease in bond length. Based on the calculated bond lengths above in Table 1, it is clear that bond lengths and bond orders of the reactants changed during the reaction and the new bonds formed at C4-C5 and C6-C1 are single bonds as they have bond lengths of 1.54 Å.
The typical Van der Waals radius of the C atom is 1.7 Å <ref name="Van der Waals radius of C"/>. As the bond lengths between C4-C5 and C6-C1 of the transition state are shorter than 2 x Van der Waals radii of C, this reflects that C-C bonds are forming at the transition state.

=== Vibration Analysis ===

The imaginary frequency at -948.32 cm-1 corresponds to the reaction path at the transition state, which shows a synchronous bond formation, which agrees with the concerted mechanism of [4+2] cycloaddition, where both reaction centres converge at the same time to form bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|[[File:Ex1 ts imaginary white yhw14.gif|center|250px]]
|-
|[[File:Ex1 ts imaginary yhw14.gif|center|250px]]
|-
|style="text-align: center;"|Reaction Path at the Transition State (Please double click to see animation)
|}

The lowest positive frequency at 145.14 cm-1 is asynchronous as shown below, where one of the C from the ethene moves towards the butadiene reaction centre and the other C moves away. This suggests that bonds are formed one at a time.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|[[File:Ex1 ts positive white yhw14.gif|center|250px]]
|-
|[[File:Ex1 ts positive yhw14.gif|center|250px]]
|-
|style="text-align: center;"|Lowest positive frequency (Please double click to see animation)
|}

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

[[File:Ex2 reactionscheme.png|550px|center|thumb|Diagram 4: Reaction Scheme of Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

Cyclohexadiene and 1,3-dioxole were optimised to their minima. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #9A03FE; color: #ffffff;" |'''Molecule'''
! '''Cyclohexadiene'''
! '''1,3-Dioxole'''
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Cyclo lumo 631g yhw14.png|center|150px]]
|[[File:Dioxole lumo 631g yhw14.png|center|150px]]
|-
|Corresponding to the orbital
|Corresponding to the orbital
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Cyclo homo 631g yhw14.png|center|150px]]
|[[File:Dioxole homo 631g yhw14.png|center|150px]]
|-
|Corresponding to the orbital
|Corresponding to the orbital
|}

The transition state was first optimised to its minimum, followed by a transition state calculation. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #BD5CFE; color: #ffffff;" |'''Molecule'''
! '''Endo Transition State'''
! '''Exo Transition State'''
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Endo ts lumo+1 yhw14.png|center|150px]]
|[[File:Exo ts lumo+1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Endo ts lumo yhw14.png|center|150px]]
|[[File:Exo ts lumo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Endo ts homo yhw14.png|center|150px]]
|[[File:Exo ts homo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Endo ts homo-1 yhw14.png|center|150px]]
|[[File:Exo ts homo-1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|}

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of cyclohexadiene and 1,3-dioxole.

[[File:|550px|center|thumb|Diagram 5: MO diagram of Reaction of Cyclohexadiene and 1,3-dioxole]]

=== Normal Demand vs Inverse Demand Diels-Alder Reaction ===

A normal electron demand Diels-Alder reaction can be defined as a reaction between electron rich diene and electron poor dienophile. An inverse electron demand is the reaction between electron poor diene and electron rich dienophile.

The LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are very close in energy, which results in strong bonding interaction between the two to form the HOMO and LUMO of both endo and exo TS. Since only the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole have the correct symmetry () to interact, they interact to form the __(symmetry) HOMO and LUMO of both TS.

This could be explained by the presence of electron rich O on 1,3-dioxole which raises the energy of both its HOMO and LUMO, making the overlap between the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole much better than the HOMO of cyclohexadiene and the LUMO of 1,3-dioxole. Thus, the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are now the frontier orbitals that interact the most, hence this is an inverse demand Diels-Alder reaction.

=== Reaction Energies and Secondary Orbital Interaction ===

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FF4AFF; color: #ffffff" |
! style="background: #FF4AFF; color: #ffffff" | Reactants
! style="background: #FF4AFF; color: #ffffff" | Transition State
! style="background: #FF4AFF; color: #ffffff" | Product
! style="background: #FF4AFF; color: #ffffff" | Activation Energy
! style="background: #FF4AFF; color: #ffffff" | Gibbs Free Energy
|-
|Endo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313622</nowiki>
|<nowiki>-1313849</nowiki>
|160
|<nowiki>-67</nowiki>
|-
|Exo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313614</nowiki>
|<nowiki>-1313846</nowiki>
|168
|<nowiki>-64</nowiki>
|+Table 2: Energies of Reactants, Transition States and Products of both Endo and Exo Pathways in Diels-Alder Reaction of Cyclohexadiene and 1,3-Dioxole (kJ mol-1)
|}

Kinetically favourable product of a reaction is the one that has the lowest activation energy; Thermodynamically favourable product is the product with lowest energy conformer, hence the more stabilised product.

The endo transition state is the kinetic product of this reaction as it has lower activation energy. This could be explained using the secondary orbital interaction between the lone pair orbital on the oxygen atom and the empty π* orbital of diene. This favourable effect stabilises the endo transition state.

As the oxygen atom lone pair is oriented away from the diene π system in the exo transition state, the secondary orbital effect is not present, hence the activation energy of exo reaction is higher.

However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, i.e. increasing temperature, formation of the exo product would be more favourable.

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

Xylylene can react with sulfur dioxide through Diels-Alder reaction via either endo or exo pathways to form a 6-membered ring, or through cheletropic reaction to form a 5-membered ring. The reaction scheme is shown below. Reaction barriers and reaction energies for each pathway are compared to determine the reaction that is most favourable.

[[File:Ex3 reactionscheme yhw14.png|550px|center|thumb|Diagram 6: Reaction Scheme of Xylylene and Sulfur Dioxide]]

=== Intrinsic Reaction Coordinate ===
The following files show the intrinsic reaction coordinates of the three different reaction pathways of xylylene and SO2. Please click to see animation.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Endo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Exo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Cheletropic TS
|-
|[[File:DA endo irc animation purple yhw14.gif|center]]
|[[File:DA exo irc animation purple yhw14.gif|center]]
|[[File: Ex3 Chele movie yhw14.gif|center]]
|-
|[[File:DA endo irc animation yhw14.gif|center]]
|[[File:DA exo irc animation yhw14.gif|center]]
|[[File:Cheletropic irc animation yhw14.gif|center]]
|-
|[[File:DA endo irc plot yhw14.png|center|500px]]
|[[File:DA exo irc plot yhw14.png|center|500px]]
|[[File:Cheletropic irc plot yhw14.png|center|650px]]
|}

=== Reaction Energies and Reaction Barriers ===

[[File:Ex3 reactionprofile yhw14.png|550px|center|thumb|Diagram 7: Reaction Profile of Xylylene and Sulfur Dioxide]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FFD1C3; color: #ffffff" |
! style="background: #FFD1C3; color: #ffffff" | Reactants
! style="background: #FFD1C3; color: #ffffff" | Transition State
! style="background: #FFD1C3; color: #ffffff" | Product
! style="background: #FFD1C3; color: #ffffff" | Activation Energy
! style="background: #FFD1C3; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|237.767824
|56.9576013
|83.391038
|<nowiki>-97.4191847</nowiki>
|-
|Exo
|154.376786
|241.753433
|56.3196048
|87.406647
|<nowiki>-98.0571812</nowiki>
|-
|Cheletropic
|154.376786
|260.08205
|0.013127501
|105.705264
|<nowiki>-154.3636585</nowiki>
|+Table 3: Energies of Reactants, Transition States and Products of Reactions between Xylylene and Sulfur Dioxide (kJ mol-1)
|}

With reference to the reaction profile and table __, the Diels-Alder reaction via the endo pathway has the lowest activation energy, making it a more kinetically favourable product, i.e. the kinetic product; the Diels-Alder exo product has a lower energy than endo, however with a higher activation energy hence it will not form under low temperature condition; the cheletropic product is the most stabilised product out of the three and it has the lowest reaction energy, therefore is the thermodynamic product.

=== Side Reaction between cis-diene in Xylylene 6-membered ring and SO2===

o-Xylylene contains another cis-butadiene fragment located in the 6-membered ring that can undergo a Diels-Alder reaction with SO2. The reaction energies and reaction barriers between endo and exo pathways are compared in the table below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #4EBEBA; color: #ffffff" |
! style="background: #4EBEBA; color: #ffffff" | Reactants
! style="background: #4EBEBA; color: #ffffff" | Transition State
! style="background: #4EBEBA; color: #ffffff" | Product
! style="background: #4EBEBA; color: #ffffff" | Activation Energy
! style="background: #4EBEBA; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|267.984805
|172.272196
|113.608019
|17.89541
|-
|Exo
|154.376786
|275.821924
|176.711916
|121.445138
|22.33513
|+Table 4: Energies of Reactants, Transition States and Products of the Side Reaction in Xylylene 6-membered ring and Sulfur Dioxide (kJ mol-1)
|}

It is clear that both endo and exo Diels-Alder side reactions are kinetically and thermodynamically unfavourable at this site as the activation energies are much higher than the previous reactions mentioned above in table __ and the reaction energies show that the reactions are endothermic.

== Conclusion ==

The transition states of three pericyclic reactions were investigated in this computational lab, using Gaussian to optimise the reactants, transition states and products respectively, and the vibrational frequencies and intrinsic reaction coordinates were computed.

In the reaction between butadiene and ethene, the importance of molecular orbital symmetry in the interaction of molecular orbitals was illustrated, such that a reaction is only allowed when the molecular orbitals with the same symmetry labels interact with each other and forbidden when symmetric molecular orbital interact with asymmetric orbitals. Furthermore, the vibration frequency calculation proved that this [4+2] Diels-Alder reaction proceeds via a concerted mechanism as synchronous bond formation was demonstrated. Bonding interaction can be further confirmed as the bond distance between the two termini carbon atoms in the transition state is shorter than the sum of two Van der Waals radii of carbon.

In the reaction of cyclohexadiene and 1,3-dioxole, both the endo and exo transition states were investigated. In general, the endo transition state is kinetically more favourable as it has lower activation barrier, possibly due to the secondary orbital interaction between the lone pair in p orbital on the oxygen atom and the empty pi* orbital in the diene, which stabilises the transition state. However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, formation of the exo product could be possible.

The final reaction between xylylene and SO2 again proved that the endo Diels-Alder transition state has the lowest activation energy, making it kinetically favourable at low temperature. However, the cheletropic product is the most stabilised and thermodynamically favourable product. Therefore the reaction would yield the cheletropic product under thermodynamic control instead of the exo Diels-Alder product.

==References==
<references>
<ref name="C-C bond lengths">L. Pauling and L. O. Brockway, ''Journal of the American Chemical Society'', '''1937''', Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref>
<ref name="Van der Waals radius of C">S. S. Batsanov, ''Inorganic Materials'', '''2001''', Volume 37, Number 9, pp. 871-885, https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf.</ref>
</references>

Rep:Mod:yhw14cts

2017-02-09T18:05:46Z

Yhw14: /* Intrinsic Reaction Coordinate */

''' Transition States and Reactivity '''

'' Yi Hang Cherie WONG (yhw14) ''
'' CID: 00933828 ''

== Introduction ==
A potential energy surface is a mathematical function that gives the energy of a molecule as a function of its geometry with the relative positions of the atoms participating in the reaction. The stationary points may be classified according to the first and second derivatives of the energy with respect to position. At the minimum of a reaction profile, the first derivative of the reaction coordinate, which indicates the gradient, is zero, while the second derivative, which indicates curvature, is positive; hence energy rises in all directions. Energy minima correspond to physically stable chemical species, which could be reactants and products. The transition state is defined as the maximum in a reaction profile, where the gradient is again, zero, while curvature is negative, hence energy decreases in one direction, which indicates the reaction pathway of the chemical reaction. The potential energy surface can be computed using Gaussview 09, where structure and energy of reactants or products can be modelled to illustrate the transition states, which can rarely be obtained experimentally. The intrinsic reaction coordinate can then be calculated and compared to predict the reaction path at a transition state and follow it to the correct minima.

In this computational lab, all of the reactants and products were optimised to their minima, and the transition states were also optimised. The calculations were done by Gaussian 09, using mainly semi-empirical method PM6 and DFT-B3LYP. Frequency calculations were performed to show molecular vibrations to confirm the position on the potential energy surface. If all the vibrational frequencies are real, this confirms the structure is a minimum, and vice versa, the presence of imaginary frequency may suggest that the structure is at its transition state. Intrinsic reaction coordinate method was carried out using calculated force constants to predict which conformer a reaction path from the transition state would lead to.

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

The reaction between butadiene and ethene is a typical pericyclic [4+2] Diels-Alder reaction that proceeds via a concerted mechanism through a cyclic transition state. The reaction scheme is shown below.

[[File:Ex1 reactionscheme revised yhw14.png|550px|center|thumb|Diagram 1: Reaction Scheme of Butadiene and Ethene]]

=== Molecular Orbital Analysis ===

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of butadiene and ethene.

[[File:Ex1 mo diagram yhw14 revised v3.png|550px|center|thumb|Diagram 2: MO diagram of Reaction of Butadiene and Ethene]]

Butadiene and ethene were optimised to their minima. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #06DCFB; color: #ffffff;" |'''Molecule'''
! '''Butadiene'''
! '''Ethene'''
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Butadiene lumo yhw14.png|center|150px]]
|[[File:Ethene lumo yhw14.png|center|150px]]
|-
|Corresponding to the s orbital (symmetric)
|Corresponding to the a orbital (asymmetric)
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Butadiene homo yhw14.png|center|150px]]
|[[File:Ethene homo yhw14.png|center|150px]]
|-
|Corresponding to the a orbital (antisymmetric)
|Corresponding to the s orbital (symmetric)
|}

The transition state was first optimised to its minimum, followed by a transition state calculation. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #01FCEF; color: #ffffff;" |'''Molecule'''
! '''Transition State'''
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Ts lumo+1 yhw14.png|center|150px]]
|-
|Corresponding to the 5 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Ts lumo 1 yhw14.png|center|150px]]
|-
|Corresponding to the 4 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Ts homo yhw14.png|center|150px]]
|-
|Corresponding to the 3 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Ts homo-1 yhw14.png|center|150px]]
|-
|Corresponding to the 2 orbital
|}

Based on the MO diagram and the computed MOs shown above, a reaction is only allowed when the MOs with the same symmetry labels interact with each other, i.e. symmetric-symmetric and asymmetric-asymmetric interactions; and a reaction is forbidden when the MOs with different symmetry labels interact with each other, i.e. symmetric-asymmetric interactions.
In the reaction between butadiene and ethene, the butadiene asymmetric MO interacts with the ethene asymmetric MO to give the 2 and 5 MOs of the transition state, and the butadiene symmetric MO interacts with the ethene symmetric MO to give the 3 and 4 MOs of the transition state. Therefore, a reaction is allowed when the symmetry labels of the MOs of the reactants are the same; and forbidden when the symmetry labels are different.

The orbital overlap integral is zero in a symmetric-asymmetric interaction and non-zero in symmetric-symmetric and asymmetric-asymmetric interactions.

=== Bond Length Analysis ===

The changes in bond lengths between carbons in reactant, transition state and product as the reaction progresses were studied by comparing the bond lengths between carbons before and after the reaction. The summary of bond lengths is shown below.
[[File:Ex1 bondlength yhw14.png|470px|center|thumb|Diagram 3: Labelled carbons]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #0000FF; color: #ffffff" | State
! style="background: #0000FF; color: #ffffff" | C1-C2
! style="background: #0000FF; color: #ffffff" | C2-C3
! style="background: #0000FF; color: #ffffff" | C3-C4
! style="background: #0000FF; color: #ffffff" | C4-C5
! style="background: #0000FF; color: #ffffff" | C5-C6
! style="background: #0000FF; color: #ffffff" | C6-C1
|-
|Reactants
|1.335
|1.468
|1.335
|/
|1.327
|/
|-
|Transition State
|1.380
|1.411
|1.380
|2.115
|1.382
|2.114
|-
|Product
|1.500
|1.338
|1.500
|1.540
|1.540
|1.540
|+Table 1: Measurements of the C-C bond lengths of the reactants, transition state and products (Å)
|}
As the reaction progresses, the bond lengths between C1-C2, C3-C4 and C5-C6 increase from ~1.3 Å to ~1.5 Å as the bond order decrease to one, whereas bond length of C2-C3 decreases from ~1.5 Å to ~1.3 Å as the bond order increases from one to two.
This could be explained as the increase in bond length suggest a change from sp2-sp2 (C-C double bond) with typical bond length of 1.33 Å <ref name="C-C bond lengths"/> to sp3-sp3 (C-C single bond) with typical bond length of 1.54 Å <ref name="C-C bond lengths"/>, and vice versa for the decrease in bond length. Based on the calculated bond lengths above in Table 1, it is clear that bond lengths and bond orders of the reactants changed during the reaction and the new bonds formed at C4-C5 and C6-C1 are single bonds as they have bond lengths of 1.54 Å.
The typical Van der Waals radius of the C atom is 1.7 Å <ref name="Van der Waals radius of C"/>. As the bond lengths between C4-C5 and C6-C1 of the transition state are shorter than 2 x Van der Waals radii of C, this reflects that C-C bonds are forming at the transition state.

=== Vibration Analysis ===

The imaginary frequency at -948.32 cm-1 corresponds to the reaction path at the transition state, which shows a synchronous bond formation, which agrees with the concerted mechanism of [4+2] cycloaddition, where both reaction centres converge at the same time to form bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|[[File:Ex1 ts imaginary white yhw14.gif|center|250px]]
|-
|[[File:Ex1 ts imaginary yhw14.gif|center|250px]]
|-
|style="text-align: center;"|Reaction Path at the Transition State (Please double click to see animation)
|}

The lowest positive frequency at 145.14 cm-1 is asynchronous as shown below, where one of the C from the ethene moves towards the butadiene reaction centre and the other C moves away. This suggests that bonds are formed one at a time.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|[[File:Ex1 ts positive white yhw14.gif|center|250px]]
|-
|[[File:Ex1 ts positive yhw14.gif|center|250px]]
|-
|style="text-align: center;"|Lowest positive frequency (Please double click to see animation)
|}

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

[[File:Ex2 reactionscheme.png|550px|center|thumb|Diagram 4: Reaction Scheme of Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

Cyclohexadiene and 1,3-dioxole were optimised to their minima. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #9A03FE; color: #ffffff;" |'''Molecule'''
! '''Cyclohexadiene'''
! '''1,3-Dioxole'''
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Cyclo lumo 631g yhw14.png|center|150px]]
|[[File:Dioxole lumo 631g yhw14.png|center|150px]]
|-
|Corresponding to the orbital
|Corresponding to the orbital
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Cyclo homo 631g yhw14.png|center|150px]]
|[[File:Dioxole homo 631g yhw14.png|center|150px]]
|-
|Corresponding to the orbital
|Corresponding to the orbital
|}

The transition state was first optimised to its minimum, followed by a transition state calculation. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #BD5CFE; color: #ffffff;" |'''Molecule'''
! '''Endo Transition State'''
! '''Exo Transition State'''
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Endo ts lumo+1 yhw14.png|center|150px]]
|[[File:Exo ts lumo+1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Endo ts lumo yhw14.png|center|150px]]
|[[File:Exo ts lumo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Endo ts homo yhw14.png|center|150px]]
|[[File:Exo ts homo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Endo ts homo-1 yhw14.png|center|150px]]
|[[File:Exo ts homo-1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|}

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of cyclohexadiene and 1,3-dioxole.

[[File:|550px|center|thumb|Diagram 5: MO diagram of Reaction of Cyclohexadiene and 1,3-dioxole]]

=== Normal Demand vs Inverse Demand Diels-Alder Reaction ===

A normal electron demand Diels-Alder reaction can be defined as a reaction between electron rich diene and electron poor dienophile. An inverse electron demand is the reaction between electron poor diene and electron rich dienophile.

The LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are very close in energy, which results in strong bonding interaction between the two to form the HOMO and LUMO of both endo and exo TS. Since only the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole have the correct symmetry () to interact, they interact to form the __(symmetry) HOMO and LUMO of both TS.

This could be explained by the presence of electron rich O on 1,3-dioxole which raises the energy of both its HOMO and LUMO, making the overlap between the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole much better than the HOMO of cyclohexadiene and the LUMO of 1,3-dioxole. Thus, the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are now the frontier orbitals that interact the most, hence this is an inverse demand Diels-Alder reaction.

=== Reaction Energies and Secondary Orbital Interaction ===

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FF4AFF; color: #ffffff" |
! style="background: #FF4AFF; color: #ffffff" | Reactants
! style="background: #FF4AFF; color: #ffffff" | Transition State
! style="background: #FF4AFF; color: #ffffff" | Product
! style="background: #FF4AFF; color: #ffffff" | Activation Energy
! style="background: #FF4AFF; color: #ffffff" | Gibbs Free Energy
|-
|Endo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313622</nowiki>
|<nowiki>-1313849</nowiki>
|160
|<nowiki>-67</nowiki>
|-
|Exo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313614</nowiki>
|<nowiki>-1313846</nowiki>
|168
|<nowiki>-64</nowiki>
|+Table 2: Energies of Reactants, Transition States and Products of both Endo and Exo Pathways in Diels-Alder Reaction of Cyclohexadiene and 1,3-Dioxole (kJ mol-1)
|}

Kinetically favourable product of a reaction is the one that has the lowest activation energy; Thermodynamically favourable product is the product with lowest energy conformer, hence the more stabilised product.

The endo transition state is the kinetic product of this reaction as it has lower activation energy. This could be explained using the secondary orbital interaction between the lone pair orbital on the oxygen atom and the empty π* orbital of diene. This favourable effect stabilises the endo transition state.

As the oxygen atom lone pair is oriented away from the diene π system in the exo transition state, the secondary orbital effect is not present, hence the activation energy of exo reaction is higher.

However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, i.e. increasing temperature, formation of the exo product would be more favourable.

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

Xylylene can react with sulfur dioxide through Diels-Alder reaction via either endo or exo pathways to form a 6-membered ring, or through cheletropic reaction to form a 5-membered ring. The reaction scheme is shown below. Reaction barriers and reaction energies for each pathway are compared to determine the reaction that is most favourable.

[[File:Ex3 reactionscheme yhw14.png|550px|center|thumb|Diagram 6: Reaction Scheme of Xylylene and Sulfur Dioxide]]

=== Intrinsic Reaction Coordinate ===
The following files show the intrinsic reaction coordinates of the three different reaction pathways of xylylene and SO2. Please click to see animation.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Endo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Exo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Cheletropic TS
|-
|[[File:DA endo irc animation purple yhw14.gif|center]]
|[[File:DA exo irc animation purple yhw14.gif|center]]
|[[File: Ex3 Chele movie yhw14.gif|center]]
|-
|[[File:DA endo irc animation yhw14.gif|center]]
|[[File:DA exo irc animation yhw14.gif|center]]
|[[File:Cheletropic irc animation yhw14.gif|center]]
|-
|[[File:DA endo irc plot yhw14.png|center|250px]]
|[[File:DA exo irc plot yhw14.png|center|250px]]
|[[File:Cheletropic irc plot yhw14.png|center|250px]]
|}

=== Reaction Energies and Reaction Barriers ===

[[File:Ex3 reactionprofile yhw14.png|550px|center|thumb|Diagram 7: Reaction Profile of Xylylene and Sulfur Dioxide]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FFD1C3; color: #ffffff" |
! style="background: #FFD1C3; color: #ffffff" | Reactants
! style="background: #FFD1C3; color: #ffffff" | Transition State
! style="background: #FFD1C3; color: #ffffff" | Product
! style="background: #FFD1C3; color: #ffffff" | Activation Energy
! style="background: #FFD1C3; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|237.767824
|56.9576013
|83.391038
|<nowiki>-97.4191847</nowiki>
|-
|Exo
|154.376786
|241.753433
|56.3196048
|87.406647
|<nowiki>-98.0571812</nowiki>
|-
|Cheletropic
|154.376786
|260.08205
|0.013127501
|105.705264
|<nowiki>-154.3636585</nowiki>
|+Table 3: Energies of Reactants, Transition States and Products of Reactions between Xylylene and Sulfur Dioxide (kJ mol-1)
|}

With reference to the reaction profile and table __, the Diels-Alder reaction via the endo pathway has the lowest activation energy, making it a more kinetically favourable product, i.e. the kinetic product; the Diels-Alder exo product has a lower energy than endo, however with a higher activation energy hence it will not form under low temperature condition; the cheletropic product is the most stabilised product out of the three and it has the lowest reaction energy, therefore is the thermodynamic product.

=== Side Reaction between cis-diene in Xylylene 6-membered ring and SO2===

o-Xylylene contains another cis-butadiene fragment located in the 6-membered ring that can undergo a Diels-Alder reaction with SO2. The reaction energies and reaction barriers between endo and exo pathways are compared in the table below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #4EBEBA; color: #ffffff" |
! style="background: #4EBEBA; color: #ffffff" | Reactants
! style="background: #4EBEBA; color: #ffffff" | Transition State
! style="background: #4EBEBA; color: #ffffff" | Product
! style="background: #4EBEBA; color: #ffffff" | Activation Energy
! style="background: #4EBEBA; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|267.984805
|172.272196
|113.608019
|17.89541
|-
|Exo
|154.376786
|275.821924
|176.711916
|121.445138
|22.33513
|+Table 4: Energies of Reactants, Transition States and Products of the Side Reaction in Xylylene 6-membered ring and Sulfur Dioxide (kJ mol-1)
|}

It is clear that both endo and exo Diels-Alder side reactions are kinetically and thermodynamically unfavourable at this site as the activation energies are much higher than the previous reactions mentioned above in table __ and the reaction energies show that the reactions are endothermic.

== Conclusion ==

The transition states of three pericyclic reactions were investigated in this computational lab, using Gaussian to optimise the reactants, transition states and products respectively, and the vibrational frequencies and intrinsic reaction coordinates were computed.

In the reaction between butadiene and ethene, the importance of molecular orbital symmetry in the interaction of molecular orbitals was illustrated, such that a reaction is only allowed when the molecular orbitals with the same symmetry labels interact with each other and forbidden when symmetric molecular orbital interact with asymmetric orbitals. Furthermore, the vibration frequency calculation proved that this [4+2] Diels-Alder reaction proceeds via a concerted mechanism as synchronous bond formation was demonstrated. Bonding interaction can be further confirmed as the bond distance between the two termini carbon atoms in the transition state is shorter than the sum of two Van der Waals radii of carbon.

In the reaction of cyclohexadiene and 1,3-dioxole, both the endo and exo transition states were investigated. In general, the endo transition state is kinetically more favourable as it has lower activation barrier, possibly due to the secondary orbital interaction between the lone pair in p orbital on the oxygen atom and the empty pi* orbital in the diene, which stabilises the transition state. However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, formation of the exo product could be possible.

The final reaction between xylylene and SO2 again proved that the endo Diels-Alder transition state has the lowest activation energy, making it kinetically favourable at low temperature. However, the cheletropic product is the most stabilised and thermodynamically favourable product. Therefore the reaction would yield the cheletropic product under thermodynamic control instead of the exo Diels-Alder product.

==References==
<references>
<ref name="C-C bond lengths">L. Pauling and L. O. Brockway, ''Journal of the American Chemical Society'', '''1937''', Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref>
<ref name="Van der Waals radius of C">S. S. Batsanov, ''Inorganic Materials'', '''2001''', Volume 37, Number 9, pp. 871-885, https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf.</ref>
</references>

Rep:Mod:yhw14cts

2017-02-09T18:00:41Z

Yhw14: /* Intrinsic Reaction Coordinate */

''' Transition States and Reactivity '''

'' Yi Hang Cherie WONG (yhw14) ''
'' CID: 00933828 ''

== Introduction ==
A potential energy surface is a mathematical function that gives the energy of a molecule as a function of its geometry with the relative positions of the atoms participating in the reaction. The stationary points may be classified according to the first and second derivatives of the energy with respect to position. At the minimum of a reaction profile, the first derivative of the reaction coordinate, which indicates the gradient, is zero, while the second derivative, which indicates curvature, is positive; hence energy rises in all directions. Energy minima correspond to physically stable chemical species, which could be reactants and products. The transition state is defined as the maximum in a reaction profile, where the gradient is again, zero, while curvature is negative, hence energy decreases in one direction, which indicates the reaction pathway of the chemical reaction. The potential energy surface can be computed using Gaussview 09, where structure and energy of reactants or products can be modelled to illustrate the transition states, which can rarely be obtained experimentally. The intrinsic reaction coordinate can then be calculated and compared to predict the reaction path at a transition state and follow it to the correct minima.

In this computational lab, all of the reactants and products were optimised to their minima, and the transition states were also optimised. The calculations were done by Gaussian 09, using mainly semi-empirical method PM6 and DFT-B3LYP. Frequency calculations were performed to show molecular vibrations to confirm the position on the potential energy surface. If all the vibrational frequencies are real, this confirms the structure is a minimum, and vice versa, the presence of imaginary frequency may suggest that the structure is at its transition state. Intrinsic reaction coordinate method was carried out using calculated force constants to predict which conformer a reaction path from the transition state would lead to.

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

The reaction between butadiene and ethene is a typical pericyclic [4+2] Diels-Alder reaction that proceeds via a concerted mechanism through a cyclic transition state. The reaction scheme is shown below.

[[File:Ex1 reactionscheme revised yhw14.png|550px|center|thumb|Diagram 1: Reaction Scheme of Butadiene and Ethene]]

=== Molecular Orbital Analysis ===

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of butadiene and ethene.

[[File:Ex1 mo diagram yhw14 revised v3.png|550px|center|thumb|Diagram 2: MO diagram of Reaction of Butadiene and Ethene]]

Butadiene and ethene were optimised to their minima. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #06DCFB; color: #ffffff;" |'''Molecule'''
! '''Butadiene'''
! '''Ethene'''
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Butadiene lumo yhw14.png|center|150px]]
|[[File:Ethene lumo yhw14.png|center|150px]]
|-
|Corresponding to the s orbital (symmetric)
|Corresponding to the a orbital (asymmetric)
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Butadiene homo yhw14.png|center|150px]]
|[[File:Ethene homo yhw14.png|center|150px]]
|-
|Corresponding to the a orbital (antisymmetric)
|Corresponding to the s orbital (symmetric)
|}

The transition state was first optimised to its minimum, followed by a transition state calculation. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #01FCEF; color: #ffffff;" |'''Molecule'''
! '''Transition State'''
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Ts lumo+1 yhw14.png|center|150px]]
|-
|Corresponding to the 5 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Ts lumo 1 yhw14.png|center|150px]]
|-
|Corresponding to the 4 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Ts homo yhw14.png|center|150px]]
|-
|Corresponding to the 3 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Ts homo-1 yhw14.png|center|150px]]
|-
|Corresponding to the 2 orbital
|}

Based on the MO diagram and the computed MOs shown above, a reaction is only allowed when the MOs with the same symmetry labels interact with each other, i.e. symmetric-symmetric and asymmetric-asymmetric interactions; and a reaction is forbidden when the MOs with different symmetry labels interact with each other, i.e. symmetric-asymmetric interactions.
In the reaction between butadiene and ethene, the butadiene asymmetric MO interacts with the ethene asymmetric MO to give the 2 and 5 MOs of the transition state, and the butadiene symmetric MO interacts with the ethene symmetric MO to give the 3 and 4 MOs of the transition state. Therefore, a reaction is allowed when the symmetry labels of the MOs of the reactants are the same; and forbidden when the symmetry labels are different.

The orbital overlap integral is zero in a symmetric-asymmetric interaction and non-zero in symmetric-symmetric and asymmetric-asymmetric interactions.

=== Bond Length Analysis ===

The changes in bond lengths between carbons in reactant, transition state and product as the reaction progresses were studied by comparing the bond lengths between carbons before and after the reaction. The summary of bond lengths is shown below.
[[File:Ex1 bondlength yhw14.png|470px|center|thumb|Diagram 3: Labelled carbons]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #0000FF; color: #ffffff" | State
! style="background: #0000FF; color: #ffffff" | C1-C2
! style="background: #0000FF; color: #ffffff" | C2-C3
! style="background: #0000FF; color: #ffffff" | C3-C4
! style="background: #0000FF; color: #ffffff" | C4-C5
! style="background: #0000FF; color: #ffffff" | C5-C6
! style="background: #0000FF; color: #ffffff" | C6-C1
|-
|Reactants
|1.335
|1.468
|1.335
|/
|1.327
|/
|-
|Transition State
|1.380
|1.411
|1.380
|2.115
|1.382
|2.114
|-
|Product
|1.500
|1.338
|1.500
|1.540
|1.540
|1.540
|+Table 1: Measurements of the C-C bond lengths of the reactants, transition state and products (Å)
|}
As the reaction progresses, the bond lengths between C1-C2, C3-C4 and C5-C6 increase from ~1.3 Å to ~1.5 Å as the bond order decrease to one, whereas bond length of C2-C3 decreases from ~1.5 Å to ~1.3 Å as the bond order increases from one to two.
This could be explained as the increase in bond length suggest a change from sp2-sp2 (C-C double bond) with typical bond length of 1.33 Å <ref name="C-C bond lengths"/> to sp3-sp3 (C-C single bond) with typical bond length of 1.54 Å <ref name="C-C bond lengths"/>, and vice versa for the decrease in bond length. Based on the calculated bond lengths above in Table 1, it is clear that bond lengths and bond orders of the reactants changed during the reaction and the new bonds formed at C4-C5 and C6-C1 are single bonds as they have bond lengths of 1.54 Å.
The typical Van der Waals radius of the C atom is 1.7 Å <ref name="Van der Waals radius of C"/>. As the bond lengths between C4-C5 and C6-C1 of the transition state are shorter than 2 x Van der Waals radii of C, this reflects that C-C bonds are forming at the transition state.

=== Vibration Analysis ===

The imaginary frequency at -948.32 cm-1 corresponds to the reaction path at the transition state, which shows a synchronous bond formation, which agrees with the concerted mechanism of [4+2] cycloaddition, where both reaction centres converge at the same time to form bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|[[File:Ex1 ts imaginary white yhw14.gif|center|250px]]
|-
|[[File:Ex1 ts imaginary yhw14.gif|center|250px]]
|-
|style="text-align: center;"|Reaction Path at the Transition State (Please double click to see animation)
|}

The lowest positive frequency at 145.14 cm-1 is asynchronous as shown below, where one of the C from the ethene moves towards the butadiene reaction centre and the other C moves away. This suggests that bonds are formed one at a time.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|[[File:Ex1 ts positive white yhw14.gif|center|250px]]
|-
|[[File:Ex1 ts positive yhw14.gif|center|250px]]
|-
|style="text-align: center;"|Lowest positive frequency (Please double click to see animation)
|}

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

[[File:Ex2 reactionscheme.png|550px|center|thumb|Diagram 4: Reaction Scheme of Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

Cyclohexadiene and 1,3-dioxole were optimised to their minima. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #9A03FE; color: #ffffff;" |'''Molecule'''
! '''Cyclohexadiene'''
! '''1,3-Dioxole'''
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Cyclo lumo 631g yhw14.png|center|150px]]
|[[File:Dioxole lumo 631g yhw14.png|center|150px]]
|-
|Corresponding to the orbital
|Corresponding to the orbital
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Cyclo homo 631g yhw14.png|center|150px]]
|[[File:Dioxole homo 631g yhw14.png|center|150px]]
|-
|Corresponding to the orbital
|Corresponding to the orbital
|}

The transition state was first optimised to its minimum, followed by a transition state calculation. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #BD5CFE; color: #ffffff;" |'''Molecule'''
! '''Endo Transition State'''
! '''Exo Transition State'''
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Endo ts lumo+1 yhw14.png|center|150px]]
|[[File:Exo ts lumo+1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Endo ts lumo yhw14.png|center|150px]]
|[[File:Exo ts lumo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Endo ts homo yhw14.png|center|150px]]
|[[File:Exo ts homo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Endo ts homo-1 yhw14.png|center|150px]]
|[[File:Exo ts homo-1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|}

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of cyclohexadiene and 1,3-dioxole.

[[File:|550px|center|thumb|Diagram 5: MO diagram of Reaction of Cyclohexadiene and 1,3-dioxole]]

=== Normal Demand vs Inverse Demand Diels-Alder Reaction ===

A normal electron demand Diels-Alder reaction can be defined as a reaction between electron rich diene and electron poor dienophile. An inverse electron demand is the reaction between electron poor diene and electron rich dienophile.

The LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are very close in energy, which results in strong bonding interaction between the two to form the HOMO and LUMO of both endo and exo TS. Since only the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole have the correct symmetry () to interact, they interact to form the __(symmetry) HOMO and LUMO of both TS.

This could be explained by the presence of electron rich O on 1,3-dioxole which raises the energy of both its HOMO and LUMO, making the overlap between the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole much better than the HOMO of cyclohexadiene and the LUMO of 1,3-dioxole. Thus, the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are now the frontier orbitals that interact the most, hence this is an inverse demand Diels-Alder reaction.

=== Reaction Energies and Secondary Orbital Interaction ===

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FF4AFF; color: #ffffff" |
! style="background: #FF4AFF; color: #ffffff" | Reactants
! style="background: #FF4AFF; color: #ffffff" | Transition State
! style="background: #FF4AFF; color: #ffffff" | Product
! style="background: #FF4AFF; color: #ffffff" | Activation Energy
! style="background: #FF4AFF; color: #ffffff" | Gibbs Free Energy
|-
|Endo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313622</nowiki>
|<nowiki>-1313849</nowiki>
|160
|<nowiki>-67</nowiki>
|-
|Exo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313614</nowiki>
|<nowiki>-1313846</nowiki>
|168
|<nowiki>-64</nowiki>
|+Table 2: Energies of Reactants, Transition States and Products of both Endo and Exo Pathways in Diels-Alder Reaction of Cyclohexadiene and 1,3-Dioxole (kJ mol-1)
|}

Kinetically favourable product of a reaction is the one that has the lowest activation energy; Thermodynamically favourable product is the product with lowest energy conformer, hence the more stabilised product.

The endo transition state is the kinetic product of this reaction as it has lower activation energy. This could be explained using the secondary orbital interaction between the lone pair orbital on the oxygen atom and the empty π* orbital of diene. This favourable effect stabilises the endo transition state.

As the oxygen atom lone pair is oriented away from the diene π system in the exo transition state, the secondary orbital effect is not present, hence the activation energy of exo reaction is higher.

However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, i.e. increasing temperature, formation of the exo product would be more favourable.

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

Xylylene can react with sulfur dioxide through Diels-Alder reaction via either endo or exo pathways to form a 6-membered ring, or through cheletropic reaction to form a 5-membered ring. The reaction scheme is shown below. Reaction barriers and reaction energies for each pathway are compared to determine the reaction that is most favourable.

[[File:Ex3 reactionscheme yhw14.png|550px|center|thumb|Diagram 6: Reaction Scheme of Xylylene and Sulfur Dioxide]]

=== Intrinsic Reaction Coordinate ===
The following files show the intrinsic reaction coordinates of the three different reaction pathways of xylylene and SO2. Please click to see animation.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Endo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Exo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Cheletropic TS
|-
|[[File:DA endo irc animation purple yhw14.gif|center|250px]]
|[[File:DA exo irc animation purple yhw14.gif|center|250px]]
|[[File: Ex3 Chele movie yhw14.gif|center|250px]]
|-
|[[File:Ex1 ts positive yhw14.gif|center|250px]]
|[[File:DA exo irc animation yhw14.gif|center|250px]]
|[[File:Cheletropic irc animation yhw14.gif|center|250px]]
|-
|[[File:DA endo irc plot yhw14.png|center|250px]]
|[[File:DA exo irc plot yhw14.png|center|250px]]
|[[File:Cheletropic irc plot yhw14.png|center|250px]]
|}

=== Reaction Energies and Reaction Barriers ===

[[File:Ex3 reactionprofile yhw14.png|550px|center|thumb|Diagram 7: Reaction Profile of Xylylene and Sulfur Dioxide]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FFD1C3; color: #ffffff" |
! style="background: #FFD1C3; color: #ffffff" | Reactants
! style="background: #FFD1C3; color: #ffffff" | Transition State
! style="background: #FFD1C3; color: #ffffff" | Product
! style="background: #FFD1C3; color: #ffffff" | Activation Energy
! style="background: #FFD1C3; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|237.767824
|56.9576013
|83.391038
|<nowiki>-97.4191847</nowiki>
|-
|Exo
|154.376786
|241.753433
|56.3196048
|87.406647
|<nowiki>-98.0571812</nowiki>
|-
|Cheletropic
|154.376786
|260.08205
|0.013127501
|105.705264
|<nowiki>-154.3636585</nowiki>
|+Table 3: Energies of Reactants, Transition States and Products of Reactions between Xylylene and Sulfur Dioxide (kJ mol-1)
|}

With reference to the reaction profile and table __, the Diels-Alder reaction via the endo pathway has the lowest activation energy, making it a more kinetically favourable product, i.e. the kinetic product; the Diels-Alder exo product has a lower energy than endo, however with a higher activation energy hence it will not form under low temperature condition; the cheletropic product is the most stabilised product out of the three and it has the lowest reaction energy, therefore is the thermodynamic product.

=== Side Reaction between cis-diene in Xylylene 6-membered ring and SO2===

o-Xylylene contains another cis-butadiene fragment located in the 6-membered ring that can undergo a Diels-Alder reaction with SO2. The reaction energies and reaction barriers between endo and exo pathways are compared in the table below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #4EBEBA; color: #ffffff" |
! style="background: #4EBEBA; color: #ffffff" | Reactants
! style="background: #4EBEBA; color: #ffffff" | Transition State
! style="background: #4EBEBA; color: #ffffff" | Product
! style="background: #4EBEBA; color: #ffffff" | Activation Energy
! style="background: #4EBEBA; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|267.984805
|172.272196
|113.608019
|17.89541
|-
|Exo
|154.376786
|275.821924
|176.711916
|121.445138
|22.33513
|+Table 4: Energies of Reactants, Transition States and Products of the Side Reaction in Xylylene 6-membered ring and Sulfur Dioxide (kJ mol-1)
|}

It is clear that both endo and exo Diels-Alder side reactions are kinetically and thermodynamically unfavourable at this site as the activation energies are much higher than the previous reactions mentioned above in table __ and the reaction energies show that the reactions are endothermic.

== Conclusion ==

The transition states of three pericyclic reactions were investigated in this computational lab, using Gaussian to optimise the reactants, transition states and products respectively, and the vibrational frequencies and intrinsic reaction coordinates were computed.

In the reaction between butadiene and ethene, the importance of molecular orbital symmetry in the interaction of molecular orbitals was illustrated, such that a reaction is only allowed when the molecular orbitals with the same symmetry labels interact with each other and forbidden when symmetric molecular orbital interact with asymmetric orbitals. Furthermore, the vibration frequency calculation proved that this [4+2] Diels-Alder reaction proceeds via a concerted mechanism as synchronous bond formation was demonstrated. Bonding interaction can be further confirmed as the bond distance between the two termini carbon atoms in the transition state is shorter than the sum of two Van der Waals radii of carbon.

In the reaction of cyclohexadiene and 1,3-dioxole, both the endo and exo transition states were investigated. In general, the endo transition state is kinetically more favourable as it has lower activation barrier, possibly due to the secondary orbital interaction between the lone pair in p orbital on the oxygen atom and the empty pi* orbital in the diene, which stabilises the transition state. However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, formation of the exo product could be possible.

The final reaction between xylylene and SO2 again proved that the endo Diels-Alder transition state has the lowest activation energy, making it kinetically favourable at low temperature. However, the cheletropic product is the most stabilised and thermodynamically favourable product. Therefore the reaction would yield the cheletropic product under thermodynamic control instead of the exo Diels-Alder product.

==References==
<references>
<ref name="C-C bond lengths">L. Pauling and L. O. Brockway, ''Journal of the American Chemical Society'', '''1937''', Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref>
<ref name="Van der Waals radius of C">S. S. Batsanov, ''Inorganic Materials'', '''2001''', Volume 37, Number 9, pp. 871-885, https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf.</ref>
</references>

Rep:Mod:yhw14cts

2017-02-09T17:56:04Z

Yhw14: /* Intrinsic Reaction Coordinate */

''' Transition States and Reactivity '''

'' Yi Hang Cherie WONG (yhw14) ''
'' CID: 00933828 ''

== Introduction ==
A potential energy surface is a mathematical function that gives the energy of a molecule as a function of its geometry with the relative positions of the atoms participating in the reaction. The stationary points may be classified according to the first and second derivatives of the energy with respect to position. At the minimum of a reaction profile, the first derivative of the reaction coordinate, which indicates the gradient, is zero, while the second derivative, which indicates curvature, is positive; hence energy rises in all directions. Energy minima correspond to physically stable chemical species, which could be reactants and products. The transition state is defined as the maximum in a reaction profile, where the gradient is again, zero, while curvature is negative, hence energy decreases in one direction, which indicates the reaction pathway of the chemical reaction. The potential energy surface can be computed using Gaussview 09, where structure and energy of reactants or products can be modelled to illustrate the transition states, which can rarely be obtained experimentally. The intrinsic reaction coordinate can then be calculated and compared to predict the reaction path at a transition state and follow it to the correct minima.

In this computational lab, all of the reactants and products were optimised to their minima, and the transition states were also optimised. The calculations were done by Gaussian 09, using mainly semi-empirical method PM6 and DFT-B3LYP. Frequency calculations were performed to show molecular vibrations to confirm the position on the potential energy surface. If all the vibrational frequencies are real, this confirms the structure is a minimum, and vice versa, the presence of imaginary frequency may suggest that the structure is at its transition state. Intrinsic reaction coordinate method was carried out using calculated force constants to predict which conformer a reaction path from the transition state would lead to.

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

The reaction between butadiene and ethene is a typical pericyclic [4+2] Diels-Alder reaction that proceeds via a concerted mechanism through a cyclic transition state. The reaction scheme is shown below.

[[File:Ex1 reactionscheme revised yhw14.png|550px|center|thumb|Diagram 1: Reaction Scheme of Butadiene and Ethene]]

=== Molecular Orbital Analysis ===

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of butadiene and ethene.

[[File:Ex1 mo diagram yhw14 revised v3.png|550px|center|thumb|Diagram 2: MO diagram of Reaction of Butadiene and Ethene]]

Butadiene and ethene were optimised to their minima. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #06DCFB; color: #ffffff;" |'''Molecule'''
! '''Butadiene'''
! '''Ethene'''
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Butadiene lumo yhw14.png|center|150px]]
|[[File:Ethene lumo yhw14.png|center|150px]]
|-
|Corresponding to the s orbital (symmetric)
|Corresponding to the a orbital (asymmetric)
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Butadiene homo yhw14.png|center|150px]]
|[[File:Ethene homo yhw14.png|center|150px]]
|-
|Corresponding to the a orbital (antisymmetric)
|Corresponding to the s orbital (symmetric)
|}

The transition state was first optimised to its minimum, followed by a transition state calculation. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #01FCEF; color: #ffffff;" |'''Molecule'''
! '''Transition State'''
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Ts lumo+1 yhw14.png|center|150px]]
|-
|Corresponding to the 5 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Ts lumo 1 yhw14.png|center|150px]]
|-
|Corresponding to the 4 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Ts homo yhw14.png|center|150px]]
|-
|Corresponding to the 3 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Ts homo-1 yhw14.png|center|150px]]
|-
|Corresponding to the 2 orbital
|}

Based on the MO diagram and the computed MOs shown above, a reaction is only allowed when the MOs with the same symmetry labels interact with each other, i.e. symmetric-symmetric and asymmetric-asymmetric interactions; and a reaction is forbidden when the MOs with different symmetry labels interact with each other, i.e. symmetric-asymmetric interactions.
In the reaction between butadiene and ethene, the butadiene asymmetric MO interacts with the ethene asymmetric MO to give the 2 and 5 MOs of the transition state, and the butadiene symmetric MO interacts with the ethene symmetric MO to give the 3 and 4 MOs of the transition state. Therefore, a reaction is allowed when the symmetry labels of the MOs of the reactants are the same; and forbidden when the symmetry labels are different.

The orbital overlap integral is zero in a symmetric-asymmetric interaction and non-zero in symmetric-symmetric and asymmetric-asymmetric interactions.

=== Bond Length Analysis ===

The changes in bond lengths between carbons in reactant, transition state and product as the reaction progresses were studied by comparing the bond lengths between carbons before and after the reaction. The summary of bond lengths is shown below.
[[File:Ex1 bondlength yhw14.png|470px|center|thumb|Diagram 3: Labelled carbons]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #0000FF; color: #ffffff" | State
! style="background: #0000FF; color: #ffffff" | C1-C2
! style="background: #0000FF; color: #ffffff" | C2-C3
! style="background: #0000FF; color: #ffffff" | C3-C4
! style="background: #0000FF; color: #ffffff" | C4-C5
! style="background: #0000FF; color: #ffffff" | C5-C6
! style="background: #0000FF; color: #ffffff" | C6-C1
|-
|Reactants
|1.335
|1.468
|1.335
|/
|1.327
|/
|-
|Transition State
|1.380
|1.411
|1.380
|2.115
|1.382
|2.114
|-
|Product
|1.500
|1.338
|1.500
|1.540
|1.540
|1.540
|+Table 1: Measurements of the C-C bond lengths of the reactants, transition state and products (Å)
|}
As the reaction progresses, the bond lengths between C1-C2, C3-C4 and C5-C6 increase from ~1.3 Å to ~1.5 Å as the bond order decrease to one, whereas bond length of C2-C3 decreases from ~1.5 Å to ~1.3 Å as the bond order increases from one to two.
This could be explained as the increase in bond length suggest a change from sp2-sp2 (C-C double bond) with typical bond length of 1.33 Å <ref name="C-C bond lengths"/> to sp3-sp3 (C-C single bond) with typical bond length of 1.54 Å <ref name="C-C bond lengths"/>, and vice versa for the decrease in bond length. Based on the calculated bond lengths above in Table 1, it is clear that bond lengths and bond orders of the reactants changed during the reaction and the new bonds formed at C4-C5 and C6-C1 are single bonds as they have bond lengths of 1.54 Å.
The typical Van der Waals radius of the C atom is 1.7 Å <ref name="Van der Waals radius of C"/>. As the bond lengths between C4-C5 and C6-C1 of the transition state are shorter than 2 x Van der Waals radii of C, this reflects that C-C bonds are forming at the transition state.

=== Vibration Analysis ===

The imaginary frequency at -948.32 cm-1 corresponds to the reaction path at the transition state, which shows a synchronous bond formation, which agrees with the concerted mechanism of [4+2] cycloaddition, where both reaction centres converge at the same time to form bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|[[File:Ex1 ts imaginary white yhw14.gif|center|250px]]
|-
|[[File:Ex1 ts imaginary yhw14.gif|center|250px]]
|-
|style="text-align: center;"|Reaction Path at the Transition State (Please double click to see animation)
|}

The lowest positive frequency at 145.14 cm-1 is asynchronous as shown below, where one of the C from the ethene moves towards the butadiene reaction centre and the other C moves away. This suggests that bonds are formed one at a time.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|[[File:Ex1 ts positive white yhw14.gif|center|250px]]
|-
|[[File:Ex1 ts positive yhw14.gif|center|250px]]
|-
|style="text-align: center;"|Lowest positive frequency (Please double click to see animation)
|}

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

[[File:Ex2 reactionscheme.png|550px|center|thumb|Diagram 4: Reaction Scheme of Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

Cyclohexadiene and 1,3-dioxole were optimised to their minima. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #9A03FE; color: #ffffff;" |'''Molecule'''
! '''Cyclohexadiene'''
! '''1,3-Dioxole'''
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Cyclo lumo 631g yhw14.png|center|150px]]
|[[File:Dioxole lumo 631g yhw14.png|center|150px]]
|-
|Corresponding to the orbital
|Corresponding to the orbital
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Cyclo homo 631g yhw14.png|center|150px]]
|[[File:Dioxole homo 631g yhw14.png|center|150px]]
|-
|Corresponding to the orbital
|Corresponding to the orbital
|}

The transition state was first optimised to its minimum, followed by a transition state calculation. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #BD5CFE; color: #ffffff;" |'''Molecule'''
! '''Endo Transition State'''
! '''Exo Transition State'''
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Endo ts lumo+1 yhw14.png|center|150px]]
|[[File:Exo ts lumo+1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Endo ts lumo yhw14.png|center|150px]]
|[[File:Exo ts lumo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Endo ts homo yhw14.png|center|150px]]
|[[File:Exo ts homo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Endo ts homo-1 yhw14.png|center|150px]]
|[[File:Exo ts homo-1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|}

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of cyclohexadiene and 1,3-dioxole.

[[File:|550px|center|thumb|Diagram 5: MO diagram of Reaction of Cyclohexadiene and 1,3-dioxole]]

=== Normal Demand vs Inverse Demand Diels-Alder Reaction ===

A normal electron demand Diels-Alder reaction can be defined as a reaction between electron rich diene and electron poor dienophile. An inverse electron demand is the reaction between electron poor diene and electron rich dienophile.

The LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are very close in energy, which results in strong bonding interaction between the two to form the HOMO and LUMO of both endo and exo TS. Since only the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole have the correct symmetry () to interact, they interact to form the __(symmetry) HOMO and LUMO of both TS.

This could be explained by the presence of electron rich O on 1,3-dioxole which raises the energy of both its HOMO and LUMO, making the overlap between the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole much better than the HOMO of cyclohexadiene and the LUMO of 1,3-dioxole. Thus, the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are now the frontier orbitals that interact the most, hence this is an inverse demand Diels-Alder reaction.

=== Reaction Energies and Secondary Orbital Interaction ===

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FF4AFF; color: #ffffff" |
! style="background: #FF4AFF; color: #ffffff" | Reactants
! style="background: #FF4AFF; color: #ffffff" | Transition State
! style="background: #FF4AFF; color: #ffffff" | Product
! style="background: #FF4AFF; color: #ffffff" | Activation Energy
! style="background: #FF4AFF; color: #ffffff" | Gibbs Free Energy
|-
|Endo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313622</nowiki>
|<nowiki>-1313849</nowiki>
|160
|<nowiki>-67</nowiki>
|-
|Exo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313614</nowiki>
|<nowiki>-1313846</nowiki>
|168
|<nowiki>-64</nowiki>
|+Table 2: Energies of Reactants, Transition States and Products of both Endo and Exo Pathways in Diels-Alder Reaction of Cyclohexadiene and 1,3-Dioxole (kJ mol-1)
|}

Kinetically favourable product of a reaction is the one that has the lowest activation energy; Thermodynamically favourable product is the product with lowest energy conformer, hence the more stabilised product.

The endo transition state is the kinetic product of this reaction as it has lower activation energy. This could be explained using the secondary orbital interaction between the lone pair orbital on the oxygen atom and the empty π* orbital of diene. This favourable effect stabilises the endo transition state.

As the oxygen atom lone pair is oriented away from the diene π system in the exo transition state, the secondary orbital effect is not present, hence the activation energy of exo reaction is higher.

However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, i.e. increasing temperature, formation of the exo product would be more favourable.

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

Xylylene can react with sulfur dioxide through Diels-Alder reaction via either endo or exo pathways to form a 6-membered ring, or through cheletropic reaction to form a 5-membered ring. The reaction scheme is shown below. Reaction barriers and reaction energies for each pathway are compared to determine the reaction that is most favourable.

[[File:Ex3 reactionscheme yhw14.png|550px|center|thumb|Diagram 6: Reaction Scheme of Xylylene and Sulfur Dioxide]]

=== Intrinsic Reaction Coordinate ===
The following files show the intrinsic reaction coordinates of the three different reaction pathways of xylylene and SO2. Please click to see animation.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Endo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Exo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Cheletropic TS
|-
|[[File:DA endo irc animation purple yhw14.gif|center|200px]]
|[[File:DA exo irc animation purple yhw14.gif|center|200px]]
|[[File: Ex3 Chele movie yhw14.gif|center|200px]]
|-
|[[File:Ex1 ts positive yhw14.gif|center|200px]]
|[[File:DA exo irc animation yhw14.gif|center|200px]]
|[[File:Cheletropic irc animation yhw14.gif|center|200px]]
|-
|[[File:DA endo irc plot yhw14.png|center|200px]]
|[[File:DA exo irc plot yhw14.png|center|200px]]
|[[File:Cheletropic irc plot yhw14.png|center|200px]]
|}

=== Reaction Energies and Reaction Barriers ===

[[File:Ex3 reactionprofile yhw14.png|550px|center|thumb|Diagram 7: Reaction Profile of Xylylene and Sulfur Dioxide]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FFD1C3; color: #ffffff" |
! style="background: #FFD1C3; color: #ffffff" | Reactants
! style="background: #FFD1C3; color: #ffffff" | Transition State
! style="background: #FFD1C3; color: #ffffff" | Product
! style="background: #FFD1C3; color: #ffffff" | Activation Energy
! style="background: #FFD1C3; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|237.767824
|56.9576013
|83.391038
|<nowiki>-97.4191847</nowiki>
|-
|Exo
|154.376786
|241.753433
|56.3196048
|87.406647
|<nowiki>-98.0571812</nowiki>
|-
|Cheletropic
|154.376786
|260.08205
|0.013127501
|105.705264
|<nowiki>-154.3636585</nowiki>
|+Table 3: Energies of Reactants, Transition States and Products of Reactions between Xylylene and Sulfur Dioxide (kJ mol-1)
|}

With reference to the reaction profile and table __, the Diels-Alder reaction via the endo pathway has the lowest activation energy, making it a more kinetically favourable product, i.e. the kinetic product; the Diels-Alder exo product has a lower energy than endo, however with a higher activation energy hence it will not form under low temperature condition; the cheletropic product is the most stabilised product out of the three and it has the lowest reaction energy, therefore is the thermodynamic product.

=== Side Reaction between cis-diene in Xylylene 6-membered ring and SO2===

o-Xylylene contains another cis-butadiene fragment located in the 6-membered ring that can undergo a Diels-Alder reaction with SO2. The reaction energies and reaction barriers between endo and exo pathways are compared in the table below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #4EBEBA; color: #ffffff" |
! style="background: #4EBEBA; color: #ffffff" | Reactants
! style="background: #4EBEBA; color: #ffffff" | Transition State
! style="background: #4EBEBA; color: #ffffff" | Product
! style="background: #4EBEBA; color: #ffffff" | Activation Energy
! style="background: #4EBEBA; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|267.984805
|172.272196
|113.608019
|17.89541
|-
|Exo
|154.376786
|275.821924
|176.711916
|121.445138
|22.33513
|+Table 4: Energies of Reactants, Transition States and Products of the Side Reaction in Xylylene 6-membered ring and Sulfur Dioxide (kJ mol-1)
|}

It is clear that both endo and exo Diels-Alder side reactions are kinetically and thermodynamically unfavourable at this site as the activation energies are much higher than the previous reactions mentioned above in table __ and the reaction energies show that the reactions are endothermic.

== Conclusion ==

The transition states of three pericyclic reactions were investigated in this computational lab, using Gaussian to optimise the reactants, transition states and products respectively, and the vibrational frequencies and intrinsic reaction coordinates were computed.

In the reaction between butadiene and ethene, the importance of molecular orbital symmetry in the interaction of molecular orbitals was illustrated, such that a reaction is only allowed when the molecular orbitals with the same symmetry labels interact with each other and forbidden when symmetric molecular orbital interact with asymmetric orbitals. Furthermore, the vibration frequency calculation proved that this [4+2] Diels-Alder reaction proceeds via a concerted mechanism as synchronous bond formation was demonstrated. Bonding interaction can be further confirmed as the bond distance between the two termini carbon atoms in the transition state is shorter than the sum of two Van der Waals radii of carbon.

In the reaction of cyclohexadiene and 1,3-dioxole, both the endo and exo transition states were investigated. In general, the endo transition state is kinetically more favourable as it has lower activation barrier, possibly due to the secondary orbital interaction between the lone pair in p orbital on the oxygen atom and the empty pi* orbital in the diene, which stabilises the transition state. However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, formation of the exo product could be possible.

The final reaction between xylylene and SO2 again proved that the endo Diels-Alder transition state has the lowest activation energy, making it kinetically favourable at low temperature. However, the cheletropic product is the most stabilised and thermodynamically favourable product. Therefore the reaction would yield the cheletropic product under thermodynamic control instead of the exo Diels-Alder product.

==References==
<references>
<ref name="C-C bond lengths">L. Pauling and L. O. Brockway, ''Journal of the American Chemical Society'', '''1937''', Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref>
<ref name="Van der Waals radius of C">S. S. Batsanov, ''Inorganic Materials'', '''2001''', Volume 37, Number 9, pp. 871-885, https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf.</ref>
</references>

File:Ex3 Chele movie yhw14.gif

2017-02-09T17:48:40Z

Yhw14:

File:DA endo irc animation yhw14.gif

2017-02-09T17:43:36Z

Yhw14: Yhw14 uploaded a new version of File:DA endo irc animation yhw14.gif

File:Cheletropic irc animation yhw14.gif

2017-02-09T17:43:35Z

Yhw14: Yhw14 uploaded a new version of File:Cheletropic irc animation yhw14.gif

Rep:Mod:yhw14cts

2017-02-09T17:30:57Z

Yhw14: /* Vibration Analysis */

''' Transition States and Reactivity '''

'' Yi Hang Cherie WONG (yhw14) ''
'' CID: 00933828 ''

== Introduction ==
A potential energy surface is a mathematical function that gives the energy of a molecule as a function of its geometry with the relative positions of the atoms participating in the reaction. The stationary points may be classified according to the first and second derivatives of the energy with respect to position. At the minimum of a reaction profile, the first derivative of the reaction coordinate, which indicates the gradient, is zero, while the second derivative, which indicates curvature, is positive; hence energy rises in all directions. Energy minima correspond to physically stable chemical species, which could be reactants and products. The transition state is defined as the maximum in a reaction profile, where the gradient is again, zero, while curvature is negative, hence energy decreases in one direction, which indicates the reaction pathway of the chemical reaction. The potential energy surface can be computed using Gaussview 09, where structure and energy of reactants or products can be modelled to illustrate the transition states, which can rarely be obtained experimentally. The intrinsic reaction coordinate can then be calculated and compared to predict the reaction path at a transition state and follow it to the correct minima.

In this computational lab, all of the reactants and products were optimised to their minima, and the transition states were also optimised. The calculations were done by Gaussian 09, using mainly semi-empirical method PM6 and DFT-B3LYP. Frequency calculations were performed to show molecular vibrations to confirm the position on the potential energy surface. If all the vibrational frequencies are real, this confirms the structure is a minimum, and vice versa, the presence of imaginary frequency may suggest that the structure is at its transition state. Intrinsic reaction coordinate method was carried out using calculated force constants to predict which conformer a reaction path from the transition state would lead to.

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

The reaction between butadiene and ethene is a typical pericyclic [4+2] Diels-Alder reaction that proceeds via a concerted mechanism through a cyclic transition state. The reaction scheme is shown below.

[[File:Ex1 reactionscheme revised yhw14.png|550px|center|thumb|Diagram 1: Reaction Scheme of Butadiene and Ethene]]

=== Molecular Orbital Analysis ===

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of butadiene and ethene.

[[File:Ex1 mo diagram yhw14 revised v3.png|550px|center|thumb|Diagram 2: MO diagram of Reaction of Butadiene and Ethene]]

Butadiene and ethene were optimised to their minima. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #06DCFB; color: #ffffff;" |'''Molecule'''
! '''Butadiene'''
! '''Ethene'''
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Butadiene lumo yhw14.png|center|150px]]
|[[File:Ethene lumo yhw14.png|center|150px]]
|-
|Corresponding to the s orbital (symmetric)
|Corresponding to the a orbital (asymmetric)
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Butadiene homo yhw14.png|center|150px]]
|[[File:Ethene homo yhw14.png|center|150px]]
|-
|Corresponding to the a orbital (antisymmetric)
|Corresponding to the s orbital (symmetric)
|}

The transition state was first optimised to its minimum, followed by a transition state calculation. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #01FCEF; color: #ffffff;" |'''Molecule'''
! '''Transition State'''
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Ts lumo+1 yhw14.png|center|150px]]
|-
|Corresponding to the 5 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Ts lumo 1 yhw14.png|center|150px]]
|-
|Corresponding to the 4 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Ts homo yhw14.png|center|150px]]
|-
|Corresponding to the 3 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Ts homo-1 yhw14.png|center|150px]]
|-
|Corresponding to the 2 orbital
|}

Based on the MO diagram and the computed MOs shown above, a reaction is only allowed when the MOs with the same symmetry labels interact with each other, i.e. symmetric-symmetric and asymmetric-asymmetric interactions; and a reaction is forbidden when the MOs with different symmetry labels interact with each other, i.e. symmetric-asymmetric interactions.
In the reaction between butadiene and ethene, the butadiene asymmetric MO interacts with the ethene asymmetric MO to give the 2 and 5 MOs of the transition state, and the butadiene symmetric MO interacts with the ethene symmetric MO to give the 3 and 4 MOs of the transition state. Therefore, a reaction is allowed when the symmetry labels of the MOs of the reactants are the same; and forbidden when the symmetry labels are different.

The orbital overlap integral is zero in a symmetric-asymmetric interaction and non-zero in symmetric-symmetric and asymmetric-asymmetric interactions.

=== Bond Length Analysis ===

The changes in bond lengths between carbons in reactant, transition state and product as the reaction progresses were studied by comparing the bond lengths between carbons before and after the reaction. The summary of bond lengths is shown below.
[[File:Ex1 bondlength yhw14.png|470px|center|thumb|Diagram 3: Labelled carbons]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #0000FF; color: #ffffff" | State
! style="background: #0000FF; color: #ffffff" | C1-C2
! style="background: #0000FF; color: #ffffff" | C2-C3
! style="background: #0000FF; color: #ffffff" | C3-C4
! style="background: #0000FF; color: #ffffff" | C4-C5
! style="background: #0000FF; color: #ffffff" | C5-C6
! style="background: #0000FF; color: #ffffff" | C6-C1
|-
|Reactants
|1.335
|1.468
|1.335
|/
|1.327
|/
|-
|Transition State
|1.380
|1.411
|1.380
|2.115
|1.382
|2.114
|-
|Product
|1.500
|1.338
|1.500
|1.540
|1.540
|1.540
|+Table 1: Measurements of the C-C bond lengths of the reactants, transition state and products (Å)
|}
As the reaction progresses, the bond lengths between C1-C2, C3-C4 and C5-C6 increase from ~1.3 Å to ~1.5 Å as the bond order decrease to one, whereas bond length of C2-C3 decreases from ~1.5 Å to ~1.3 Å as the bond order increases from one to two.
This could be explained as the increase in bond length suggest a change from sp2-sp2 (C-C double bond) with typical bond length of 1.33 Å <ref name="C-C bond lengths"/> to sp3-sp3 (C-C single bond) with typical bond length of 1.54 Å <ref name="C-C bond lengths"/>, and vice versa for the decrease in bond length. Based on the calculated bond lengths above in Table 1, it is clear that bond lengths and bond orders of the reactants changed during the reaction and the new bonds formed at C4-C5 and C6-C1 are single bonds as they have bond lengths of 1.54 Å.
The typical Van der Waals radius of the C atom is 1.7 Å <ref name="Van der Waals radius of C"/>. As the bond lengths between C4-C5 and C6-C1 of the transition state are shorter than 2 x Van der Waals radii of C, this reflects that C-C bonds are forming at the transition state.

=== Vibration Analysis ===

The imaginary frequency at -948.32 cm-1 corresponds to the reaction path at the transition state, which shows a synchronous bond formation, which agrees with the concerted mechanism of [4+2] cycloaddition, where both reaction centres converge at the same time to form bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|[[File:Ex1 ts imaginary white yhw14.gif|center|250px]]
|-
|[[File:Ex1 ts imaginary yhw14.gif|center|250px]]
|-
|style="text-align: center;"|Reaction Path at the Transition State (Please double click to see animation)
|}

The lowest positive frequency at 145.14 cm-1 is asynchronous as shown below, where one of the C from the ethene moves towards the butadiene reaction centre and the other C moves away. This suggests that bonds are formed one at a time.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|[[File:Ex1 ts positive white yhw14.gif|center|250px]]
|-
|[[File:Ex1 ts positive yhw14.gif|center|250px]]
|-
|style="text-align: center;"|Lowest positive frequency (Please double click to see animation)
|}

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

[[File:Ex2 reactionscheme.png|550px|center|thumb|Diagram 4: Reaction Scheme of Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

Cyclohexadiene and 1,3-dioxole were optimised to their minima. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #9A03FE; color: #ffffff;" |'''Molecule'''
! '''Cyclohexadiene'''
! '''1,3-Dioxole'''
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Cyclo lumo 631g yhw14.png|center|150px]]
|[[File:Dioxole lumo 631g yhw14.png|center|150px]]
|-
|Corresponding to the orbital
|Corresponding to the orbital
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Cyclo homo 631g yhw14.png|center|150px]]
|[[File:Dioxole homo 631g yhw14.png|center|150px]]
|-
|Corresponding to the orbital
|Corresponding to the orbital
|}

The transition state was first optimised to its minimum, followed by a transition state calculation. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #BD5CFE; color: #ffffff;" |'''Molecule'''
! '''Endo Transition State'''
! '''Exo Transition State'''
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Endo ts lumo+1 yhw14.png|center|150px]]
|[[File:Exo ts lumo+1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Endo ts lumo yhw14.png|center|150px]]
|[[File:Exo ts lumo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Endo ts homo yhw14.png|center|150px]]
|[[File:Exo ts homo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Endo ts homo-1 yhw14.png|center|150px]]
|[[File:Exo ts homo-1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|}

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of cyclohexadiene and 1,3-dioxole.

[[File:|550px|center|thumb|Diagram 5: MO diagram of Reaction of Cyclohexadiene and 1,3-dioxole]]

=== Normal Demand vs Inverse Demand Diels-Alder Reaction ===

A normal electron demand Diels-Alder reaction can be defined as a reaction between electron rich diene and electron poor dienophile. An inverse electron demand is the reaction between electron poor diene and electron rich dienophile.

The LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are very close in energy, which results in strong bonding interaction between the two to form the HOMO and LUMO of both endo and exo TS. Since only the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole have the correct symmetry () to interact, they interact to form the __(symmetry) HOMO and LUMO of both TS.

This could be explained by the presence of electron rich O on 1,3-dioxole which raises the energy of both its HOMO and LUMO, making the overlap between the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole much better than the HOMO of cyclohexadiene and the LUMO of 1,3-dioxole. Thus, the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are now the frontier orbitals that interact the most, hence this is an inverse demand Diels-Alder reaction.

=== Reaction Energies and Secondary Orbital Interaction ===

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FF4AFF; color: #ffffff" |
! style="background: #FF4AFF; color: #ffffff" | Reactants
! style="background: #FF4AFF; color: #ffffff" | Transition State
! style="background: #FF4AFF; color: #ffffff" | Product
! style="background: #FF4AFF; color: #ffffff" | Activation Energy
! style="background: #FF4AFF; color: #ffffff" | Gibbs Free Energy
|-
|Endo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313622</nowiki>
|<nowiki>-1313849</nowiki>
|160
|<nowiki>-67</nowiki>
|-
|Exo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313614</nowiki>
|<nowiki>-1313846</nowiki>
|168
|<nowiki>-64</nowiki>
|+Table 2: Energies of Reactants, Transition States and Products of both Endo and Exo Pathways in Diels-Alder Reaction of Cyclohexadiene and 1,3-Dioxole (kJ mol-1)
|}

Kinetically favourable product of a reaction is the one that has the lowest activation energy; Thermodynamically favourable product is the product with lowest energy conformer, hence the more stabilised product.

The endo transition state is the kinetic product of this reaction as it has lower activation energy. This could be explained using the secondary orbital interaction between the lone pair orbital on the oxygen atom and the empty π* orbital of diene. This favourable effect stabilises the endo transition state.

As the oxygen atom lone pair is oriented away from the diene π system in the exo transition state, the secondary orbital effect is not present, hence the activation energy of exo reaction is higher.

However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, i.e. increasing temperature, formation of the exo product would be more favourable.

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

Xylylene can react with sulfur dioxide through Diels-Alder reaction via either endo or exo pathways to form a 6-membered ring, or through cheletropic reaction to form a 5-membered ring. The reaction scheme is shown below. Reaction barriers and reaction energies for each pathway are compared to determine the reaction that is most favourable.

[[File:Ex3 reactionscheme yhw14.png|550px|center|thumb|Diagram 6: Reaction Scheme of Xylylene and Sulfur Dioxide]]

=== Intrinsic Reaction Coordinate ===
The following files show the intrinsic reaction coordinates of the three different reaction pathways of xylylene and SO2. Please click to see animation.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Endo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Exo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Cheletropic TS
|-
|[[File:DA endo irc animation purple yhw14.gif|center|200px]]
|[[File:DA exo irc animation purple yhw14.gif|center|200px]]
|[[File:Cheletropic irc animation purple yhw14.gif|center|200px]]
|-
|[[File:DA endo irc animation yhw14.gif|center|200px]]
|[[File:DA exo irc animation yhw14.gif|center|200px]]
|[[File:Cheletropic irc animation yhw14.gif|center|200px]]
|-
|[[File:DA endo irc plot yhw14.png|center|200px]]
|[[File:DA exo irc plot yhw14.png|center|200px]]
|[[File:Cheletropic irc plot yhw14.png|center|200px]]
|}

=== Reaction Energies and Reaction Barriers ===

[[File:Ex3 reactionprofile yhw14.png|550px|center|thumb|Diagram 7: Reaction Profile of Xylylene and Sulfur Dioxide]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FFD1C3; color: #ffffff" |
! style="background: #FFD1C3; color: #ffffff" | Reactants
! style="background: #FFD1C3; color: #ffffff" | Transition State
! style="background: #FFD1C3; color: #ffffff" | Product
! style="background: #FFD1C3; color: #ffffff" | Activation Energy
! style="background: #FFD1C3; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|237.767824
|56.9576013
|83.391038
|<nowiki>-97.4191847</nowiki>
|-
|Exo
|154.376786
|241.753433
|56.3196048
|87.406647
|<nowiki>-98.0571812</nowiki>
|-
|Cheletropic
|154.376786
|260.08205
|0.013127501
|105.705264
|<nowiki>-154.3636585</nowiki>
|+Table 3: Energies of Reactants, Transition States and Products of Reactions between Xylylene and Sulfur Dioxide (kJ mol-1)
|}

With reference to the reaction profile and table __, the Diels-Alder reaction via the endo pathway has the lowest activation energy, making it a more kinetically favourable product, i.e. the kinetic product; the Diels-Alder exo product has a lower energy than endo, however with a higher activation energy hence it will not form under low temperature condition; the cheletropic product is the most stabilised product out of the three and it has the lowest reaction energy, therefore is the thermodynamic product.

=== Side Reaction between cis-diene in Xylylene 6-membered ring and SO2===

o-Xylylene contains another cis-butadiene fragment located in the 6-membered ring that can undergo a Diels-Alder reaction with SO2. The reaction energies and reaction barriers between endo and exo pathways are compared in the table below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #4EBEBA; color: #ffffff" |
! style="background: #4EBEBA; color: #ffffff" | Reactants
! style="background: #4EBEBA; color: #ffffff" | Transition State
! style="background: #4EBEBA; color: #ffffff" | Product
! style="background: #4EBEBA; color: #ffffff" | Activation Energy
! style="background: #4EBEBA; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|267.984805
|172.272196
|113.608019
|17.89541
|-
|Exo
|154.376786
|275.821924
|176.711916
|121.445138
|22.33513
|+Table 4: Energies of Reactants, Transition States and Products of the Side Reaction in Xylylene 6-membered ring and Sulfur Dioxide (kJ mol-1)
|}

It is clear that both endo and exo Diels-Alder side reactions are kinetically and thermodynamically unfavourable at this site as the activation energies are much higher than the previous reactions mentioned above in table __ and the reaction energies show that the reactions are endothermic.

== Conclusion ==

The transition states of three pericyclic reactions were investigated in this computational lab, using Gaussian to optimise the reactants, transition states and products respectively, and the vibrational frequencies and intrinsic reaction coordinates were computed.

In the reaction between butadiene and ethene, the importance of molecular orbital symmetry in the interaction of molecular orbitals was illustrated, such that a reaction is only allowed when the molecular orbitals with the same symmetry labels interact with each other and forbidden when symmetric molecular orbital interact with asymmetric orbitals. Furthermore, the vibration frequency calculation proved that this [4+2] Diels-Alder reaction proceeds via a concerted mechanism as synchronous bond formation was demonstrated. Bonding interaction can be further confirmed as the bond distance between the two termini carbon atoms in the transition state is shorter than the sum of two Van der Waals radii of carbon.

In the reaction of cyclohexadiene and 1,3-dioxole, both the endo and exo transition states were investigated. In general, the endo transition state is kinetically more favourable as it has lower activation barrier, possibly due to the secondary orbital interaction between the lone pair in p orbital on the oxygen atom and the empty pi* orbital in the diene, which stabilises the transition state. However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, formation of the exo product could be possible.

The final reaction between xylylene and SO2 again proved that the endo Diels-Alder transition state has the lowest activation energy, making it kinetically favourable at low temperature. However, the cheletropic product is the most stabilised and thermodynamically favourable product. Therefore the reaction would yield the cheletropic product under thermodynamic control instead of the exo Diels-Alder product.

==References==
<references>
<ref name="C-C bond lengths">L. Pauling and L. O. Brockway, ''Journal of the American Chemical Society'', '''1937''', Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref>
<ref name="Van der Waals radius of C">S. S. Batsanov, ''Inorganic Materials'', '''2001''', Volume 37, Number 9, pp. 871-885, https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf.</ref>
</references>

File:Ex1 ts imaginary yhw14.gif

2017-02-09T17:28:24Z

Yhw14:

File:Ex1 ts positive yhw14.gif

2017-02-09T17:28:24Z

Yhw14:

File:Ex1 ts positive white yhw14.gif

2017-02-09T17:28:23Z

Yhw14:

File:Ex1 ts imaginary white yhw14.gif

2017-02-09T17:28:23Z

Yhw14:

Rep:Mod:yhw14cts

2017-02-09T17:19:35Z

Yhw14: /* Molecular Orbital Analysis */

''' Transition States and Reactivity '''

'' Yi Hang Cherie WONG (yhw14) ''
'' CID: 00933828 ''

== Introduction ==
A potential energy surface is a mathematical function that gives the energy of a molecule as a function of its geometry with the relative positions of the atoms participating in the reaction. The stationary points may be classified according to the first and second derivatives of the energy with respect to position. At the minimum of a reaction profile, the first derivative of the reaction coordinate, which indicates the gradient, is zero, while the second derivative, which indicates curvature, is positive; hence energy rises in all directions. Energy minima correspond to physically stable chemical species, which could be reactants and products. The transition state is defined as the maximum in a reaction profile, where the gradient is again, zero, while curvature is negative, hence energy decreases in one direction, which indicates the reaction pathway of the chemical reaction. The potential energy surface can be computed using Gaussview 09, where structure and energy of reactants or products can be modelled to illustrate the transition states, which can rarely be obtained experimentally. The intrinsic reaction coordinate can then be calculated and compared to predict the reaction path at a transition state and follow it to the correct minima.

In this computational lab, all of the reactants and products were optimised to their minima, and the transition states were also optimised. The calculations were done by Gaussian 09, using mainly semi-empirical method PM6 and DFT-B3LYP. Frequency calculations were performed to show molecular vibrations to confirm the position on the potential energy surface. If all the vibrational frequencies are real, this confirms the structure is a minimum, and vice versa, the presence of imaginary frequency may suggest that the structure is at its transition state. Intrinsic reaction coordinate method was carried out using calculated force constants to predict which conformer a reaction path from the transition state would lead to.

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

The reaction between butadiene and ethene is a typical pericyclic [4+2] Diels-Alder reaction that proceeds via a concerted mechanism through a cyclic transition state. The reaction scheme is shown below.

[[File:Ex1 reactionscheme revised yhw14.png|550px|center|thumb|Diagram 1: Reaction Scheme of Butadiene and Ethene]]

=== Molecular Orbital Analysis ===

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of butadiene and ethene.

[[File:Ex1 mo diagram yhw14 revised v3.png|550px|center|thumb|Diagram 2: MO diagram of Reaction of Butadiene and Ethene]]

Butadiene and ethene were optimised to their minima. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #06DCFB; color: #ffffff;" |'''Molecule'''
! '''Butadiene'''
! '''Ethene'''
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Butadiene lumo yhw14.png|center|150px]]
|[[File:Ethene lumo yhw14.png|center|150px]]
|-
|Corresponding to the s orbital (symmetric)
|Corresponding to the a orbital (asymmetric)
|-
| style="background: #06DCFB; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Butadiene homo yhw14.png|center|150px]]
|[[File:Ethene homo yhw14.png|center|150px]]
|-
|Corresponding to the a orbital (antisymmetric)
|Corresponding to the s orbital (symmetric)
|}

The transition state was first optimised to its minimum, followed by a transition state calculation. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #01FCEF; color: #ffffff;" |'''Molecule'''
! '''Transition State'''
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Ts lumo+1 yhw14.png|center|150px]]
|-
|Corresponding to the 5 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Ts lumo 1 yhw14.png|center|150px]]
|-
|Corresponding to the 4 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Ts homo yhw14.png|center|150px]]
|-
|Corresponding to the 3 orbital
|-
| style="background: #01FCEF; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Ts homo-1 yhw14.png|center|150px]]
|-
|Corresponding to the 2 orbital
|}

Based on the MO diagram and the computed MOs shown above, a reaction is only allowed when the MOs with the same symmetry labels interact with each other, i.e. symmetric-symmetric and asymmetric-asymmetric interactions; and a reaction is forbidden when the MOs with different symmetry labels interact with each other, i.e. symmetric-asymmetric interactions.
In the reaction between butadiene and ethene, the butadiene asymmetric MO interacts with the ethene asymmetric MO to give the 2 and 5 MOs of the transition state, and the butadiene symmetric MO interacts with the ethene symmetric MO to give the 3 and 4 MOs of the transition state. Therefore, a reaction is allowed when the symmetry labels of the MOs of the reactants are the same; and forbidden when the symmetry labels are different.

The orbital overlap integral is zero in a symmetric-asymmetric interaction and non-zero in symmetric-symmetric and asymmetric-asymmetric interactions.

=== Bond Length Analysis ===

The changes in bond lengths between carbons in reactant, transition state and product as the reaction progresses were studied by comparing the bond lengths between carbons before and after the reaction. The summary of bond lengths is shown below.
[[File:Ex1 bondlength yhw14.png|470px|center|thumb|Diagram 3: Labelled carbons]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #0000FF; color: #ffffff" | State
! style="background: #0000FF; color: #ffffff" | C1-C2
! style="background: #0000FF; color: #ffffff" | C2-C3
! style="background: #0000FF; color: #ffffff" | C3-C4
! style="background: #0000FF; color: #ffffff" | C4-C5
! style="background: #0000FF; color: #ffffff" | C5-C6
! style="background: #0000FF; color: #ffffff" | C6-C1
|-
|Reactants
|1.335
|1.468
|1.335
|/
|1.327
|/
|-
|Transition State
|1.380
|1.411
|1.380
|2.115
|1.382
|2.114
|-
|Product
|1.500
|1.338
|1.500
|1.540
|1.540
|1.540
|+Table 1: Measurements of the C-C bond lengths of the reactants, transition state and products (Å)
|}
As the reaction progresses, the bond lengths between C1-C2, C3-C4 and C5-C6 increase from ~1.3 Å to ~1.5 Å as the bond order decrease to one, whereas bond length of C2-C3 decreases from ~1.5 Å to ~1.3 Å as the bond order increases from one to two.
This could be explained as the increase in bond length suggest a change from sp2-sp2 (C-C double bond) with typical bond length of 1.33 Å <ref name="C-C bond lengths"/> to sp3-sp3 (C-C single bond) with typical bond length of 1.54 Å <ref name="C-C bond lengths"/>, and vice versa for the decrease in bond length. Based on the calculated bond lengths above in Table 1, it is clear that bond lengths and bond orders of the reactants changed during the reaction and the new bonds formed at C4-C5 and C6-C1 are single bonds as they have bond lengths of 1.54 Å.
The typical Van der Waals radius of the C atom is 1.7 Å <ref name="Van der Waals radius of C"/>. As the bond lengths between C4-C5 and C6-C1 of the transition state are shorter than 2 x Van der Waals radii of C, this reflects that C-C bonds are forming at the transition state.

=== Vibration Analysis ===

The imaginary frequency at -948.32 cm-1 corresponds to the reaction path at the transition state, which shows a synchronous bond formation, which agrees with the concerted mechanism of [4+2] cycloaddition, where both reaction centres converge at the same time to form bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|[[File:|center|200px]]
|-
|style="text-align: center;"|Reaction Path at the Transition State (Please double click to see animation)
|}

The lowest positive frequency at 145.14 cm-1 is asynchronous as shown below, where one of the C from the ethene moves towards the butadiene reaction centre and the other C moves away. This suggests that bonds are formed one at a time.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|[[File:|center|200px]]
|-
|style="text-align: center;"|Lowest positive frequency (Please double click to see animation)
|}

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

[[File:Ex2 reactionscheme.png|550px|center|thumb|Diagram 4: Reaction Scheme of Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

Cyclohexadiene and 1,3-dioxole were optimised to their minima. The computed π MOs were shown in the following table.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #9A03FE; color: #ffffff;" |'''Molecule'''
! '''Cyclohexadiene'''
! '''1,3-Dioxole'''
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Cyclo lumo 631g yhw14.png|center|150px]]
|[[File:Dioxole lumo 631g yhw14.png|center|150px]]
|-
|Corresponding to the orbital
|Corresponding to the orbital
|-
| style="background: #9A03FE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Cyclo homo 631g yhw14.png|center|150px]]
|[[File:Dioxole homo 631g yhw14.png|center|150px]]
|-
|Corresponding to the orbital
|Corresponding to the orbital
|}

The transition state was first optimised to its minimum, followed by a transition state calculation. The MOs computed were shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #BD5CFE; color: #ffffff;" |'''Molecule'''
! '''Endo Transition State'''
! '''Exo Transition State'''
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO+1'''
|[[File:Endo ts lumo+1 yhw14.png|center|150px]]
|[[File:Exo ts lumo+1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''LUMO'''
|[[File:Endo ts lumo yhw14.png|center|150px]]
|[[File:Exo ts lumo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO'''
|[[File:Endo ts homo yhw14.png|center|150px]]
|[[File:Exo ts homo yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|-
| style="background: #BD5CFE; color: #ffffff" rowspan="2" |'''HOMO-1'''
|[[File:Endo ts homo-1 yhw14.png|center|150px]]
|[[File:Exo ts homo-1 yhw14.png|center|150px]]
|-
|colspan="2" style="text-align: center"|Corresponding to the orbital
|}

The diagram below illustrates the π molecular orbitals involved in the formation of the transition state between the HOMO and LUMO of cyclohexadiene and 1,3-dioxole.

[[File:|550px|center|thumb|Diagram 5: MO diagram of Reaction of Cyclohexadiene and 1,3-dioxole]]

=== Normal Demand vs Inverse Demand Diels-Alder Reaction ===

A normal electron demand Diels-Alder reaction can be defined as a reaction between electron rich diene and electron poor dienophile. An inverse electron demand is the reaction between electron poor diene and electron rich dienophile.

The LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are very close in energy, which results in strong bonding interaction between the two to form the HOMO and LUMO of both endo and exo TS. Since only the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole have the correct symmetry () to interact, they interact to form the __(symmetry) HOMO and LUMO of both TS.

This could be explained by the presence of electron rich O on 1,3-dioxole which raises the energy of both its HOMO and LUMO, making the overlap between the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole much better than the HOMO of cyclohexadiene and the LUMO of 1,3-dioxole. Thus, the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole are now the frontier orbitals that interact the most, hence this is an inverse demand Diels-Alder reaction.

=== Reaction Energies and Secondary Orbital Interaction ===

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FF4AFF; color: #ffffff" |
! style="background: #FF4AFF; color: #ffffff" | Reactants
! style="background: #FF4AFF; color: #ffffff" | Transition State
! style="background: #FF4AFF; color: #ffffff" | Product
! style="background: #FF4AFF; color: #ffffff" | Activation Energy
! style="background: #FF4AFF; color: #ffffff" | Gibbs Free Energy
|-
|Endo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313622</nowiki>
|<nowiki>-1313849</nowiki>
|160
|<nowiki>-67</nowiki>
|-
|Exo
|<nowiki>-1313782</nowiki>
|<nowiki>-1313614</nowiki>
|<nowiki>-1313846</nowiki>
|168
|<nowiki>-64</nowiki>
|+Table 2: Energies of Reactants, Transition States and Products of both Endo and Exo Pathways in Diels-Alder Reaction of Cyclohexadiene and 1,3-Dioxole (kJ mol-1)
|}

Kinetically favourable product of a reaction is the one that has the lowest activation energy; Thermodynamically favourable product is the product with lowest energy conformer, hence the more stabilised product.

The endo transition state is the kinetic product of this reaction as it has lower activation energy. This could be explained using the secondary orbital interaction between the lone pair orbital on the oxygen atom and the empty π* orbital of diene. This favourable effect stabilises the endo transition state.

As the oxygen atom lone pair is oriented away from the diene π system in the exo transition state, the secondary orbital effect is not present, hence the activation energy of exo reaction is higher.

However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, i.e. increasing temperature, formation of the exo product would be more favourable.

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

Xylylene can react with sulfur dioxide through Diels-Alder reaction via either endo or exo pathways to form a 6-membered ring, or through cheletropic reaction to form a 5-membered ring. The reaction scheme is shown below. Reaction barriers and reaction energies for each pathway are compared to determine the reaction that is most favourable.

[[File:Ex3 reactionscheme yhw14.png|550px|center|thumb|Diagram 6: Reaction Scheme of Xylylene and Sulfur Dioxide]]

=== Intrinsic Reaction Coordinate ===
The following files show the intrinsic reaction coordinates of the three different reaction pathways of xylylene and SO2. Please click to see animation.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Endo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Diels Alder Reaction via Exo TS
! style="background: #93F3F3; color: #ffffff" | IRC of Cheletropic TS
|-
|[[File:DA endo irc animation purple yhw14.gif|center|200px]]
|[[File:DA exo irc animation purple yhw14.gif|center|200px]]
|[[File:Cheletropic irc animation purple yhw14.gif|center|200px]]
|-
|[[File:DA endo irc animation yhw14.gif|center|200px]]
|[[File:DA exo irc animation yhw14.gif|center|200px]]
|[[File:Cheletropic irc animation yhw14.gif|center|200px]]
|-
|[[File:DA endo irc plot yhw14.png|center|200px]]
|[[File:DA exo irc plot yhw14.png|center|200px]]
|[[File:Cheletropic irc plot yhw14.png|center|200px]]
|}

=== Reaction Energies and Reaction Barriers ===

[[File:Ex3 reactionprofile yhw14.png|550px|center|thumb|Diagram 7: Reaction Profile of Xylylene and Sulfur Dioxide]]

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #FFD1C3; color: #ffffff" |
! style="background: #FFD1C3; color: #ffffff" | Reactants
! style="background: #FFD1C3; color: #ffffff" | Transition State
! style="background: #FFD1C3; color: #ffffff" | Product
! style="background: #FFD1C3; color: #ffffff" | Activation Energy
! style="background: #FFD1C3; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|237.767824
|56.9576013
|83.391038
|<nowiki>-97.4191847</nowiki>
|-
|Exo
|154.376786
|241.753433
|56.3196048
|87.406647
|<nowiki>-98.0571812</nowiki>
|-
|Cheletropic
|154.376786
|260.08205
|0.013127501
|105.705264
|<nowiki>-154.3636585</nowiki>
|+Table 3: Energies of Reactants, Transition States and Products of Reactions between Xylylene and Sulfur Dioxide (kJ mol-1)
|}

With reference to the reaction profile and table __, the Diels-Alder reaction via the endo pathway has the lowest activation energy, making it a more kinetically favourable product, i.e. the kinetic product; the Diels-Alder exo product has a lower energy than endo, however with a higher activation energy hence it will not form under low temperature condition; the cheletropic product is the most stabilised product out of the three and it has the lowest reaction energy, therefore is the thermodynamic product.

=== Side Reaction between cis-diene in Xylylene 6-membered ring and SO2===

o-Xylylene contains another cis-butadiene fragment located in the 6-membered ring that can undergo a Diels-Alder reaction with SO2. The reaction energies and reaction barriers between endo and exo pathways are compared in the table below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #4EBEBA; color: #ffffff" |
! style="background: #4EBEBA; color: #ffffff" | Reactants
! style="background: #4EBEBA; color: #ffffff" | Transition State
! style="background: #4EBEBA; color: #ffffff" | Product
! style="background: #4EBEBA; color: #ffffff" | Activation Energy
! style="background: #4EBEBA; color: #ffffff" | Reaction Energy
|-
|Endo
|154.376786
|267.984805
|172.272196
|113.608019
|17.89541
|-
|Exo
|154.376786
|275.821924
|176.711916
|121.445138
|22.33513
|+Table 4: Energies of Reactants, Transition States and Products of the Side Reaction in Xylylene 6-membered ring and Sulfur Dioxide (kJ mol-1)
|}

It is clear that both endo and exo Diels-Alder side reactions are kinetically and thermodynamically unfavourable at this site as the activation energies are much higher than the previous reactions mentioned above in table __ and the reaction energies show that the reactions are endothermic.

== Conclusion ==

The transition states of three pericyclic reactions were investigated in this computational lab, using Gaussian to optimise the reactants, transition states and products respectively, and the vibrational frequencies and intrinsic reaction coordinates were computed.

In the reaction between butadiene and ethene, the importance of molecular orbital symmetry in the interaction of molecular orbitals was illustrated, such that a reaction is only allowed when the molecular orbitals with the same symmetry labels interact with each other and forbidden when symmetric molecular orbital interact with asymmetric orbitals. Furthermore, the vibration frequency calculation proved that this [4+2] Diels-Alder reaction proceeds via a concerted mechanism as synchronous bond formation was demonstrated. Bonding interaction can be further confirmed as the bond distance between the two termini carbon atoms in the transition state is shorter than the sum of two Van der Waals radii of carbon.

In the reaction of cyclohexadiene and 1,3-dioxole, both the endo and exo transition states were investigated. In general, the endo transition state is kinetically more favourable as it has lower activation barrier, possibly due to the secondary orbital interaction between the lone pair in p orbital on the oxygen atom and the empty pi* orbital in the diene, which stabilises the transition state. However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, formation of the exo product could be possible.

The final reaction between xylylene and SO2 again proved that the endo Diels-Alder transition state has the lowest activation energy, making it kinetically favourable at low temperature. However, the cheletropic product is the most stabilised and thermodynamically favourable product. Therefore the reaction would yield the cheletropic product under thermodynamic control instead of the exo Diels-Alder product.

==References==
<references>
<ref name="C-C bond lengths">L. Pauling and L. O. Brockway, ''Journal of the American Chemical Society'', '''1937''', Volume 59, Issue 7, pp. 1223-1236, DOI: 10.1021/ja01286a021, http://pubs.acs.org/doi/abs/10.1021/ja01286a021</ref>
<ref name="Van der Waals radius of C">S. S. Batsanov, ''Inorganic Materials'', '''2001''', Volume 37, Number 9, pp. 871-885, https://physlab.lums.edu.pk/images/f/f6/Franck_ref2.pdf.</ref>
</references>

File:Endo ts lumo+1 yhw14.png

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Yhw14:

File:Endo ts lumo yhw14.png

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Yhw14:

File:Endo ts homo-1 yhw14.png

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Yhw14:

File:Endo ts homo yhw14.png

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Yhw14:

File:Exo ts homo-1 yhw14.png

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Yhw14:

File:Exo ts homo yhw14.png

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Yhw14:

File:Exo ts lumo yhw14.png

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Yhw14:

File:Exo ts lumo+1 yhw14.png

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Yhw14: