ChemWiki - User contributions [en]

Rep:Mod:TP1414

2017-03-23T17:12:36Z

Tp1414: /* Introduction */

== Introduction ==

=== Gaussian and Transition State Characterization ===

[[File:Energy surface TP1414.jpg|500px|thumb| 2D energy surface showing the locations of transition state (TS), local minimum (LM) and global minimum (GM).<ref name="ManyParticlePhysics"/>]]

Gaussian is a molecular modelling software that allows researchers to carry out extensive investigation of molecules and their reactions. In these exercises, the transition states of several Diels-Alder reactions are located and characterized using Gaussian. A transition state is a first order saddle point on a potential energy surface (PES). It is the maximum along the minimum energy path (or reaction path) between two minima (the reactants and the products). ''Geometry optimization'' to find the minimum energy structure will usually lead to a stationary point that is closest to the initial geometry. The stationary point, where the first derivative of energy is zero, can be a global minimum, a local minimum or a saddle point. In a reaction path, the minima (global or local) correspond to the reactants and the products, while the saddle point corresponds to the transition state. To differentiate between a minimum and a saddle point, the second derivatives of energy will have to be analysed. For global or local minima, where energy rises in all directions, the second derivative of energy is positive. In contrast, for transition state, where the energy decreases in one direction (reaction path), the second derivative of energy along the reaction coordinate is negative. The analysis of the second derivatives of energy can be done by a ''frequency calculation'' of the optimized structure. If the structure corresponds to the reactants or products, all the vibrational frequencies (''v'') are real. In contrast, if the structure corresponds to a transition state, there will be one imaginary frequency. This imaginary frequency indicates that the force constant (k), which is given by the second derivative, is negative. <ref name="ComputationalChemistry"/>

<center> <math>\textit{v}=\frac{1}{2\pi }\cdot \sqrt{\frac{k}{\mu }}</math> where <math>k=\frac{\partial ^{2}E}{\partial q^{2}}</math> </center>

Following a successful frequency calculation (one imaginary frequency) of the transition state, an ''Intrinsic Reaction Coordinate (IRC) calculation'' may be set up to examine the transition state along the minimum energy path more closely. The reaction path, or minimum energy path, can be defined as the steepest descent path from the transition state to the reactions and products.

In this exercise, two calculation methods are used. The first is the semi-empirical method PM6, a fitted method used to obtain the initial geometry of the molecule or transition state so as to save time during calculations. The second is the Density Functional Theory (DFT) method B3LYP, a method that is capable of reproducing chemical data and is used to further optimise the geometry obtained from the PM6 method.

=== Diels-Alder Reactions ===

A Diels-Alder reaction is a [4+2] cycloadditon between a conjugated s-cis diene (4π-electron system) and a dienophile (2π-electron system). The reaction has a cyclic transition state with 6π-electrons, is concerted, and results in the formation of two new sigma bonds. According to the Woodward-Hoffmann Rules, the Diels-Alder reaction is thermally allowed and is an orbital-controlled reaction, in which the six electrons are interacting suprafacially. The reaction can mainly proceed in two ways:

# Normal electron demand: HOMO of diene overlaps with LUMO of dienophile
# Inverse electron demand: LUMO of diene overlaps with HOMO of dienophile

Several papers divide the Diels-Alder reactions into three categories instead of two <ref name="InverseElectronDemand"/> <ref name="TransitionsofElectronDemand"/>, the third being a neutral electron demand Diels-Alder, in which the energy separation between the HOMO and LUMO of both reactants is similar. <ref name="InverseElectronDemand"/> Neutral electron demand Diels-Alder reactions are seldom observed and believed to be a transition between normal electron demand and inverse electron demand Diels Alder reactions.<ref name="TransitionsofElectronDemand"/> Below is a comparison of the energy levels of the HOMO and LUMO of the reactants in each case of Diels-Alder reaction where EDG = electron donating group and EWG = electron withdrawing group.

[[File:normalinverseneutral.jpeg|center|500px]]

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

The reaction between butadiene and ethylene presents the simplest type of Diels-Alder reaction, in which butadiene is the diene and ethylene is the dienophile. This reaction yields cyclohexene as the product, and the reaction scheme is as follow:

[[File:exercise 1 reaction scheme.jpg|center]]

=== Molecular Orbital Diagram ===

[[File:MO diagram for exercise 1 TP1414.jpg|500px|thumb|center|Molecular orbital (MO) diagram for the reaction of butadiene with ethylene]]
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Jmol
! style="background: #0D4F8B; color: white;" | Symmetry
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Jmol
! style="background: #0D4F8B; color: white;" | Symmetry
|-
! rowspan="2" style="background: #0D4F8B; color: white;"| Butadiene
! style="background: #0D4F8B; color: white;"| LUMO
|style="text-align: center;"| [[File:ex1butadieneLUMOtp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 BUTADIENE BREAK SYMMETRY JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 22; rotate x -90; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
! rowspan="4" style="background: #0D4F8B; color: white;"| Transition State
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex1mo4tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
|-
! style="background: #0D4F8B; color: white;"| HOMO
|style="text-align: center;"| [[File:ex1butadieneHOMOtp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 BUTADIENE BREAK SYMMETRY JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 22; rotate x -90; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex1mo3tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
|-
! rowspan="2" style="background: #0D4F8B; color: white;"| Ethylene
! style="background: #0D4F8B; color: white;"| LUMO
|style="text-align: center;"| [[File:ex1ethyleneLUMOtp1414.png|100px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 ETHYLENE JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 14; rotate z 90; rotate x 90; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex1mo2tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| HOMO
|style="text-align: center;"| [[File:ex1ethyleneHOMOtp1414.png|100px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 ETHYLENE JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 14; rotate z 90; rotate x 90; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex1mo1tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
|-
|}

<br style="clear:right">

Only orbitals of the same symmetry can interact to form molecular orbitals. This means that only symmetric-symmetric interactions and antisymmetric-antisymmetric interactions are allowed. Symmetric-antisymmetric interactions, on the other hand, are forbidden. This is because the orbital overlap integral is non-zero for interactions between orbitals of the same symmetry and zero for interactions between orbitals of different symmetry.

As shown on the MO diagram above, both interactions (between the HOMO of butadiene and the LUMO of ethylene, and between the LUMO of butadiene and the HOMO of ethylene) occur, generating four molecular orbitals for the transition state. As the energy separation for the two interactions is similar, the reaction between butadiene and ethylene progress with aspects of both normal electron demand and inverse electron demand. This is because both butadiene and ethylene are neutral molecules without any obvious nucleophilic or electrophilic reacting centrers. Both molecules are neither electron-rich nor electron-poor. As a result, orbital overlap is possible for both HOMO-LUMO sets. Several papers classify this reaction as a neutral electron demand Diels-Alder. <ref name="InverseElectronDemand"/> <ref name="TransitionsofElectronDemand"/> This particular Diels-Alder reaction between butadiene and ethylene is well-known for its poor yield.

<br style="clear:left">

=== Internuclear Distances ===

[[File:internuclear distance.pdf|600px|thumb|right|Internuclear distances for the reaction of butadiene with ethylene to form cyclohexene.]]

[[File:butadiene and ethylene.jpg]]

{| class="wikitable"
|+ Internuclear Distances (Å)
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | C1-C2
! style="background: #0D4F8B; color: white;" | C2-C3
! style="background: #0D4F8B; color: white;" | C3-C4
! style="background: #0D4F8B; color: white;" | C4-C5
! style="background: #0D4F8B; color: white;" | C5-C6
! style="background: #0D4F8B; color: white;" | C6-C1
|-
! style="background: #0D4F8B; color: white;"| Reactants
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|style="text-align: center;"| -
|-
! style="background: #0D4F8B; color: white;"| Transition State
|style="text-align: center;"| 1.38
|style="text-align: center;"| 1.41
|style="text-align: center;"| 1.38
|style="text-align: center;"| 2.11
|style="text-align: center;"| 1.38
|style="text-align: center;"| 2.11
|-
! style="background: #0D4F8B; color: white;"| Product
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}

As the reaction progresses, C1-C2, C3-C4 and C5-C6 elongate as the double bond breaks to form single carbon-carbon bonds, while C2-C3 shortens to form carbon-carbon double bond. Simultaneously, C4-C5 and C6-C1 decrease in distance and ultimately single carbon-carbon bonds are formed. A more detailed overview of how the internuclear distances change over the course of the reaction is shown on the graph on the right.

A typical carbon-carbon single bond length is 1.54 Å and a typical carbon-carbon double bond length is 1.34 Å. <ref name="OrganicChemistryJoseph" />

The Van der Waals radius of one carbon atom is 1.70 Å. <ref name="TheMoleculesofLife" /> The length of the partly formed carbon-carbon bonds in the transition state is about 2.11 Å. This distance is shorter than twice the Van der Waals radius of carbon atom (3.40 Å), indicating bonding interactions are occuring.
<br style="clear:right">

=== Vibration and Reaction Path ===

[[File:exercisa1imaginaryfrequency.jpg]]

The vibration that corresponds to the reaction path at the transition state is illustrated above. This vibration has an imaginary frequency that occurs at 948.97i cm<sup>-1</sup>.

The formation of the two bonds are synchronous as shown below. This means that the two sigma bonds are formed simultaneously. hence, the reaction between butadiene and ethylene goes by a concerted synchronous mechanism.

[[File:IRCgif.jpg]]

=== Calculation Files ===

[[File:TP1414 Exercise 1 Ethylene.log]]

[[File:TP1414 Exercise 1 Butadiene.log]]

[[File:TP1414 Exercise 1 Product.log]]

[[File:TP1414 Exercise 1 Transition State.log]]

[[File:TP1414 Exercise 1 IRC.log]]

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

[[File:exercise 2 reaction schemetp1414.jpg|center]]

=== Molecular Orbital Diagram ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|style="text-align: center;"| [[File:ex 2 MO diagram for exo TS TP1414.jpg|500px]]
Molecular orbital (MO) diagram for the reaction of cyclohexadiene and 1,3-dioxole (exo).
|style="text-align: center;"| [[File:ex 2 MO diagram for endo TS TP1414.jpg|500px]]
Molecular orbital (MO) diagram for the reaction of cyclohexadiene and 1,3-dioxole (endo)
|-
|}

<br style="clear:left">

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Image
! style="background: #0D4F8B; color: white;" | Symmetry
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Image
! style="background: #0D4F8B; color: white;" | Symmetry
|-
! rowspan="4" style="background: #0D4F8B; color: white;"| Exo
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex2exoMO4tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO3 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
! rowspan="4" style="background: #0D4F8B; color: white;"| Endo
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex2endoMO4tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO4 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
|-
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex2exoMO3tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO4 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex2endoMO3tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO3 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex2exoMO2tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO2 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex2endoMO2tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO2 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex2exoMO1tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO1 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex2endoMO1tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO1 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
|-
|}

The exo and endo Diels-Alder between cyclohexadiene and 1,3-dioxole proceed in a similar fashion as the Diels-Alder between butadiene and ethylene in Exercise 1. However, unlike in Exercise 1, the dienophile, 1,3-dioxole, contains two pi electron donating oxygen adjacent to the C-C double bond. This increases the energy of the molecular orbitals of the dienophile, resulting in higher energies HOMO and LUMO of the dienophile relative to neutral ethylene in Exercise 1. As a consequence, the HOMO of the dienophile and the LUMO of the diene are much closer in energy and thus, interact more strongly. This reaction between cyclohexadiene and 1,3-dioxole is said to proceed via inverse electron demand Diels-Alder. The stronger interaction between the HOMO and LUMO results in a faster and more favourable reaction as compared to the neutral electron demand Diels-Alder between butadiene and ethylene in Exercise 1.

=== Thermochemistry ===
[[File:ex2energyprofiletp1414.jpeg|600px|thumb|Energy profile diagram for the reactions between cyclohexadiene and 1,3-dioxole]]
The energies of the reactants, transition state and product for both the exo and endo reactions are tabulated below. These are obtained from optimization at B3LYP/6-31G(d) level.

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;"| Exo
|style="text-align: center;"|-612591.48
|style="text-align: center;"|-701187.43
|style="text-align: center;"|-1313778.91
|style="text-align: center;"|-1313614.33
|style="text-align: center;"|-1313845.77
|style="text-align: center;"|164.58
|style="text-align: center;"|-66.86
|-
!style="background: #0D4F8B; color: white;"| Endo
|style="text-align: center;"|-612591.48
|style="text-align: center;"|-701187.43
|style="text-align: center;"|-1313778.91
|style="text-align: center;"|-1313622.15
|style="text-align: center;"|-1313849.37
|style="text-align: center;"|156.76
|style="text-align: center;"|-70.46
|-
|}

Both the exo and endo reactions are exothermic. However, it can be seen that the energy of the endo product is lower (or more negative) than the energy of the exo product, and the endo reaction also has a lower reaction barrier as compared to the exo reaction. This means that the endo product is both the thermodynamically and kinetically favourable product. This can be explained by considering both electronic and steric factors

[[File:seondaryorbitalinteractionstp1414.png|500px|thumb|left|Secondary orbital interactions in endo transition state]] Secondary orbital interactions stabilize the endo transition state, reducing the reaction barrier. On the left is the HOMO of the endo transition state in which there are obvious secondary orbital interactions between the oxygen p orbitals of the 1,3-dioxole and the p orbitals of the diene. An MO representation of this HOMO is shown below.
[[File:secondaryorbitalinteractionMOrepresentationtp1414.jpeg|350px]]
<br style="clear:left">

[[File:stericclashtp1414.png|500px|thumb|left|Steric clash in exo product]] Steric clash between the sp<sup>3</sup> CH<sub>2</sub> of the dioxole ring and the sp<sup>3</sup> CH<sub>2</sub>'s of the cyclohexadiene destabilize both the exo transition state and the exo product.
<br style="clear:left">

=== Vibration and Reaction Path ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
! style="background: #0D4F8B; color: white;"| Vibration
|style="text-align: center;"| [[File:exercise2 exo vibration tp1414.gif]]
|style="text-align: center;"| [[File:exercise2 endo vibration tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Vibrational Frequency
|style="text-align: center;"| 520.90i cm<sup>-1</sup>
|style="text-align: center;"| 528.85i cm<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| Reaction Pathway
|style="text-align: center;"| [[File:exercise2 exo reaction path tp1414.gif]]
|style="text-align: center;"| [[File:exercise2 endo reaction path tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Mechanism
|style="text-align: center;"| Synchronous concerted
|style="text-align: center;"| Synchronous concerted
|-
|}

=== Calculation Files ===

[[File:TP1414 Exercise 2 Cyclohexadiene 631Gd.log]]

[[File:TP1414 Exercise 2 1,2-Dioxole 631Gd.log]]

[[File:TP1414 Exercise 2 Exo Product 631Gd.log]]

[[File:TP1414 Exercise 2 Endo Product 631Gd.log]]

[[File:TP1414 Exercise 2 Exo Transition State 631Gd.log]]

[[File:TP1414 Exercise 2 Endo Transition State 631Gd.log]]

[[File:TP1414 Exercise 2 Exo IRC 631Gd.log]]

[[File:TP1414 Exercise 2 Endo IRC 631Gd.log]]

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

[[File:exercise3reactionschemetp1414.jpg|center]]

=== Molecular Orbital Diagram ===

The exo and endo Diels-Alder reaction between o-xylylene and SO<sub>2</sub> proceed in a similar fashion as the reactions in Exercise 1 and 2. However, in this case, the dienophile, SO<sub>2</sub>, is electron-deficient and has lower energies HOMO and LUMO compared to the dienophiles in Exercise 1 and 2. As a result, the most significant frontier orbital interaction is between the HOMO of o-xylylene and the LUMO of SO<sub>2</sub>. The Diels-Alder reaction between o-xylylene and SO<sub>2</sub> proceeds via normal electron demand.

The exo and endo Diels-Alder reaction between o-xylylene and SO<sub>2</sub> have another competing pericyclic reaction - cheletropic reaction. Woodward Hoffmann defines cheletropic reactions as pericyclic reactions in which two sigma bonds are formed or broken in a single atom. It is sometimes considered to be a subclass of cycloadditions. <ref name="Cheletropic"/> The MO diagram for the cheletropic reaction is shown below.

[[File:tp1414 cheletropic MOdiagram.jpg|500px|thumb|center|Molecular orbital (MO) diagram for the cheletropic reaction between o-xylylene and SO<sub>2</sub> <ref name="OrganicReactions"/>]]

=== Thermochemistry ===
[[File:ex3energyprofiletp1414.jpg|600px|thumb|Energy profile diagram for the reactions between o-xylylene and SO<sub>2</sub>]]
The energies of the reactants, transition state and product for the exo, endo and cheletropic reactions are tabulated below. These are obtained from optimization at PM6 level.

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | o-Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;"| Exo
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|241.75
|style="text-align: center;"|56.31
|style="text-align: center;"|85.18
|style="text-align: center;"|-100.26
|-
!style="background: #0D4F8B; color: white;"| Endo
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|237.77
|style="text-align: center;"|56.98
|style="text-align: center;"|81.20
|style="text-align: center;"|-99.59
|-
!style="background: #0D4F8B; color: white;"| Cheletropic
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|260.09
|style="text-align: center;"|-0.01
|style="text-align: center;"|103.52
|style="text-align: center;"|-156.58
|-
|}

All three reactions are exothermic. The endo product is the kinetically favourable product as it has the lowest reaction barrier, while the cheletropic product is the thermodynamically favourable product as it has the lowest energy. This is consistent with experimental works that have been conducted in which a Diels-Alder adduct is observed to be the kinetic product and cheletropic adduct is observed to be the thermodynamic product. Experimental work shows that the Diels-Alder adduct is thermally unstable and will undergo a retro-Diels-Alder reaction to form back the starting materials, before forming the more stable five membered ring cheletropic product. <ref name="Cheletropic"/>
<br style="clear:right">

=== Vibration and Reaction Path ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
! style="background: #0D4F8B; color: white;" | Cheletropic
|-
! style="background: #0D4F8B; color: white;"| Vibration
|style="text-align: center;"| [[File:ex3 exo vibration tp1414.gif]]
|style="text-align: center;"| [[File:ex3 endo vibration tp1414.gif]]
|style="text-align: center;"| [[File:cheletropic vibration tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Vibrational Frequency
|style="text-align: center;"| 351.78i cm<sup>-1</sup>
|style="text-align: center;"| 334.38i cm<sup>-1</sup>
|style="text-align: center;"| 486.58i cm<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| Reaction Pathway
|style="text-align: center;"| [[File:exo IRC tp1414.gif]]
|style="text-align: center;"| [[File:endo IRC tp1414.gif]]
|style="text-align: center;"| [[File:cheletropic IRC tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Mechanism
|style="text-align: center;"| Asynchronous concerted
|style="text-align: center;"| Asynchronous concerted
|style="text-align: center;"| Synchronous concerted
|-
! style="background: #0D4F8B; color: white;"| IRC
|style="text-align: center;"| [[File:exoIRCtp1414.png]]
|style="text-align: center;"| [[File:endoIRCtp1414.png]]
|style="text-align: center;"| [[File:cheletropicIRCtp1414energy.png]]
|-
|}

It is interesting to note that the exo and endo reactions proceed via asynchronous mechanism in which the C-O bond is formed first before the C-S bond, while the cheletropic reaction proceeds via synchronous mechanism in which the two C-S bonds are formed simultaneously. However, even though the formation of the two bonds are asynchronous in the exo and endo reactions, the total energy along IRC tells us that both reactions are concerted as the reactions do not have any intermediate steps.

In all three reaction pathways, the steepest part on the the total energy versus IRC graph corresponds to the re-aromatisation of the 6-membered ring on the o-xylylene, giving these reactions an aromatic driving force. This also shows the instability of the o-xylylene molecule. O-Xylylene is highly unstable as it is antiaromatic (planar and 4n electrons), and it will undergo an electrocyclic ring closure to form the stable aromatic isomer, benzocyclobutene as shown below.<ref name="Benzocyclobutene"/>

[[File:xylyleneelectrocyclicreactionscheme.jpg|centre]]

A quick transition state optimisation followed by IRC calculation of the above reaction on Gaussian gives the total energy along IRC graph below.

[[File:xylyleneelectrocyclicIRCtp1414.jpg|500px|centre]]

[[File:xylyleneelectrocyclicIRC.gif|500px|centre]]

=== Alternate Diels-Alder Reaction ===

There is a second cis-butadiene fragment in o-xylylene that can undergo a Diels-Alder reaction. This second cis-butadiene is part of the cyclohexadiene ring. The exo and endo for this alternate Diels-Alder reaction proceed as follow:

[[File:alternatedielsalderexotp1414.gif]] [[File:alternatedielsalderendotp1414.gif]]

Both reactions proceed via an asynchronous mechanism.

[[File:energyprofilewithalternatedielsaldertp1414.jpg|600px|thumb|Energy profile diagram for the reactions between o-xylylene and SO<sub>2</sub>]]
The thermochemistry for this alternate Diels-Alder reaction is as follows:

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | o-Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;" | Exo
| style="text-align: center;" |467.99
| style="text-align: center;" |-311.42
| style="text-align: center;" |156.57
| style="text-align: center;" |275.82
| style="text-align: center;" |176.71
| style="text-align: center;" |119.25
| style="text-align: center;" |20.14
|-
! style="background: #0D4F8B; color: white;" | Endo
| style="text-align: center;" |467.99
| style="text-align: center;" |-311.42
| style="text-align: center;" |156.57
| style="text-align: center;" |267.98
| style="text-align: center;" |172.26
| style="text-align: center;" |111.41
| style="text-align: center;" |15.96
|-
|}

Comparing the energies for this alternate Diels-Alder reaction with the energies for the normal Diels-Alder and the cheletropic reactions, it can be seen that both the exo and endo alternate Diels-Alder reactoions are kinetically and thermodynamically unfavourable. The products are also higher in energies than the reactants, making the reactions endothermic.
<br style="clear:right">

=== Calculation Files ===

[[File:TP1414 Exercise 3 Xylylene.log]]

[[File:TP1414 Exercise 3 SO2.log]]

[[File:TP1414 Exercise 3 Exo Product.log]]

[[File:TP1414 Exercise 3 Endo Product.log]]

[[File:TP1414 Exercise 3 Cheletropic Product.log]]

[[File:TP1414 Exercise 3 Exo Transition State.log]]

[[File:TP1414 Exercise 3 Endo Transition State.log]]

[[File:TP1414 Exercise 3 Cheletropic Transition State.log]]

[[File:TP1414 Exercise 3 Exo IRC.log]]

[[File:TP1414 Exercise 3 Endo IRC.log]]

[[File:TP1414 Exercise 3 Cheletropic IRC.log]]

[[File:TP1414 Exercise 3 Xylylene Electrocyclic Transition State.log]]

[[File:TP1414 Exercise 3 Xylylene Electrocyclic IRC.log]]

[[File:TP1414 Exercise 3 Alternate Exo Product.log]]

[[File:TP1414 Exercise 3 Alternate Endo Product.log]]

[[File:TP1414 Exercise 3 Alternate Exo Transition State.log]]

[[File:TP1414 Exercise 3 Alternate Endo Transition State.log]]

[[File:TP1414 Exercise 3 Alternate Exo IRC.log]]

[[File:TP1414 Exercise 3 Alternate Endo IRC.log]]

== Conclusion ==

Two calculation methods were used to study three different Diels-Alder reactions. The semi-empirical method PM6 was used to calculate the geometries of the transition state and product of the reactions in all three exercises for faster calculations. In exercise 2, the geometries were further optimised by the DFT method B3LYP at 6-31G(d) level for better accuracy.

Exercises 1 to 3 illustrate the three different ways in which Diels-Alder reaction can proceed: neutral electron demand, inverse electron demand and normal electron demand respectively. In exercise 1, the frontier orbital interactions of the simplest Diels-Alder reaction was studied and it shows that only orbitals of the same symmetry can interact. Exercise 1 also illustrates how internuclear distances vary as a Diels-Alder reaction proceeds, and how these compare with the Van der Waals radii of the atoms. Exercise 2 presents a more complex Diels-Alder reaction which can proceed in two different orientations - endo and exo. It demonstrates how secondary orbital interactions and steric factors could affect the energies of the transition states and products, and hence, determine the kinetically and thermodynamically favourable reactions. Exercise 3 illustrates an even more complex system where there are two diene functional groups and in which another competing pericyclic cheletropic reaction is possible. It also demonstrates that pericyclic reactions can proceed via synchronous concerted or asynchronous concerted mechanisms depending on the symmetry of the interacting molecules.

In conclusion, Gaussian proves to be a useful molecular modelling software to investigate the molecules and their reactions. Transition states were located and characterized, and frontier orbital interactions and thermochemistry were analysed. Results obtained from these calculations also proved to be consistent with theory and experimental observations.

== References ==

<references>
<ref name="ComputationalChemistry"> Lecture notes: ''Quantum Mechanics 3/3rd Year Computational Chemistry Laboratory'', Michael Bearpark, Imperial College. </ref>
<ref name="OrganicChemistryJoseph"> J. M. Hornback, ''Organic Chemistry'', Thomson Learning. Inc., Belmont, Second., 2006, pp. 94.</ref>
<ref name="TheMoleculesofLife"> J. Kuriyan, B. Konforti and D. Wemmer, ''The Molecules of Life: Physical and Chemical Principles'', Garland Science, New York, 2013.</ref>
<ref name="InverseElectronDemand"> A.-C. Knall and C. Slugovc, ''Chem Soc Rev'', 2013, '''42''', 5131–5142.</ref>
<ref name="TransitionsofElectronDemand"> E. Eibler, P. Hocht, B. Prantl, H. Rormaier, H. M. Schuhbauer and H. Wiest, ''Liebigs Ann.lRemei'', 1997, '''1997''', 2471–2484.</ref>
<ref name="Benzocyclobutene"> G. Mehta and S. Kotha, ''Tetrahedron'', 2001, '''57''', 626.</ref>
<ref name="ManyParticlePhysics"> H. Fehske, R. Schneider and A. Weiβe, Eds., ''Computational Many-Particle Physics'', Springer, Berlin, 2008, pp. 438.</ref>
<ref name="Cheletropic"> D. Suarez, T. L. Sordo and A. Sordo, ''J. Org. Chem.'', 1995, '''60''', 2848–2852.</ref>
<ref name="OrganicReactions"> P. S. Kalsi, ''Organic Reactions Stereochemistry and Mechanism'', New Age International Publishers, New Delhi, Fourth., 2006, pp. 550.</ref>
</references>

File:Tp1414 cheletropic MOdiagram.jpg

2017-03-20T16:39:57Z

Tp1414:

Rep:Mod:TP1414

2017-03-20T16:39:09Z

Tp1414: /* Molecular Orbital Diagram */

== Introduction ==

=== Gaussian and Transition State Characterization ===

[[File:Energy surface TP1414.jpg|500px|thumb| Energy surface showing the locations of transition state (TS), local minimum (LM) and global minimum (GM).<ref name="ManyParticlePhysics"/>]]

Gaussian is a molecular modelling software that allows researchers to carry out extensive investigation of molecules and their reactions. In these exercises, the transition states of several Diels-Alder reactions are located and characterized using Gaussian. A transition state is a first order saddle point on a potential energy surface (PES). It is the maximum along the minimum energy path (or reaction path) between two minima (the reactants and the products). ''Geometry optimization'' to find the minimum energy structure will usually lead to a stationary point that is closest to the initial geometry. The stationary point, where the first derivative of energy is zero, can be a global minimum, a local minimum or a saddle point. In a reaction path, the minima (global or local) correspond to the reactants and the products, while the saddle point corresponds to the transition state. To differentiate between a minimum and a saddle point, the second derivatives of energy will have to be analysed. For global or local minima, where energy rises in all directions, the second derivative of energy is positive. In contrast, for transition state, where the energy decreases in one direction (reaction path), the second derivative of energy along the reaction coordinate is negative. The analysis of the second derivatives of energy can be done by a ''frequency calculation'' of the optimized structure. If the structure corresponds to the reactants or products, all the vibrational frequencies (''v'') are real. In contrast, if the structure corresponds to a transition state, there will be one imaginary frequency. This imaginary frequency indicates that the force constant (k), which is given by the second derivative, is negative. <ref name="ComputationalChemistry"/>

<center> <math>\textit{v}=\frac{1}{2\pi }\cdot \sqrt{\frac{k}{\mu }}</math> where <math>k=\frac{\partial ^{2}E}{\partial q^{2}}</math> </center>

Following a successful frequency calculation (one imaginary frequency) of the transition state, an ''Intrinsic Reaction Coordinate (IRC) calculation'' may be set up to examine the transition state along the minimum energy path more closely. The reaction path, or minimum energy path, can be defined as the steepest descent path from the transition state to the reactions and products.

In this exercise, two calculation methods are used. The first is the semi-empirical method PM6, a fitted method used to obtain the initial geometry of the molecule or transition state so as to save time during calculations. The second is the Density Functional Theory (DFT) method B3LYP, a method that is capable of reproducing chemical data and is used to further optimise the geometry obtained from the PM6 method.

=== Diels-Alder Reactions ===

A Diels-Alder reaction is a [4+2] cycloadditon between a conjugated s-cis diene (4π-electron system) and a dienophile (2π-electron system). The reaction has a cyclic transition state with 6π-electrons, is concerted, and results in the formation of two new sigma bonds. According to the Woodward-Hoffmann Rules, the Diels-Alder reaction is thermally allowed and is an orbital-controlled reaction, in which the six electrons are interacting suprafacially. The reaction can mainly proceed in two ways:

# Normal electron demand: HOMO of diene overlaps with LUMO of dienophile
# Inverse electron demand: LUMO of diene overlaps with HOMO of dienophile

Several papers divide the Diels-Alder reactions into three categories instead of two <ref name="InverseElectronDemand"/> <ref name="TransitionsofElectronDemand"/>, the third being a neutral electron demand Diels-Alder, in which the energy separation between the HOMO and LUMO of both reactants is similar. <ref name="InverseElectronDemand"/> Neutral electron demand Diels-Alder reactions are seldom observed and believed to be a transition between normal electron demand and inverse electron demand Diels Alder reactions.<ref name="TransitionsofElectronDemand"/>

[[File:normalinverseneutral.jpeg|center|500px]]

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

The reaction between butadiene and ethylene presents the simplest type of Diels-Alder reaction, in which butadiene is the diene and ethylene is the dienophile. This reaction yields cyclohexene as the product, and the reaction scheme is as follow:

[[File:exercise 1 reaction scheme.jpg|center]]

=== Molecular Orbital Diagram ===

[[File:MO diagram for exercise 1 TP1414.jpg|500px|thumb|center|Molecular orbital (MO) diagram for the reaction of butadiene with ethylene]]
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Jmol
! style="background: #0D4F8B; color: white;" | Symmetry
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Jmol
! style="background: #0D4F8B; color: white;" | Symmetry
|-
! rowspan="2" style="background: #0D4F8B; color: white;"| Butadiene
! style="background: #0D4F8B; color: white;"| LUMO
|style="text-align: center;"| [[File:ex1butadieneLUMOtp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 BUTADIENE BREAK SYMMETRY JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 22; rotate x -90; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
! rowspan="4" style="background: #0D4F8B; color: white;"| Transition State
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex1mo4tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
|-
! style="background: #0D4F8B; color: white;"| HOMO
|style="text-align: center;"| [[File:ex1butadieneHOMOtp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 BUTADIENE BREAK SYMMETRY JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 22; rotate x -90; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex1mo3tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
|-
! rowspan="2" style="background: #0D4F8B; color: white;"| Ethylene
! style="background: #0D4F8B; color: white;"| LUMO
|style="text-align: center;"| [[File:ex1ethyleneLUMOtp1414.png|100px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 ETHYLENE JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 14; rotate z 90; rotate x 90; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex1mo2tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| HOMO
|style="text-align: center;"| [[File:ex1ethyleneHOMOtp1414.png|100px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 ETHYLENE JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 14; rotate z 90; rotate x 90; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex1mo1tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
|-
|}

<br style="clear:right">

Only orbitals of the same symmetry can interact to form molecular orbitals. This means that only symmetric-symmetric interactions and antisymmetric-antisymmetric interactions are allowed. Symmetric-antisymmetric interactions, on the other hand, are forbidden. This is because the orbital overlap integral is non-zero for interactions between orbitals of the same symmetry and zero for interactions between orbitals of different symmetry.

As shown on the MO diagram above, both interactions (between the HOMO of butadiene and the LUMO of ethylene, and between the LUMO of butadiene and the HOMO of ethylene) occur, generating four molecular orbitals for the transition state. As the energy separation for the two interactions is similar, the reaction between butadiene and ethylene progress with aspects of both normal electron demand and inverse electron demand. This is because both butadiene and ethylene are neutral molecules without any obvious nucleophilic or electrophilic reacting centrers. Both molecules are neither electron-rich nor electron-poor. As a result, orbital overlap is possible for both HOMO-LUMO sets. Several papers classify this reaction as a neutral electron demand Diels-Alder. <ref name="InverseElectronDemand"/> <ref name="TransitionsofElectronDemand"/> This particular Diels-Alder reaction between butadiene and ethylene is well-known for its poor yield.

<br style="clear:left">

=== Internuclear Distances ===

[[File:internuclear distance.pdf|600px|thumb|right|Internuclear distances for the reaction of butadiene with ethylene to form cyclohexene.]]

[[File:butadiene and ethylene.jpg]]

{| class="wikitable"
|+ Internuclear Distances (Å)
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | C1-C2
! style="background: #0D4F8B; color: white;" | C2-C3
! style="background: #0D4F8B; color: white;" | C3-C4
! style="background: #0D4F8B; color: white;" | C4-C5
! style="background: #0D4F8B; color: white;" | C5-C6
! style="background: #0D4F8B; color: white;" | C6-C1
|-
! style="background: #0D4F8B; color: white;"| Reactants
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|style="text-align: center;"| -
|-
! style="background: #0D4F8B; color: white;"| Transition State
|style="text-align: center;"| 1.38
|style="text-align: center;"| 1.41
|style="text-align: center;"| 1.38
|style="text-align: center;"| 2.11
|style="text-align: center;"| 1.38
|style="text-align: center;"| 2.11
|-
! style="background: #0D4F8B; color: white;"| Product
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}

As the reaction progresses, C1-C2, C3-C4 and C5-C6 elongate as the double bond breaks to form single carbon-carbon bonds, while C2-C3 shortens to form carbon-carbon double bond. Simultaneously, C4-C5 and C6-C1 decrease in distance and ultimately single carbon-carbon bonds are formed. A more detailed overview of how the internuclear distances change over the course of the reaction is shown on the graph on the right.

A typical carbon-carbon single bond length is 1.54 Å and a typical carbon-carbon double bond length is 1.34 Å. <ref name="OrganicChemistryJoseph" />

The Van der Waals radius of one carbon atom is 1.70 Å. <ref name="TheMoleculesofLife" /> The length of the partly formed carbon-carbon bonds in the transition state is about 2.11 Å. This distance is shorter than twice the Van der Waals radius of carbon atom (3.40 Å), indicating bonding interactions are occuring.
<br style="clear:right">

=== Vibration and Reaction Path ===

[[File:exercisa1imaginaryfrequency.jpg]]

The vibration that corresponds to the reaction path at the transition state is illustrated above. This vibration has an imaginary frequency that occurs at 948.97i cm<sup>-1</sup>.

The formation of the two bonds are synchronous as shown below. This means that the two sigma bonds are formed simultaneously. hence, the reaction between butadiene and ethylene goes by a concerted synchronous mechanism.

[[File:IRCgif.jpg]]

=== Calculation Files ===

[[File:TP1414 Exercise 1 Ethylene.log]]

[[File:TP1414 Exercise 1 Butadiene.log]]

[[File:TP1414 Exercise 1 Product.log]]

[[File:TP1414 Exercise 1 Transition State.log]]

[[File:TP1414 Exercise 1 IRC.log]]

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

[[File:exercise 2 reaction schemetp1414.jpg|center]]

=== Molecular Orbital Diagram ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|style="text-align: center;"| [[File:ex 2 MO diagram for exo TS TP1414.jpg|500px]]
Molecular orbital (MO) diagram for the reaction of cyclohexadiene and 1,3-dioxole (exo).
|style="text-align: center;"| [[File:ex 2 MO diagram for endo TS TP1414.jpg|500px]]
Molecular orbital (MO) diagram for the reaction of cyclohexadiene and 1,3-dioxole (endo)
|-
|}

<br style="clear:left">

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Image
! style="background: #0D4F8B; color: white;" | Symmetry
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Image
! style="background: #0D4F8B; color: white;" | Symmetry
|-
! rowspan="4" style="background: #0D4F8B; color: white;"| Exo
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex2exoMO4tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO3 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
! rowspan="4" style="background: #0D4F8B; color: white;"| Endo
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex2endoMO4tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO4 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
|-
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex2exoMO3tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO4 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex2endoMO3tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO3 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex2exoMO2tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO2 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex2endoMO2tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO2 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex2exoMO1tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO1 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex2endoMO1tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO1 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
|-
|}

The exo and endo Diels-Alder between cyclohexadiene and 1,3-dioxole proceed in a similar fashion as the Diels-Alder between butadiene and ethylene in Exercise 1. However, unlike in Exercise 1, the dienophile, 1,3-dioxole, contains two pi electron donating oxygen adjacent to the C-C double bond. This increases the energy of the molecular orbitals of the dienophile, resulting in higher energies HOMO and LUMO of the dienophile relative to neutral ethylene in Exercise 1. As a consequence, the HOMO of the dienophile and the LUMO of the diene are much closer in energy and thus, interact more strongly. This reaction between cyclohexadiene and 1,3-dioxole is said to proceed via inverse electron demand Diels-Alder. The stronger interaction between the HOMO and LUMO results in a faster and more favourable reaction as compared to the neutral electron demand Diels-Alder between butadiene and ethylene in Exercise 1.

=== Thermochemistry ===
[[File:ex2energyprofiletp1414.jpeg|600px|thumb|Energy profile diagram for the reactions between cyclohexadiene and 1,3-dioxole]]
The energies of the reactants, transition state and product for both the exo and endo reactions are tabulated below. These are obtained from optimization at B3LYP/6-31G(d) level.

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;"| Exo
|style="text-align: center;"|-612591.48
|style="text-align: center;"|-701187.43
|style="text-align: center;"|-1313778.91
|style="text-align: center;"|-1313614.33
|style="text-align: center;"|-1313845.77
|style="text-align: center;"|164.58
|style="text-align: center;"|-66.86
|-
!style="background: #0D4F8B; color: white;"| Endo
|style="text-align: center;"|-612591.48
|style="text-align: center;"|-701187.43
|style="text-align: center;"|-1313778.91
|style="text-align: center;"|-1313622.15
|style="text-align: center;"|-1313849.37
|style="text-align: center;"|156.76
|style="text-align: center;"|-70.46
|-
|}

Both the exo and endo reactions are exothermic. However, it can be seen that the energy of the endo product is lower (or more negative) than the energy of the exo product, and the endo reaction also has a lower reaction barrier as compared to the exo reaction. This means that the endo product is both the thermodynamically and kinetically favourable product. This can be explained by considering both electronic and steric factors

[[File:seondaryorbitalinteractionstp1414.png|500px|thumb|left|Secondary orbital interactions in endo transition state]] Secondary orbital interactions stabilize the endo transition state, reducing the reaction barrier. On the left is the HOMO of the endo transition state in which there are obvious secondary orbital interactions between the oxygen p orbitals of the 1,3-dioxole and the p orbitals of the diene. An MO representation of this HOMO is shown below.
[[File:secondaryorbitalinteractionMOrepresentationtp1414.jpeg|350px]]
<br style="clear:left">

[[File:stericclashtp1414.png|500px|thumb|left|Steric clash in exo product]] Steric clash between the sp<sup>3</sup> CH<sub>2</sub> of the dioxole ring and the sp<sup>3</sup> CH<sub>2</sub>'s of the cyclohexadiene destabilize both the exo transition state and the exo product.
<br style="clear:left">

=== Vibration and Reaction Path ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
! style="background: #0D4F8B; color: white;"| Vibration
|style="text-align: center;"| [[File:exercise2 exo vibration tp1414.gif]]
|style="text-align: center;"| [[File:exercise2 endo vibration tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Vibrational Frequency
|style="text-align: center;"| 520.90i cm<sup>-1</sup>
|style="text-align: center;"| 528.85i cm<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| Reaction Pathway
|style="text-align: center;"| [[File:exercise2 exo reaction path tp1414.gif]]
|style="text-align: center;"| [[File:exercise2 endo reaction path tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Mechanism
|style="text-align: center;"| Synchronous concerted
|style="text-align: center;"| Synchronous concerted
|-
|}

=== Calculation Files ===

[[File:TP1414 Exercise 2 Cyclohexadiene 631Gd.log]]

[[File:TP1414 Exercise 2 1,2-Dioxole 631Gd.log]]

[[File:TP1414 Exercise 2 Exo Product 631Gd.log]]

[[File:TP1414 Exercise 2 Endo Product 631Gd.log]]

[[File:TP1414 Exercise 2 Exo Transition State 631Gd.log]]

[[File:TP1414 Exercise 2 Endo Transition State 631Gd.log]]

[[File:TP1414 Exercise 2 Exo IRC 631Gd.log]]

[[File:TP1414 Exercise 2 Endo IRC 631Gd.log]]

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

[[File:exercise3reactionschemetp1414.jpg|center]]

=== Molecular Orbital Diagram ===

The exo and endo Diels-Alder reaction between o-xylylene and SO<sub>2</sub> proceed in a similar fashion as the reactions in Exercise 1 and 2. However, in this case, the dienophile, SO<sub>2</sub>, is electron-deficient and has lower energies HOMO and LUMO compared to the dienophiles in Exercise 1 and 2. As a result, the most significant frontier orbital interaction is between the HOMO of o-xylylene and the LUMO of SO<sub>2</sub>. The Diels-Alder reaction between o-xylylene and SO<sub>2</sub> proceeds via normal electron demand.

The exo and endo Diels-Alder reaction between o-xylylene and SO<sub>2</sub> have another competing pericyclic reaction - cheletropic reaction. Woodward Hoffmann defines cheletropic reactions as pericyclic reactions in which two sigma bonds are formed or broken in a single atom. It is sometimes considered to be a subclass of cycloadditions. <ref name="Cheletropic"/> The MO diagram for the cheletropic reaction is shown below.

[[File:tp1414 cheletropic MOdiagram.jpg|500px|thumb|center|Molecular orbital (MO) diagram for the cheletropic reaction between o-xylylene and SO<sub>2</sub> <ref name="OrganicReactions"/>]]

=== Thermochemistry ===
[[File:ex3energyprofiletp1414.jpg|600px|thumb|Energy profile diagram for the reactions between o-xylylene and SO<sub>2</sub>]]
The energies of the reactants, transition state and product for the exo, endo and cheletropic reactions are tabulated below. These are obtained from optimization at PM6 level.

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | o-Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;"| Exo
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|241.75
|style="text-align: center;"|56.31
|style="text-align: center;"|85.18
|style="text-align: center;"|-100.26
|-
!style="background: #0D4F8B; color: white;"| Endo
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|237.77
|style="text-align: center;"|56.98
|style="text-align: center;"|81.20
|style="text-align: center;"|-99.59
|-
!style="background: #0D4F8B; color: white;"| Cheletropic
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|260.09
|style="text-align: center;"|-0.01
|style="text-align: center;"|103.52
|style="text-align: center;"|-156.58
|-
|}

All three reactions are exothermic. The endo product is the kinetically favourable product as it has the lowest reaction barrier, while the cheletropic product is the thermodynamically favourable product as it has the lowest energy. This is consistent with experimental works that have been conducted in which a Diels-Alder adduct is observed to be the kinetic product and cheletropic adduct is observed to be the thermodynamic product. Experimental work shows that the Diels-Alder adduct is thermally unstable and will undergo a retro-Diels-Alder reaction to form back the starting materials, before forming the more stable five membered ring cheletropic product. <ref name="Cheletropic"/>
<br style="clear:right">

=== Vibration and Reaction Path ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
! style="background: #0D4F8B; color: white;" | Cheletropic
|-
! style="background: #0D4F8B; color: white;"| Vibration
|style="text-align: center;"| [[File:ex3 exo vibration tp1414.gif]]
|style="text-align: center;"| [[File:ex3 endo vibration tp1414.gif]]
|style="text-align: center;"| [[File:cheletropic vibration tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Vibrational Frequency
|style="text-align: center;"| 351.78i cm<sup>-1</sup>
|style="text-align: center;"| 334.38i cm<sup>-1</sup>
|style="text-align: center;"| 486.58i cm<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| Reaction Pathway
|style="text-align: center;"| [[File:exo IRC tp1414.gif]]
|style="text-align: center;"| [[File:endo IRC tp1414.gif]]
|style="text-align: center;"| [[File:cheletropic IRC tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Mechanism
|style="text-align: center;"| Asynchronous concerted
|style="text-align: center;"| Asynchronous concerted
|style="text-align: center;"| Synchronous concerted
|-
! style="background: #0D4F8B; color: white;"| IRC
|style="text-align: center;"| [[File:exoIRCtp1414.png]]
|style="text-align: center;"| [[File:endoIRCtp1414.png]]
|style="text-align: center;"| [[File:cheletropicIRCtp1414energy.png]]
|-
|}

It is interesting to note that the exo and endo reactions proceed via asynchronous mechanism in which the C-O bond is formed first before the C-S bond, while the cheletropic reaction proceeds via synchronous mechanism in which the two C-S bonds are formed simultaneously. However, even though the formation of the two bonds are asynchronous in the exo and endo reactions, the total energy along IRC tells us that both reactions are concerted as the reactions do not have any intermediate steps.

In all three reaction pathways, the steepest part on the the total energy versus IRC graph corresponds to the re-aromatisation of the 6-membered ring on the o-xylylene, giving these reactions an aromatic driving force. This also shows the instability of the o-xylylene molecule. O-Xylylene is highly unstable as it is antiaromatic (planar and 4n electrons), and it will undergo an electrocyclic ring closure to form the stable aromatic isomer, benzocyclobutene as shown below.<ref name="Benzocyclobutene"/>

[[File:xylyleneelectrocyclicreactionscheme.jpg|centre]]

A quick transition state optimisation followed by IRC calculation of the above reaction on Gaussian gives the total energy along IRC graph below.

[[File:xylyleneelectrocyclicIRCtp1414.jpg|500px|centre]]

[[File:xylyleneelectrocyclicIRC.gif|500px|centre]]

=== Alternate Diels-Alder Reaction ===

There is a second cis-butadiene fragment in o-xylylene that can undergo a Diels-Alder reaction. This second cis-butadiene is part of the cyclohexadiene ring. The exo and endo for this alternate Diels-Alder reaction proceed as follow:

[[File:alternatedielsalderexotp1414.gif]] [[File:alternatedielsalderendotp1414.gif]]

Both reactions proceed via an asynchronous mechanism.

[[File:energyprofilewithalternatedielsaldertp1414.jpg|600px|thumb|Energy profile diagram for the reactions between o-xylylene and SO<sub>2</sub>]]
The thermochemistry for this alternate Diels-Alder reaction is as follows:

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | o-Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;" | Exo
| style="text-align: center;" |467.99
| style="text-align: center;" |-311.42
| style="text-align: center;" |156.57
| style="text-align: center;" |275.82
| style="text-align: center;" |176.71
| style="text-align: center;" |119.25
| style="text-align: center;" |20.14
|-
! style="background: #0D4F8B; color: white;" | Endo
| style="text-align: center;" |467.99
| style="text-align: center;" |-311.42
| style="text-align: center;" |156.57
| style="text-align: center;" |267.98
| style="text-align: center;" |172.26
| style="text-align: center;" |111.41
| style="text-align: center;" |15.96
|-
|}

Comparing the energies for this alternate Diels-Alder reaction with the energies for the normal Diels-Alder and the cheletropic reactions, it can be seen that both the exo and endo alternate Diels-Alder reactoions are kinetically and thermodynamically unfavourable. The products are also higher in energies than the reactants, making the reactions endothermic.
<br style="clear:right">

=== Calculation Files ===

[[File:TP1414 Exercise 3 Xylylene.log]]

[[File:TP1414 Exercise 3 SO2.log]]

[[File:TP1414 Exercise 3 Exo Product.log]]

[[File:TP1414 Exercise 3 Endo Product.log]]

[[File:TP1414 Exercise 3 Cheletropic Product.log]]

[[File:TP1414 Exercise 3 Exo Transition State.log]]

[[File:TP1414 Exercise 3 Endo Transition State.log]]

[[File:TP1414 Exercise 3 Cheletropic Transition State.log]]

[[File:TP1414 Exercise 3 Exo IRC.log]]

[[File:TP1414 Exercise 3 Endo IRC.log]]

[[File:TP1414 Exercise 3 Cheletropic IRC.log]]

[[File:TP1414 Exercise 3 Xylylene Electrocyclic Transition State.log]]

[[File:TP1414 Exercise 3 Xylylene Electrocyclic IRC.log]]

[[File:TP1414 Exercise 3 Alternate Exo Product.log]]

[[File:TP1414 Exercise 3 Alternate Endo Product.log]]

[[File:TP1414 Exercise 3 Alternate Exo Transition State.log]]

[[File:TP1414 Exercise 3 Alternate Endo Transition State.log]]

[[File:TP1414 Exercise 3 Alternate Exo IRC.log]]

[[File:TP1414 Exercise 3 Alternate Endo IRC.log]]

== Conclusion ==

Two calculation methods were used to study three different Diels-Alder reactions. The semi-empirical method PM6 was used to calculate the geometries of the transition state and product of the reactions in all three exercises for faster calculations. In exercise 2, the geometries were further optimised by the DFT method B3LYP at 6-31G(d) level for better accuracy.

Exercises 1 to 3 illustrate the three different ways in which Diels-Alder reaction can proceed: neutral electron demand, inverse electron demand and normal electron demand respectively. In exercise 1, the frontier orbital interactions of the simplest Diels-Alder reaction was studied and it shows that only orbitals of the same symmetry can interact. Exercise 1 also illustrates how internuclear distances vary as a Diels-Alder reaction proceeds, and how these compare with the Van der Waals radii of the atoms. Exercise 2 presents a more complex Diels-Alder reaction which can proceed in two different orientations - endo and exo. It demonstrates how secondary orbital interactions and steric factors could affect the energies of the transition states and products, and hence, determine the kinetically and thermodynamically favourable reactions. Exercise 3 illustrates an even more complex system where there are two diene functional groups and in which another competing pericyclic cheletropic reaction is possible. It also demonstrates that pericyclic reactions can proceed via synchronous concerted or asynchronous concerted mechanisms depending on the symmetry of the interacting molecules.

In conclusion, Gaussian proves to be a useful molecular modelling software to investigate the molecules and their reactions. Transition states were located and characterized, and frontier orbital interactions and thermochemistry were analysed. Results obtained from these calculations also proved to be consistent with theory and experimental observations.

== References ==

<references>
<ref name="ComputationalChemistry"> Lecture notes: ''Quantum Mechanics 3/3rd Year Computational Chemistry Laboratory'', Michael Bearpark, Imperial College. </ref>
<ref name="OrganicChemistryJoseph"> J. M. Hornback, ''Organic Chemistry'', Thomson Learning. Inc., Belmont, Second., 2006, pp. 94.</ref>
<ref name="TheMoleculesofLife"> J. Kuriyan, B. Konforti and D. Wemmer, ''The Molecules of Life: Physical and Chemical Principles'', Garland Science, New York, 2013.</ref>
<ref name="InverseElectronDemand"> A.-C. Knall and C. Slugovc, ''Chem Soc Rev'', 2013, '''42''', 5131–5142.</ref>
<ref name="TransitionsofElectronDemand"> E. Eibler, P. Hocht, B. Prantl, H. Rormaier, H. M. Schuhbauer and H. Wiest, ''Liebigs Ann.lRemei'', 1997, '''1997''', 2471–2484.</ref>
<ref name="Benzocyclobutene"> G. Mehta and S. Kotha, ''Tetrahedron'', 2001, '''57''', 626.</ref>
<ref name="ManyParticlePhysics"> H. Fehske, R. Schneider and A. Weiβe, Eds., ''Computational Many-Particle Physics'', Springer, Berlin, 2008, pp. 438.</ref>
<ref name="Cheletropic"> D. Suarez, T. L. Sordo and A. Sordo, ''J. Org. Chem.'', 1995, '''60''', 2848–2852.</ref>
<ref name="OrganicReactions"> P. S. Kalsi, ''Organic Reactions Stereochemistry and Mechanism'', New Age International Publishers, New Delhi, Fourth., 2006, pp. 550.</ref>
</references>

Rep:Mod:TP1414

2017-03-20T15:07:01Z

Tp1414: /* References */

== Introduction ==

=== Gaussian and Transition State Characterization ===

[[File:Energy surface TP1414.jpg|500px|thumb| Energy surface showing the locations of transition state (TS), local minimum (LM) and global minimum (GM).<ref name="ManyParticlePhysics"/>]]

Gaussian is a molecular modelling software that allows researchers to carry out extensive investigation of molecules and their reactions. In these exercises, the transition states of several Diels-Alder reactions are located and characterized using Gaussian. A transition state is a first order saddle point on a potential energy surface (PES). It is the maximum along the minimum energy path (or reaction path) between two minima (the reactants and the products). ''Geometry optimization'' to find the minimum energy structure will usually lead to a stationary point that is closest to the initial geometry. The stationary point, where the first derivative of energy is zero, can be a global minimum, a local minimum or a saddle point. In a reaction path, the minima (global or local) correspond to the reactants and the products, while the saddle point corresponds to the transition state. To differentiate between a minimum and a saddle point, the second derivatives of energy will have to be analysed. For global or local minima, where energy rises in all directions, the second derivative of energy is positive. In contrast, for transition state, where the energy decreases in one direction (reaction path), the second derivative of energy along the reaction coordinate is negative. The analysis of the second derivatives of energy can be done by a ''frequency calculation'' of the optimized structure. If the structure corresponds to the reactants or products, all the vibrational frequencies (''v'') are real. In contrast, if the structure corresponds to a transition state, there will be one imaginary frequency. This imaginary frequency indicates that the force constant (k), which is given by the second derivative, is negative. <ref name="ComputationalChemistry"/>

<center> <math>\textit{v}=\frac{1}{2\pi }\cdot \sqrt{\frac{k}{\mu }}</math> where <math>k=\frac{\partial ^{2}E}{\partial q^{2}}</math> </center>

Following a successful frequency calculation (one imaginary frequency) of the transition state, an ''Intrinsic Reaction Coordinate (IRC) calculation'' may be set up to examine the transition state along the minimum energy path more closely. The reaction path, or minimum energy path, can be defined as the steepest descent path from the transition state to the reactions and products.

In this exercise, two calculation methods are used. The first is the semi-empirical method PM6, a fitted method used to obtain the initial geometry of the molecule or transition state so as to save time during calculations. The second is the Density Functional Theory (DFT) method B3LYP, a method that is capable of reproducing chemical data and is used to further optimise the geometry obtained from the PM6 method.

=== Diels-Alder Reactions ===

A Diels-Alder reaction is a [4+2] cycloadditon between a conjugated s-cis diene (4π-electron system) and a dienophile (2π-electron system). The reaction has a cyclic transition state with 6π-electrons, is concerted, and results in the formation of two new sigma bonds. According to the Woodward-Hoffmann Rules, the Diels-Alder reaction is thermally allowed and is an orbital-controlled reaction, in which the six electrons are interacting suprafacially. The reaction can mainly proceed in two ways:

# Normal electron demand: HOMO of diene overlaps with LUMO of dienophile
# Inverse electron demand: LUMO of diene overlaps with HOMO of dienophile

Several papers divide the Diels-Alder reactions into three categories instead of two <ref name="InverseElectronDemand"/> <ref name="TransitionsofElectronDemand"/>, the third being a neutral electron demand Diels-Alder, in which the energy separation between the HOMO and LUMO of both reactants is similar. <ref name="InverseElectronDemand"/> Neutral electron demand Diels-Alder reactions are seldom observed and believed to be a transition between normal electron demand and inverse electron demand Diels Alder reactions.<ref name="TransitionsofElectronDemand"/>

[[File:normalinverseneutral.jpeg|center|500px]]

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

The reaction between butadiene and ethylene presents the simplest type of Diels-Alder reaction, in which butadiene is the diene and ethylene is the dienophile. This reaction yields cyclohexene as the product, and the reaction scheme is as follow:

[[File:exercise 1 reaction scheme.jpg|center]]

=== Molecular Orbital Diagram ===

[[File:MO diagram for exercise 1 TP1414.jpg|500px|thumb|center|Molecular orbital (MO) diagram for the reaction of butadiene with ethylene]]
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Jmol
! style="background: #0D4F8B; color: white;" | Symmetry
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Jmol
! style="background: #0D4F8B; color: white;" | Symmetry
|-
! rowspan="2" style="background: #0D4F8B; color: white;"| Butadiene
! style="background: #0D4F8B; color: white;"| LUMO
|style="text-align: center;"| [[File:ex1butadieneLUMOtp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 BUTADIENE BREAK SYMMETRY JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 22; rotate x -90; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
! rowspan="4" style="background: #0D4F8B; color: white;"| Transition State
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex1mo4tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
|-
! style="background: #0D4F8B; color: white;"| HOMO
|style="text-align: center;"| [[File:ex1butadieneHOMOtp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 BUTADIENE BREAK SYMMETRY JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 22; rotate x -90; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex1mo3tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
|-
! rowspan="2" style="background: #0D4F8B; color: white;"| Ethylene
! style="background: #0D4F8B; color: white;"| LUMO
|style="text-align: center;"| [[File:ex1ethyleneLUMOtp1414.png|100px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 ETHYLENE JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 14; rotate z 90; rotate x 90; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex1mo2tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| HOMO
|style="text-align: center;"| [[File:ex1ethyleneHOMOtp1414.png|100px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 ETHYLENE JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 14; rotate z 90; rotate x 90; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex1mo1tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
|-
|}

<br style="clear:right">

Only orbitals of the same symmetry can interact to form molecular orbitals. This means that only symmetric-symmetric interactions and antisymmetric-antisymmetric interactions are allowed. Symmetric-antisymmetric interactions, on the other hand, are forbidden. This is because the orbital overlap integral is non-zero for interactions between orbitals of the same symmetry and zero for interactions between orbitals of different symmetry.

As shown on the MO diagram above, both interactions (between the HOMO of butadiene and the LUMO of ethylene, and between the LUMO of butadiene and the HOMO of ethylene) occur, generating four molecular orbitals for the transition state. As the energy separation for the two interactions is similar, the reaction between butadiene and ethylene progress with aspects of both normal electron demand and inverse electron demand. This is because both butadiene and ethylene are neutral molecules without any obvious nucleophilic or electrophilic reacting centrers. Both molecules are neither electron-rich nor electron-poor. As a result, orbital overlap is possible for both HOMO-LUMO sets. Several papers classify this reaction as a neutral electron demand Diels-Alder. <ref name="InverseElectronDemand"/> <ref name="TransitionsofElectronDemand"/> This particular Diels-Alder reaction between butadiene and ethylene is well-known for its poor yield.

<br style="clear:left">

=== Internuclear Distances ===

[[File:internuclear distance.pdf|600px|thumb|right|Internuclear distances for the reaction of butadiene with ethylene to form cyclohexene.]]

[[File:butadiene and ethylene.jpg]]

{| class="wikitable"
|+ Internuclear Distances (Å)
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | C1-C2
! style="background: #0D4F8B; color: white;" | C2-C3
! style="background: #0D4F8B; color: white;" | C3-C4
! style="background: #0D4F8B; color: white;" | C4-C5
! style="background: #0D4F8B; color: white;" | C5-C6
! style="background: #0D4F8B; color: white;" | C6-C1
|-
! style="background: #0D4F8B; color: white;"| Reactants
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|style="text-align: center;"| -
|-
! style="background: #0D4F8B; color: white;"| Transition State
|style="text-align: center;"| 1.38
|style="text-align: center;"| 1.41
|style="text-align: center;"| 1.38
|style="text-align: center;"| 2.11
|style="text-align: center;"| 1.38
|style="text-align: center;"| 2.11
|-
! style="background: #0D4F8B; color: white;"| Product
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}

As the reaction progresses, C1-C2, C3-C4 and C5-C6 elongate as the double bond breaks to form single carbon-carbon bonds, while C2-C3 shortens to form carbon-carbon double bond. Simultaneously, C4-C5 and C6-C1 decrease in distance and ultimately single carbon-carbon bonds are formed. A more detailed overview of how the internuclear distances change over the course of the reaction is shown on the graph on the right.

A typical carbon-carbon single bond length is 1.54 Å and a typical carbon-carbon double bond length is 1.34 Å. <ref name="OrganicChemistryJoseph" />

The Van der Waals radius of one carbon atom is 1.70 Å. <ref name="TheMoleculesofLife" /> The length of the partly formed carbon-carbon bonds in the transition state is about 2.11 Å. This distance is shorter than twice the Van der Waals radius of carbon atom (3.40 Å), indicating bonding interactions are occuring.
<br style="clear:right">

=== Vibration and Reaction Path ===

[[File:exercisa1imaginaryfrequency.jpg]]

The vibration that corresponds to the reaction path at the transition state is illustrated above. This vibration has an imaginary frequency that occurs at 948.97i cm<sup>-1</sup>.

The formation of the two bonds are synchronous as shown below. This means that the two sigma bonds are formed simultaneously. hence, the reaction between butadiene and ethylene goes by a concerted synchronous mechanism.

[[File:IRCgif.jpg]]

=== Calculation Files ===

[[File:TP1414 Exercise 1 Ethylene.log]]

[[File:TP1414 Exercise 1 Butadiene.log]]

[[File:TP1414 Exercise 1 Product.log]]

[[File:TP1414 Exercise 1 Transition State.log]]

[[File:TP1414 Exercise 1 IRC.log]]

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

[[File:exercise 2 reaction schemetp1414.jpg|center]]

=== Molecular Orbital Diagram ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|style="text-align: center;"| [[File:ex 2 MO diagram for exo TS TP1414.jpg|500px]]
Molecular orbital (MO) diagram for the reaction of cyclohexadiene and 1,3-dioxole (exo).
|style="text-align: center;"| [[File:ex 2 MO diagram for endo TS TP1414.jpg|500px]]
Molecular orbital (MO) diagram for the reaction of cyclohexadiene and 1,3-dioxole (endo)
|-
|}

<br style="clear:left">

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Image
! style="background: #0D4F8B; color: white;" | Symmetry
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Image
! style="background: #0D4F8B; color: white;" | Symmetry
|-
! rowspan="4" style="background: #0D4F8B; color: white;"| Exo
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex2exoMO4tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO3 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
! rowspan="4" style="background: #0D4F8B; color: white;"| Endo
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex2endoMO4tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO4 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
|-
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex2exoMO3tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO4 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex2endoMO3tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO3 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex2exoMO2tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO2 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex2endoMO2tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO2 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex2exoMO1tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO1 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex2endoMO1tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO1 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
|-
|}

The exo and endo Diels-Alder between cyclohexadiene and 1,3-dioxole proceed in a similar fashion as the Diels-Alder between butadiene and ethylene in Exercise 1. However, unlike in Exercise 1, the dienophile, 1,3-dioxole, contains two pi electron donating oxygen adjacent to the C-C double bond. This increases the energy of the molecular orbitals of the dienophile, resulting in higher energies HOMO and LUMO of the dienophile relative to neutral ethylene in Exercise 1. As a consequence, the HOMO of the dienophile and the LUMO of the diene are much closer in energy and thus, interact more strongly. This reaction between cyclohexadiene and 1,3-dioxole is said to proceed via inverse electron demand Diels-Alder. The stronger interaction between the HOMO and LUMO results in a faster and more favourable reaction as compared to the neutral electron demand Diels-Alder between butadiene and ethylene in Exercise 1.

=== Thermochemistry ===
[[File:ex2energyprofiletp1414.jpeg|600px|thumb|Energy profile diagram for the reactions between cyclohexadiene and 1,3-dioxole]]
The energies of the reactants, transition state and product for both the exo and endo reactions are tabulated below. These are obtained from optimization at B3LYP/6-31G(d) level.

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;"| Exo
|style="text-align: center;"|-612591.48
|style="text-align: center;"|-701187.43
|style="text-align: center;"|-1313778.91
|style="text-align: center;"|-1313614.33
|style="text-align: center;"|-1313845.77
|style="text-align: center;"|164.58
|style="text-align: center;"|-66.86
|-
!style="background: #0D4F8B; color: white;"| Endo
|style="text-align: center;"|-612591.48
|style="text-align: center;"|-701187.43
|style="text-align: center;"|-1313778.91
|style="text-align: center;"|-1313622.15
|style="text-align: center;"|-1313849.37
|style="text-align: center;"|156.76
|style="text-align: center;"|-70.46
|-
|}

Both the exo and endo reactions are exothermic. However, it can be seen that the energy of the endo product is lower (or more negative) than the energy of the exo product, and the endo reaction also has a lower reaction barrier as compared to the exo reaction. This means that the endo product is both the thermodynamically and kinetically favourable product. This can be explained by considering both electronic and steric factors

[[File:seondaryorbitalinteractionstp1414.png|500px|thumb|left|Secondary orbital interactions in endo transition state]] Secondary orbital interactions stabilize the endo transition state, reducing the reaction barrier. On the left is the HOMO of the endo transition state in which there are obvious secondary orbital interactions between the oxygen p orbitals of the 1,3-dioxole and the p orbitals of the diene. An MO representation of this HOMO is shown below.
[[File:secondaryorbitalinteractionMOrepresentationtp1414.jpeg|350px]]
<br style="clear:left">

[[File:stericclashtp1414.png|500px|thumb|left|Steric clash in exo product]] Steric clash between the sp<sup>3</sup> CH<sub>2</sub> of the dioxole ring and the sp<sup>3</sup> CH<sub>2</sub>'s of the cyclohexadiene destabilize both the exo transition state and the exo product.
<br style="clear:left">

=== Vibration and Reaction Path ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
! style="background: #0D4F8B; color: white;"| Vibration
|style="text-align: center;"| [[File:exercise2 exo vibration tp1414.gif]]
|style="text-align: center;"| [[File:exercise2 endo vibration tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Vibrational Frequency
|style="text-align: center;"| 520.90i cm<sup>-1</sup>
|style="text-align: center;"| 528.85i cm<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| Reaction Pathway
|style="text-align: center;"| [[File:exercise2 exo reaction path tp1414.gif]]
|style="text-align: center;"| [[File:exercise2 endo reaction path tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Mechanism
|style="text-align: center;"| Synchronous concerted
|style="text-align: center;"| Synchronous concerted
|-
|}

=== Calculation Files ===

[[File:TP1414 Exercise 2 Cyclohexadiene 631Gd.log]]

[[File:TP1414 Exercise 2 1,2-Dioxole 631Gd.log]]

[[File:TP1414 Exercise 2 Exo Product 631Gd.log]]

[[File:TP1414 Exercise 2 Endo Product 631Gd.log]]

[[File:TP1414 Exercise 2 Exo Transition State 631Gd.log]]

[[File:TP1414 Exercise 2 Endo Transition State 631Gd.log]]

[[File:TP1414 Exercise 2 Exo IRC 631Gd.log]]

[[File:TP1414 Exercise 2 Endo IRC 631Gd.log]]

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

[[File:exercise3reactionschemetp1414.jpg|center]]

=== Molecular Orbital Diagram ===

The exo and endo Diels-Alder reaction between o-xylylene and SO<sub>2</sub> proceed in a similar fashion as the reactions in Exercise 1 and 2. However, in this case, the dienophile, SO<sub>2</sub>, is electron-deficient and has lower energies HOMO and LUMO compared to the dienophiles in Exercise 1 and 2. As a result, the most significant frontier orbital interaction is between the HOMO of o-xylylene and the LUMO of SO<sub>2</sub>. The Diels-Alder reaction between o-xylylene and SO<sub>2</sub> proceeds via normal electron demand.

The exo and endo Diels-Alder reaction between o-xylylene and SO<sub>2</sub> have another competing pericyclic reaction - cheletropic reaction. Woodward Hoffmann defines cheletropic reactions as pericyclic reactions in which two sigma bonds are formed or broken in a single atom. It is sometimes considered to be a subclass of cycloadditions. <ref name="Cheletropic"/> The MO diagram for the cheletropic reaction is shown below.

[[File:tp1414cheletropicMOdiagram.jpg|500px|thumb|center|Molecular orbital (MO) diagram for the cheletropic reaction between o-xylylene and SO<sub>2</sub> <ref name="OrganicReactions"/>]]

=== Thermochemistry ===
[[File:ex3energyprofiletp1414.jpg|600px|thumb|Energy profile diagram for the reactions between o-xylylene and SO<sub>2</sub>]]
The energies of the reactants, transition state and product for the exo, endo and cheletropic reactions are tabulated below. These are obtained from optimization at PM6 level.

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | o-Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;"| Exo
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|241.75
|style="text-align: center;"|56.31
|style="text-align: center;"|85.18
|style="text-align: center;"|-100.26
|-
!style="background: #0D4F8B; color: white;"| Endo
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|237.77
|style="text-align: center;"|56.98
|style="text-align: center;"|81.20
|style="text-align: center;"|-99.59
|-
!style="background: #0D4F8B; color: white;"| Cheletropic
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|260.09
|style="text-align: center;"|-0.01
|style="text-align: center;"|103.52
|style="text-align: center;"|-156.58
|-
|}

All three reactions are exothermic. The endo product is the kinetically favourable product as it has the lowest reaction barrier, while the cheletropic product is the thermodynamically favourable product as it has the lowest energy. This is consistent with experimental works that have been conducted in which a Diels-Alder adduct is observed to be the kinetic product and cheletropic adduct is observed to be the thermodynamic product. Experimental work shows that the Diels-Alder adduct is thermally unstable and will undergo a retro-Diels-Alder reaction to form back the starting materials, before forming the more stable five membered ring cheletropic product. <ref name="Cheletropic"/>
<br style="clear:right">

=== Vibration and Reaction Path ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
! style="background: #0D4F8B; color: white;" | Cheletropic
|-
! style="background: #0D4F8B; color: white;"| Vibration
|style="text-align: center;"| [[File:ex3 exo vibration tp1414.gif]]
|style="text-align: center;"| [[File:ex3 endo vibration tp1414.gif]]
|style="text-align: center;"| [[File:cheletropic vibration tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Vibrational Frequency
|style="text-align: center;"| 351.78i cm<sup>-1</sup>
|style="text-align: center;"| 334.38i cm<sup>-1</sup>
|style="text-align: center;"| 486.58i cm<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| Reaction Pathway
|style="text-align: center;"| [[File:exo IRC tp1414.gif]]
|style="text-align: center;"| [[File:endo IRC tp1414.gif]]
|style="text-align: center;"| [[File:cheletropic IRC tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Mechanism
|style="text-align: center;"| Asynchronous concerted
|style="text-align: center;"| Asynchronous concerted
|style="text-align: center;"| Synchronous concerted
|-
! style="background: #0D4F8B; color: white;"| IRC
|style="text-align: center;"| [[File:exoIRCtp1414.png]]
|style="text-align: center;"| [[File:endoIRCtp1414.png]]
|style="text-align: center;"| [[File:cheletropicIRCtp1414energy.png]]
|-
|}

It is interesting to note that the exo and endo reactions proceed via asynchronous mechanism in which the C-O bond is formed first before the C-S bond, while the cheletropic reaction proceeds via synchronous mechanism in which the two C-S bonds are formed simultaneously. However, even though the formation of the two bonds are asynchronous in the exo and endo reactions, the total energy along IRC tells us that both reactions are concerted as the reactions do not have any intermediate steps.

In all three reaction pathways, the steepest part on the the total energy versus IRC graph corresponds to the re-aromatisation of the 6-membered ring on the o-xylylene, giving these reactions an aromatic driving force. This also shows the instability of the o-xylylene molecule. O-Xylylene is highly unstable as it is antiaromatic (planar and 4n electrons), and it will undergo an electrocyclic ring closure to form the stable aromatic isomer, benzocyclobutene as shown below.<ref name="Benzocyclobutene"/>

[[File:xylyleneelectrocyclicreactionscheme.jpg|centre]]

A quick transition state optimisation followed by IRC calculation of the above reaction on Gaussian gives the total energy along IRC graph below.

[[File:xylyleneelectrocyclicIRCtp1414.jpg|500px|centre]]

[[File:xylyleneelectrocyclicIRC.gif|500px|centre]]

=== Alternate Diels-Alder Reaction ===

There is a second cis-butadiene fragment in o-xylylene that can undergo a Diels-Alder reaction. This second cis-butadiene is part of the cyclohexadiene ring. The exo and endo for this alternate Diels-Alder reaction proceed as follow:

[[File:alternatedielsalderexotp1414.gif]] [[File:alternatedielsalderendotp1414.gif]]

Both reactions proceed via an asynchronous mechanism.

[[File:energyprofilewithalternatedielsaldertp1414.jpg|600px|thumb|Energy profile diagram for the reactions between o-xylylene and SO<sub>2</sub>]]
The thermochemistry for this alternate Diels-Alder reaction is as follows:

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | o-Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;" | Exo
| style="text-align: center;" |467.99
| style="text-align: center;" |-311.42
| style="text-align: center;" |156.57
| style="text-align: center;" |275.82
| style="text-align: center;" |176.71
| style="text-align: center;" |119.25
| style="text-align: center;" |20.14
|-
! style="background: #0D4F8B; color: white;" | Endo
| style="text-align: center;" |467.99
| style="text-align: center;" |-311.42
| style="text-align: center;" |156.57
| style="text-align: center;" |267.98
| style="text-align: center;" |172.26
| style="text-align: center;" |111.41
| style="text-align: center;" |15.96
|-
|}

Comparing the energies for this alternate Diels-Alder reaction with the energies for the normal Diels-Alder and the cheletropic reactions, it can be seen that both the exo and endo alternate Diels-Alder reactoions are kinetically and thermodynamically unfavourable. The products are also higher in energies than the reactants, making the reactions endothermic.
<br style="clear:right">

=== Calculation Files ===

[[File:TP1414 Exercise 3 Xylylene.log]]

[[File:TP1414 Exercise 3 SO2.log]]

[[File:TP1414 Exercise 3 Exo Product.log]]

[[File:TP1414 Exercise 3 Endo Product.log]]

[[File:TP1414 Exercise 3 Cheletropic Product.log]]

[[File:TP1414 Exercise 3 Exo Transition State.log]]

[[File:TP1414 Exercise 3 Endo Transition State.log]]

[[File:TP1414 Exercise 3 Cheletropic Transition State.log]]

[[File:TP1414 Exercise 3 Exo IRC.log]]

[[File:TP1414 Exercise 3 Endo IRC.log]]

[[File:TP1414 Exercise 3 Cheletropic IRC.log]]

[[File:TP1414 Exercise 3 Xylylene Electrocyclic Transition State.log]]

[[File:TP1414 Exercise 3 Xylylene Electrocyclic IRC.log]]

[[File:TP1414 Exercise 3 Alternate Exo Product.log]]

[[File:TP1414 Exercise 3 Alternate Endo Product.log]]

[[File:TP1414 Exercise 3 Alternate Exo Transition State.log]]

[[File:TP1414 Exercise 3 Alternate Endo Transition State.log]]

[[File:TP1414 Exercise 3 Alternate Exo IRC.log]]

[[File:TP1414 Exercise 3 Alternate Endo IRC.log]]

== Conclusion ==

Two calculation methods were used to study three different Diels-Alder reactions. The semi-empirical method PM6 was used to calculate the geometries of the transition state and product of the reactions in all three exercises for faster calculations. In exercise 2, the geometries were further optimised by the DFT method B3LYP at 6-31G(d) level for better accuracy.

Exercises 1 to 3 illustrate the three different ways in which Diels-Alder reaction can proceed: neutral electron demand, inverse electron demand and normal electron demand respectively. In exercise 1, the frontier orbital interactions of the simplest Diels-Alder reaction was studied and it shows that only orbitals of the same symmetry can interact. Exercise 1 also illustrates how internuclear distances vary as a Diels-Alder reaction proceeds, and how these compare with the Van der Waals radii of the atoms. Exercise 2 presents a more complex Diels-Alder reaction which can proceed in two different orientations - endo and exo. It demonstrates how secondary orbital interactions and steric factors could affect the energies of the transition states and products, and hence, determine the kinetically and thermodynamically favourable reactions. Exercise 3 illustrates an even more complex system where there are two diene functional groups and in which another competing pericyclic cheletropic reaction is possible. It also demonstrates that pericyclic reactions can proceed via synchronous concerted or asynchronous concerted mechanisms depending on the symmetry of the interacting molecules.

In conclusion, Gaussian proves to be a useful molecular modelling software to investigate the molecules and their reactions. Transition states were located and characterized, and frontier orbital interactions and thermochemistry were analysed. Results obtained from these calculations also proved to be consistent with theory and experimental observations.

== References ==

<references>
<ref name="ComputationalChemistry"> Lecture notes: ''Quantum Mechanics 3/3rd Year Computational Chemistry Laboratory'', Michael Bearpark, Imperial College. </ref>
<ref name="OrganicChemistryJoseph"> J. M. Hornback, ''Organic Chemistry'', Thomson Learning. Inc., Belmont, Second., 2006, pp. 94.</ref>
<ref name="TheMoleculesofLife"> J. Kuriyan, B. Konforti and D. Wemmer, ''The Molecules of Life: Physical and Chemical Principles'', Garland Science, New York, 2013.</ref>
<ref name="InverseElectronDemand"> A.-C. Knall and C. Slugovc, ''Chem Soc Rev'', 2013, '''42''', 5131–5142.</ref>
<ref name="TransitionsofElectronDemand"> E. Eibler, P. Hocht, B. Prantl, H. Rormaier, H. M. Schuhbauer and H. Wiest, ''Liebigs Ann.lRemei'', 1997, '''1997''', 2471–2484.</ref>
<ref name="Benzocyclobutene"> G. Mehta and S. Kotha, ''Tetrahedron'', 2001, '''57''', 626.</ref>
<ref name="ManyParticlePhysics"> H. Fehske, R. Schneider and A. Weiβe, Eds., ''Computational Many-Particle Physics'', Springer, Berlin, 2008, pp. 438.</ref>
<ref name="Cheletropic"> D. Suarez, T. L. Sordo and A. Sordo, ''J. Org. Chem.'', 1995, '''60''', 2848–2852.</ref>
<ref name="OrganicReactions"> P. S. Kalsi, ''Organic Reactions Stereochemistry and Mechanism'', New Age International Publishers, New Delhi, Fourth., 2006, pp. 550.</ref>
</references>

Rep:Mod:TP1414

2017-03-20T14:59:07Z

Tp1414: /* References */

== Introduction ==

=== Gaussian and Transition State Characterization ===

[[File:Energy surface TP1414.jpg|500px|thumb| Energy surface showing the locations of transition state (TS), local minimum (LM) and global minimum (GM).<ref name="ManyParticlePhysics"/>]]

Gaussian is a molecular modelling software that allows researchers to carry out extensive investigation of molecules and their reactions. In these exercises, the transition states of several Diels-Alder reactions are located and characterized using Gaussian. A transition state is a first order saddle point on a potential energy surface (PES). It is the maximum along the minimum energy path (or reaction path) between two minima (the reactants and the products). ''Geometry optimization'' to find the minimum energy structure will usually lead to a stationary point that is closest to the initial geometry. The stationary point, where the first derivative of energy is zero, can be a global minimum, a local minimum or a saddle point. In a reaction path, the minima (global or local) correspond to the reactants and the products, while the saddle point corresponds to the transition state. To differentiate between a minimum and a saddle point, the second derivatives of energy will have to be analysed. For global or local minima, where energy rises in all directions, the second derivative of energy is positive. In contrast, for transition state, where the energy decreases in one direction (reaction path), the second derivative of energy along the reaction coordinate is negative. The analysis of the second derivatives of energy can be done by a ''frequency calculation'' of the optimized structure. If the structure corresponds to the reactants or products, all the vibrational frequencies (''v'') are real. In contrast, if the structure corresponds to a transition state, there will be one imaginary frequency. This imaginary frequency indicates that the force constant (k), which is given by the second derivative, is negative. <ref name="ComputationalChemistry"/>

<center> <math>\textit{v}=\frac{1}{2\pi }\cdot \sqrt{\frac{k}{\mu }}</math> where <math>k=\frac{\partial ^{2}E}{\partial q^{2}}</math> </center>

Following a successful frequency calculation (one imaginary frequency) of the transition state, an ''Intrinsic Reaction Coordinate (IRC) calculation'' may be set up to examine the transition state along the minimum energy path more closely. The reaction path, or minimum energy path, can be defined as the steepest descent path from the transition state to the reactions and products.

In this exercise, two calculation methods are used. The first is the semi-empirical method PM6, a fitted method used to obtain the initial geometry of the molecule or transition state so as to save time during calculations. The second is the Density Functional Theory (DFT) method B3LYP, a method that is capable of reproducing chemical data and is used to further optimise the geometry obtained from the PM6 method.

=== Diels-Alder Reactions ===

A Diels-Alder reaction is a [4+2] cycloadditon between a conjugated s-cis diene (4π-electron system) and a dienophile (2π-electron system). The reaction has a cyclic transition state with 6π-electrons, is concerted, and results in the formation of two new sigma bonds. According to the Woodward-Hoffmann Rules, the Diels-Alder reaction is thermally allowed and is an orbital-controlled reaction, in which the six electrons are interacting suprafacially. The reaction can mainly proceed in two ways:

# Normal electron demand: HOMO of diene overlaps with LUMO of dienophile
# Inverse electron demand: LUMO of diene overlaps with HOMO of dienophile

Several papers divide the Diels-Alder reactions into three categories instead of two <ref name="InverseElectronDemand"/> <ref name="TransitionsofElectronDemand"/>, the third being a neutral electron demand Diels-Alder, in which the energy separation between the HOMO and LUMO of both reactants is similar. <ref name="InverseElectronDemand"/> Neutral electron demand Diels-Alder reactions are seldom observed and believed to be a transition between normal electron demand and inverse electron demand Diels Alder reactions.<ref name="TransitionsofElectronDemand"/>

[[File:normalinverseneutral.jpeg|center|500px]]

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

The reaction between butadiene and ethylene presents the simplest type of Diels-Alder reaction, in which butadiene is the diene and ethylene is the dienophile. This reaction yields cyclohexene as the product, and the reaction scheme is as follow:

[[File:exercise 1 reaction scheme.jpg|center]]

=== Molecular Orbital Diagram ===

[[File:MO diagram for exercise 1 TP1414.jpg|500px|thumb|center|Molecular orbital (MO) diagram for the reaction of butadiene with ethylene]]
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Jmol
! style="background: #0D4F8B; color: white;" | Symmetry
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Jmol
! style="background: #0D4F8B; color: white;" | Symmetry
|-
! rowspan="2" style="background: #0D4F8B; color: white;"| Butadiene
! style="background: #0D4F8B; color: white;"| LUMO
|style="text-align: center;"| [[File:ex1butadieneLUMOtp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 BUTADIENE BREAK SYMMETRY JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 22; rotate x -90; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
! rowspan="4" style="background: #0D4F8B; color: white;"| Transition State
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex1mo4tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
|-
! style="background: #0D4F8B; color: white;"| HOMO
|style="text-align: center;"| [[File:ex1butadieneHOMOtp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 BUTADIENE BREAK SYMMETRY JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 22; rotate x -90; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex1mo3tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
|-
! rowspan="2" style="background: #0D4F8B; color: white;"| Ethylene
! style="background: #0D4F8B; color: white;"| LUMO
|style="text-align: center;"| [[File:ex1ethyleneLUMOtp1414.png|100px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 ETHYLENE JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 14; rotate z 90; rotate x 90; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex1mo2tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| HOMO
|style="text-align: center;"| [[File:ex1ethyleneHOMOtp1414.png|100px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 ETHYLENE JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 14; rotate z 90; rotate x 90; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex1mo1tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
|-
|}

<br style="clear:right">

Only orbitals of the same symmetry can interact to form molecular orbitals. This means that only symmetric-symmetric interactions and antisymmetric-antisymmetric interactions are allowed. Symmetric-antisymmetric interactions, on the other hand, are forbidden. This is because the orbital overlap integral is non-zero for interactions between orbitals of the same symmetry and zero for interactions between orbitals of different symmetry.

As shown on the MO diagram above, both interactions (between the HOMO of butadiene and the LUMO of ethylene, and between the LUMO of butadiene and the HOMO of ethylene) occur, generating four molecular orbitals for the transition state. As the energy separation for the two interactions is similar, the reaction between butadiene and ethylene progress with aspects of both normal electron demand and inverse electron demand. This is because both butadiene and ethylene are neutral molecules without any obvious nucleophilic or electrophilic reacting centrers. Both molecules are neither electron-rich nor electron-poor. As a result, orbital overlap is possible for both HOMO-LUMO sets. Several papers classify this reaction as a neutral electron demand Diels-Alder. <ref name="InverseElectronDemand"/> <ref name="TransitionsofElectronDemand"/> This particular Diels-Alder reaction between butadiene and ethylene is well-known for its poor yield.

<br style="clear:left">

=== Internuclear Distances ===

[[File:internuclear distance.pdf|600px|thumb|right|Internuclear distances for the reaction of butadiene with ethylene to form cyclohexene.]]

[[File:butadiene and ethylene.jpg]]

{| class="wikitable"
|+ Internuclear Distances (Å)
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | C1-C2
! style="background: #0D4F8B; color: white;" | C2-C3
! style="background: #0D4F8B; color: white;" | C3-C4
! style="background: #0D4F8B; color: white;" | C4-C5
! style="background: #0D4F8B; color: white;" | C5-C6
! style="background: #0D4F8B; color: white;" | C6-C1
|-
! style="background: #0D4F8B; color: white;"| Reactants
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|style="text-align: center;"| -
|-
! style="background: #0D4F8B; color: white;"| Transition State
|style="text-align: center;"| 1.38
|style="text-align: center;"| 1.41
|style="text-align: center;"| 1.38
|style="text-align: center;"| 2.11
|style="text-align: center;"| 1.38
|style="text-align: center;"| 2.11
|-
! style="background: #0D4F8B; color: white;"| Product
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}

As the reaction progresses, C1-C2, C3-C4 and C5-C6 elongate as the double bond breaks to form single carbon-carbon bonds, while C2-C3 shortens to form carbon-carbon double bond. Simultaneously, C4-C5 and C6-C1 decrease in distance and ultimately single carbon-carbon bonds are formed. A more detailed overview of how the internuclear distances change over the course of the reaction is shown on the graph on the right.

A typical carbon-carbon single bond length is 1.54 Å and a typical carbon-carbon double bond length is 1.34 Å. <ref name="OrganicChemistryJoseph" />

The Van der Waals radius of one carbon atom is 1.70 Å. <ref name="TheMoleculesofLife" /> The length of the partly formed carbon-carbon bonds in the transition state is about 2.11 Å. This distance is shorter than twice the Van der Waals radius of carbon atom (3.40 Å), indicating bonding interactions are occuring.
<br style="clear:right">

=== Vibration and Reaction Path ===

[[File:exercisa1imaginaryfrequency.jpg]]

The vibration that corresponds to the reaction path at the transition state is illustrated above. This vibration has an imaginary frequency that occurs at 948.97i cm<sup>-1</sup>.

The formation of the two bonds are synchronous as shown below. This means that the two sigma bonds are formed simultaneously. hence, the reaction between butadiene and ethylene goes by a concerted synchronous mechanism.

[[File:IRCgif.jpg]]

=== Calculation Files ===

[[File:TP1414 Exercise 1 Ethylene.log]]

[[File:TP1414 Exercise 1 Butadiene.log]]

[[File:TP1414 Exercise 1 Product.log]]

[[File:TP1414 Exercise 1 Transition State.log]]

[[File:TP1414 Exercise 1 IRC.log]]

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

[[File:exercise 2 reaction schemetp1414.jpg|center]]

=== Molecular Orbital Diagram ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|style="text-align: center;"| [[File:ex 2 MO diagram for exo TS TP1414.jpg|500px]]
Molecular orbital (MO) diagram for the reaction of cyclohexadiene and 1,3-dioxole (exo).
|style="text-align: center;"| [[File:ex 2 MO diagram for endo TS TP1414.jpg|500px]]
Molecular orbital (MO) diagram for the reaction of cyclohexadiene and 1,3-dioxole (endo)
|-
|}

<br style="clear:left">

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Image
! style="background: #0D4F8B; color: white;" | Symmetry
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Image
! style="background: #0D4F8B; color: white;" | Symmetry
|-
! rowspan="4" style="background: #0D4F8B; color: white;"| Exo
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex2exoMO4tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO3 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
! rowspan="4" style="background: #0D4F8B; color: white;"| Endo
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex2endoMO4tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO4 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
|-
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex2exoMO3tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO4 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex2endoMO3tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO3 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex2exoMO2tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO2 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex2endoMO2tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO2 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex2exoMO1tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO1 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex2endoMO1tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO1 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
|-
|}

The exo and endo Diels-Alder between cyclohexadiene and 1,3-dioxole proceed in a similar fashion as the Diels-Alder between butadiene and ethylene in Exercise 1. However, unlike in Exercise 1, the dienophile, 1,3-dioxole, contains two pi electron donating oxygen adjacent to the C-C double bond. This increases the energy of the molecular orbitals of the dienophile, resulting in higher energies HOMO and LUMO of the dienophile relative to neutral ethylene in Exercise 1. As a consequence, the HOMO of the dienophile and the LUMO of the diene are much closer in energy and thus, interact more strongly. This reaction between cyclohexadiene and 1,3-dioxole is said to proceed via inverse electron demand Diels-Alder. The stronger interaction between the HOMO and LUMO results in a faster and more favourable reaction as compared to the neutral electron demand Diels-Alder between butadiene and ethylene in Exercise 1.

=== Thermochemistry ===
[[File:ex2energyprofiletp1414.jpeg|600px|thumb|Energy profile diagram for the reactions between cyclohexadiene and 1,3-dioxole]]
The energies of the reactants, transition state and product for both the exo and endo reactions are tabulated below. These are obtained from optimization at B3LYP/6-31G(d) level.

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;"| Exo
|style="text-align: center;"|-612591.48
|style="text-align: center;"|-701187.43
|style="text-align: center;"|-1313778.91
|style="text-align: center;"|-1313614.33
|style="text-align: center;"|-1313845.77
|style="text-align: center;"|164.58
|style="text-align: center;"|-66.86
|-
!style="background: #0D4F8B; color: white;"| Endo
|style="text-align: center;"|-612591.48
|style="text-align: center;"|-701187.43
|style="text-align: center;"|-1313778.91
|style="text-align: center;"|-1313622.15
|style="text-align: center;"|-1313849.37
|style="text-align: center;"|156.76
|style="text-align: center;"|-70.46
|-
|}

Both the exo and endo reactions are exothermic. However, it can be seen that the energy of the endo product is lower (or more negative) than the energy of the exo product, and the endo reaction also has a lower reaction barrier as compared to the exo reaction. This means that the endo product is both the thermodynamically and kinetically favourable product. This can be explained by considering both electronic and steric factors

[[File:seondaryorbitalinteractionstp1414.png|500px|thumb|left|Secondary orbital interactions in endo transition state]] Secondary orbital interactions stabilize the endo transition state, reducing the reaction barrier. On the left is the HOMO of the endo transition state in which there are obvious secondary orbital interactions between the oxygen p orbitals of the 1,3-dioxole and the p orbitals of the diene. An MO representation of this HOMO is shown below.
[[File:secondaryorbitalinteractionMOrepresentationtp1414.jpeg|350px]]
<br style="clear:left">

[[File:stericclashtp1414.png|500px|thumb|left|Steric clash in exo product]] Steric clash between the sp<sup>3</sup> CH<sub>2</sub> of the dioxole ring and the sp<sup>3</sup> CH<sub>2</sub>'s of the cyclohexadiene destabilize both the exo transition state and the exo product.
<br style="clear:left">

=== Vibration and Reaction Path ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
! style="background: #0D4F8B; color: white;"| Vibration
|style="text-align: center;"| [[File:exercise2 exo vibration tp1414.gif]]
|style="text-align: center;"| [[File:exercise2 endo vibration tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Vibrational Frequency
|style="text-align: center;"| 520.90i cm<sup>-1</sup>
|style="text-align: center;"| 528.85i cm<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| Reaction Pathway
|style="text-align: center;"| [[File:exercise2 exo reaction path tp1414.gif]]
|style="text-align: center;"| [[File:exercise2 endo reaction path tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Mechanism
|style="text-align: center;"| Synchronous concerted
|style="text-align: center;"| Synchronous concerted
|-
|}

=== Calculation Files ===

[[File:TP1414 Exercise 2 Cyclohexadiene 631Gd.log]]

[[File:TP1414 Exercise 2 1,2-Dioxole 631Gd.log]]

[[File:TP1414 Exercise 2 Exo Product 631Gd.log]]

[[File:TP1414 Exercise 2 Endo Product 631Gd.log]]

[[File:TP1414 Exercise 2 Exo Transition State 631Gd.log]]

[[File:TP1414 Exercise 2 Endo Transition State 631Gd.log]]

[[File:TP1414 Exercise 2 Exo IRC 631Gd.log]]

[[File:TP1414 Exercise 2 Endo IRC 631Gd.log]]

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

[[File:exercise3reactionschemetp1414.jpg|center]]

=== Molecular Orbital Diagram ===

The exo and endo Diels-Alder reaction between o-xylylene and SO<sub>2</sub> proceed in a similar fashion as the reactions in Exercise 1 and 2. However, in this case, the dienophile, SO<sub>2</sub>, is electron-deficient and has lower energies HOMO and LUMO compared to the dienophiles in Exercise 1 and 2. As a result, the most significant frontier orbital interaction is between the HOMO of o-xylylene and the LUMO of SO<sub>2</sub>. The Diels-Alder reaction between o-xylylene and SO<sub>2</sub> proceeds via normal electron demand.

The exo and endo Diels-Alder reaction between o-xylylene and SO<sub>2</sub> have another competing pericyclic reaction - cheletropic reaction. Woodward Hoffmann defines cheletropic reactions as pericyclic reactions in which two sigma bonds are formed or broken in a single atom. It is sometimes considered to be a subclass of cycloadditions. <ref name="Cheletropic"/> The MO diagram for the cheletropic reaction is shown below.

[[File:tp1414cheletropicMOdiagram.jpg|500px|thumb|center|Molecular orbital (MO) diagram for the cheletropic reaction between o-xylylene and SO<sub>2</sub> <ref name="OrganicReactions"/>]]

=== Thermochemistry ===
[[File:ex3energyprofiletp1414.jpg|600px|thumb|Energy profile diagram for the reactions between o-xylylene and SO<sub>2</sub>]]
The energies of the reactants, transition state and product for the exo, endo and cheletropic reactions are tabulated below. These are obtained from optimization at PM6 level.

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | o-Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;"| Exo
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|241.75
|style="text-align: center;"|56.31
|style="text-align: center;"|85.18
|style="text-align: center;"|-100.26
|-
!style="background: #0D4F8B; color: white;"| Endo
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|237.77
|style="text-align: center;"|56.98
|style="text-align: center;"|81.20
|style="text-align: center;"|-99.59
|-
!style="background: #0D4F8B; color: white;"| Cheletropic
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|260.09
|style="text-align: center;"|-0.01
|style="text-align: center;"|103.52
|style="text-align: center;"|-156.58
|-
|}

All three reactions are exothermic. The endo product is the kinetically favourable product as it has the lowest reaction barrier, while the cheletropic product is the thermodynamically favourable product as it has the lowest energy. This is consistent with experimental works that have been conducted in which a Diels-Alder adduct is observed to be the kinetic product and cheletropic adduct is observed to be the thermodynamic product. Experimental work shows that the Diels-Alder adduct is thermally unstable and will undergo a retro-Diels-Alder reaction to form back the starting materials, before forming the more stable five membered ring cheletropic product. <ref name="Cheletropic"/>
<br style="clear:right">

=== Vibration and Reaction Path ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
! style="background: #0D4F8B; color: white;" | Cheletropic
|-
! style="background: #0D4F8B; color: white;"| Vibration
|style="text-align: center;"| [[File:ex3 exo vibration tp1414.gif]]
|style="text-align: center;"| [[File:ex3 endo vibration tp1414.gif]]
|style="text-align: center;"| [[File:cheletropic vibration tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Vibrational Frequency
|style="text-align: center;"| 351.78i cm<sup>-1</sup>
|style="text-align: center;"| 334.38i cm<sup>-1</sup>
|style="text-align: center;"| 486.58i cm<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| Reaction Pathway
|style="text-align: center;"| [[File:exo IRC tp1414.gif]]
|style="text-align: center;"| [[File:endo IRC tp1414.gif]]
|style="text-align: center;"| [[File:cheletropic IRC tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Mechanism
|style="text-align: center;"| Asynchronous concerted
|style="text-align: center;"| Asynchronous concerted
|style="text-align: center;"| Synchronous concerted
|-
! style="background: #0D4F8B; color: white;"| IRC
|style="text-align: center;"| [[File:exoIRCtp1414.png]]
|style="text-align: center;"| [[File:endoIRCtp1414.png]]
|style="text-align: center;"| [[File:cheletropicIRCtp1414energy.png]]
|-
|}

It is interesting to note that the exo and endo reactions proceed via asynchronous mechanism in which the C-O bond is formed first before the C-S bond, while the cheletropic reaction proceeds via synchronous mechanism in which the two C-S bonds are formed simultaneously. However, even though the formation of the two bonds are asynchronous in the exo and endo reactions, the total energy along IRC tells us that both reactions are concerted as the reactions do not have any intermediate steps.

In all three reaction pathways, the steepest part on the the total energy versus IRC graph corresponds to the re-aromatisation of the 6-membered ring on the o-xylylene, giving these reactions an aromatic driving force. This also shows the instability of the o-xylylene molecule. O-Xylylene is highly unstable as it is antiaromatic (planar and 4n electrons), and it will undergo an electrocyclic ring closure to form the stable aromatic isomer, benzocyclobutene as shown below.<ref name="Benzocyclobutene"/>

[[File:xylyleneelectrocyclicreactionscheme.jpg|centre]]

A quick transition state optimisation followed by IRC calculation of the above reaction on Gaussian gives the total energy along IRC graph below.

[[File:xylyleneelectrocyclicIRCtp1414.jpg|500px|centre]]

[[File:xylyleneelectrocyclicIRC.gif|500px|centre]]

=== Alternate Diels-Alder Reaction ===

There is a second cis-butadiene fragment in o-xylylene that can undergo a Diels-Alder reaction. This second cis-butadiene is part of the cyclohexadiene ring. The exo and endo for this alternate Diels-Alder reaction proceed as follow:

[[File:alternatedielsalderexotp1414.gif]] [[File:alternatedielsalderendotp1414.gif]]

Both reactions proceed via an asynchronous mechanism.

[[File:energyprofilewithalternatedielsaldertp1414.jpg|600px|thumb|Energy profile diagram for the reactions between o-xylylene and SO<sub>2</sub>]]
The thermochemistry for this alternate Diels-Alder reaction is as follows:

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | o-Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;" | Exo
| style="text-align: center;" |467.99
| style="text-align: center;" |-311.42
| style="text-align: center;" |156.57
| style="text-align: center;" |275.82
| style="text-align: center;" |176.71
| style="text-align: center;" |119.25
| style="text-align: center;" |20.14
|-
! style="background: #0D4F8B; color: white;" | Endo
| style="text-align: center;" |467.99
| style="text-align: center;" |-311.42
| style="text-align: center;" |156.57
| style="text-align: center;" |267.98
| style="text-align: center;" |172.26
| style="text-align: center;" |111.41
| style="text-align: center;" |15.96
|-
|}

Comparing the energies for this alternate Diels-Alder reaction with the energies for the normal Diels-Alder and the cheletropic reactions, it can be seen that both the exo and endo alternate Diels-Alder reactoions are kinetically and thermodynamically unfavourable. The products are also higher in energies than the reactants, making the reactions endothermic.
<br style="clear:right">

=== Calculation Files ===

[[File:TP1414 Exercise 3 Xylylene.log]]

[[File:TP1414 Exercise 3 SO2.log]]

[[File:TP1414 Exercise 3 Exo Product.log]]

[[File:TP1414 Exercise 3 Endo Product.log]]

[[File:TP1414 Exercise 3 Cheletropic Product.log]]

[[File:TP1414 Exercise 3 Exo Transition State.log]]

[[File:TP1414 Exercise 3 Endo Transition State.log]]

[[File:TP1414 Exercise 3 Cheletropic Transition State.log]]

[[File:TP1414 Exercise 3 Exo IRC.log]]

[[File:TP1414 Exercise 3 Endo IRC.log]]

[[File:TP1414 Exercise 3 Cheletropic IRC.log]]

[[File:TP1414 Exercise 3 Xylylene Electrocyclic Transition State.log]]

[[File:TP1414 Exercise 3 Xylylene Electrocyclic IRC.log]]

[[File:TP1414 Exercise 3 Alternate Exo Product.log]]

[[File:TP1414 Exercise 3 Alternate Endo Product.log]]

[[File:TP1414 Exercise 3 Alternate Exo Transition State.log]]

[[File:TP1414 Exercise 3 Alternate Endo Transition State.log]]

[[File:TP1414 Exercise 3 Alternate Exo IRC.log]]

[[File:TP1414 Exercise 3 Alternate Endo IRC.log]]

== Conclusion ==

Two calculation methods were used to study three different Diels-Alder reactions. The semi-empirical method PM6 was used to calculate the geometries of the transition state and product of the reactions in all three exercises for faster calculations. In exercise 2, the geometries were further optimised by the DFT method B3LYP at 6-31G(d) level for better accuracy.

Exercises 1 to 3 illustrate the three different ways in which Diels-Alder reaction can proceed: neutral electron demand, inverse electron demand and normal electron demand respectively. In exercise 1, the frontier orbital interactions of the simplest Diels-Alder reaction was studied and it shows that only orbitals of the same symmetry can interact. Exercise 1 also illustrates how internuclear distances vary as a Diels-Alder reaction proceeds, and how these compare with the Van der Waals radii of the atoms. Exercise 2 presents a more complex Diels-Alder reaction which can proceed in two different orientations - endo and exo. It demonstrates how secondary orbital interactions and steric factors could affect the energies of the transition states and products, and hence, determine the kinetically and thermodynamically favourable reactions. Exercise 3 illustrates an even more complex system where there are two diene functional groups and in which another competing pericyclic cheletropic reaction is possible. It also demonstrates that pericyclic reactions can proceed via synchronous concerted or asynchronous concerted mechanisms depending on the symmetry of the interacting molecules.

In conclusion, Gaussian proves to be a useful molecular modelling software to investigate the molecules and their reactions. Transition states were located and characterized, and frontier orbital interactions and thermochemistry were analysed. Results obtained from these calculations also proved to be consistent with theory and experimental observations.

== References ==

<references>
<ref name="ComputationalChemistry"> Lecture notes: ''Quantum Mechanics 3/3rd Year Computational Chemistry Laboratory'', Michael Bearpark, Imperial College. </ref>
<ref name="OrganicChemistryJoseph"> J. M. Hornback, ''Organic Chemistry'', Thomson Learning. Inc., Belmont, Second., 2006.</ref>
<ref name="TheMoleculesofLife"> J. Kuriyan, B. Konforti and D. Wemmer, ''The Molecules of Life: Physical and Chemical Principles'', Garland Science, New York, 2013.</ref>
<ref name="InverseElectronDemand"> A.-C. Knall and C. Slugovc, ''Chem Soc Rev'', 2013, '''42''', 5131–5142.</ref>
<ref name="TransitionsofElectronDemand"> E. Eibler, P. Hocht, B. Prantl, H. Rormaier, H. M. Schuhbauer and H. Wiest, ''Liebigs Ann.lRemei'', 1997, '''1997''', 2471–2484.</ref>
<ref name="Benzocyclobutene"> G. Mehta and S. Kotha, ''Tetrahedron'', 2001, '''57''', 626.</ref>
<ref name="ManyParticlePhysics"> H. Fehske, R. Schneider and A. Weiβe, Eds., ''Computational Many-Particle Physics'', Springer, Berlin, 2008, pp. 438.</ref>
<ref name="Cheletropic"> D. Suarez, T. L. Sordo and A. Sordo, ''J. Org. Chem.'', 1995, '''60''', 2848–2852.</ref>
<ref name="OrganicReactions"> P. S. Kalsi, ''Organic Reactions Stereochemistry and Mechanism'', New Age International Publishers, New Delhi, Fourth., 2006, pp. 550.</ref>
</references>

Rep:Mod:TP1414

2017-03-20T14:57:28Z

Tp1414:

== Introduction ==

=== Gaussian and Transition State Characterization ===

[[File:Energy surface TP1414.jpg|500px|thumb| Energy surface showing the locations of transition state (TS), local minimum (LM) and global minimum (GM).<ref name="ManyParticlePhysics"/>]]

Gaussian is a molecular modelling software that allows researchers to carry out extensive investigation of molecules and their reactions. In these exercises, the transition states of several Diels-Alder reactions are located and characterized using Gaussian. A transition state is a first order saddle point on a potential energy surface (PES). It is the maximum along the minimum energy path (or reaction path) between two minima (the reactants and the products). ''Geometry optimization'' to find the minimum energy structure will usually lead to a stationary point that is closest to the initial geometry. The stationary point, where the first derivative of energy is zero, can be a global minimum, a local minimum or a saddle point. In a reaction path, the minima (global or local) correspond to the reactants and the products, while the saddle point corresponds to the transition state. To differentiate between a minimum and a saddle point, the second derivatives of energy will have to be analysed. For global or local minima, where energy rises in all directions, the second derivative of energy is positive. In contrast, for transition state, where the energy decreases in one direction (reaction path), the second derivative of energy along the reaction coordinate is negative. The analysis of the second derivatives of energy can be done by a ''frequency calculation'' of the optimized structure. If the structure corresponds to the reactants or products, all the vibrational frequencies (''v'') are real. In contrast, if the structure corresponds to a transition state, there will be one imaginary frequency. This imaginary frequency indicates that the force constant (k), which is given by the second derivative, is negative. <ref name="ComputationalChemistry"/>

<center> <math>\textit{v}=\frac{1}{2\pi }\cdot \sqrt{\frac{k}{\mu }}</math> where <math>k=\frac{\partial ^{2}E}{\partial q^{2}}</math> </center>

Following a successful frequency calculation (one imaginary frequency) of the transition state, an ''Intrinsic Reaction Coordinate (IRC) calculation'' may be set up to examine the transition state along the minimum energy path more closely. The reaction path, or minimum energy path, can be defined as the steepest descent path from the transition state to the reactions and products.

In this exercise, two calculation methods are used. The first is the semi-empirical method PM6, a fitted method used to obtain the initial geometry of the molecule or transition state so as to save time during calculations. The second is the Density Functional Theory (DFT) method B3LYP, a method that is capable of reproducing chemical data and is used to further optimise the geometry obtained from the PM6 method.

=== Diels-Alder Reactions ===

A Diels-Alder reaction is a [4+2] cycloadditon between a conjugated s-cis diene (4π-electron system) and a dienophile (2π-electron system). The reaction has a cyclic transition state with 6π-electrons, is concerted, and results in the formation of two new sigma bonds. According to the Woodward-Hoffmann Rules, the Diels-Alder reaction is thermally allowed and is an orbital-controlled reaction, in which the six electrons are interacting suprafacially. The reaction can mainly proceed in two ways:

# Normal electron demand: HOMO of diene overlaps with LUMO of dienophile
# Inverse electron demand: LUMO of diene overlaps with HOMO of dienophile

Several papers divide the Diels-Alder reactions into three categories instead of two <ref name="InverseElectronDemand"/> <ref name="TransitionsofElectronDemand"/>, the third being a neutral electron demand Diels-Alder, in which the energy separation between the HOMO and LUMO of both reactants is similar. <ref name="InverseElectronDemand"/> Neutral electron demand Diels-Alder reactions are seldom observed and believed to be a transition between normal electron demand and inverse electron demand Diels Alder reactions.<ref name="TransitionsofElectronDemand"/>

[[File:normalinverseneutral.jpeg|center|500px]]

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

The reaction between butadiene and ethylene presents the simplest type of Diels-Alder reaction, in which butadiene is the diene and ethylene is the dienophile. This reaction yields cyclohexene as the product, and the reaction scheme is as follow:

[[File:exercise 1 reaction scheme.jpg|center]]

=== Molecular Orbital Diagram ===

[[File:MO diagram for exercise 1 TP1414.jpg|500px|thumb|center|Molecular orbital (MO) diagram for the reaction of butadiene with ethylene]]
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Jmol
! style="background: #0D4F8B; color: white;" | Symmetry
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Jmol
! style="background: #0D4F8B; color: white;" | Symmetry
|-
! rowspan="2" style="background: #0D4F8B; color: white;"| Butadiene
! style="background: #0D4F8B; color: white;"| LUMO
|style="text-align: center;"| [[File:ex1butadieneLUMOtp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 BUTADIENE BREAK SYMMETRY JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 22; rotate x -90; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
! rowspan="4" style="background: #0D4F8B; color: white;"| Transition State
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex1mo4tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
|-
! style="background: #0D4F8B; color: white;"| HOMO
|style="text-align: center;"| [[File:ex1butadieneHOMOtp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 BUTADIENE BREAK SYMMETRY JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 22; rotate x -90; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex1mo3tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
|-
! rowspan="2" style="background: #0D4F8B; color: white;"| Ethylene
! style="background: #0D4F8B; color: white;"| LUMO
|style="text-align: center;"| [[File:ex1ethyleneLUMOtp1414.png|100px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 ETHYLENE JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 14; rotate z 90; rotate x 90; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex1mo2tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| HOMO
|style="text-align: center;"| [[File:ex1ethyleneHOMOtp1414.png|100px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 ETHYLENE JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 14; rotate z 90; rotate x 90; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex1mo1tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
|-
|}

<br style="clear:right">

Only orbitals of the same symmetry can interact to form molecular orbitals. This means that only symmetric-symmetric interactions and antisymmetric-antisymmetric interactions are allowed. Symmetric-antisymmetric interactions, on the other hand, are forbidden. This is because the orbital overlap integral is non-zero for interactions between orbitals of the same symmetry and zero for interactions between orbitals of different symmetry.

As shown on the MO diagram above, both interactions (between the HOMO of butadiene and the LUMO of ethylene, and between the LUMO of butadiene and the HOMO of ethylene) occur, generating four molecular orbitals for the transition state. As the energy separation for the two interactions is similar, the reaction between butadiene and ethylene progress with aspects of both normal electron demand and inverse electron demand. This is because both butadiene and ethylene are neutral molecules without any obvious nucleophilic or electrophilic reacting centrers. Both molecules are neither electron-rich nor electron-poor. As a result, orbital overlap is possible for both HOMO-LUMO sets. Several papers classify this reaction as a neutral electron demand Diels-Alder. <ref name="InverseElectronDemand"/> <ref name="TransitionsofElectronDemand"/> This particular Diels-Alder reaction between butadiene and ethylene is well-known for its poor yield.

<br style="clear:left">

=== Internuclear Distances ===

[[File:internuclear distance.pdf|600px|thumb|right|Internuclear distances for the reaction of butadiene with ethylene to form cyclohexene.]]

[[File:butadiene and ethylene.jpg]]

{| class="wikitable"
|+ Internuclear Distances (Å)
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | C1-C2
! style="background: #0D4F8B; color: white;" | C2-C3
! style="background: #0D4F8B; color: white;" | C3-C4
! style="background: #0D4F8B; color: white;" | C4-C5
! style="background: #0D4F8B; color: white;" | C5-C6
! style="background: #0D4F8B; color: white;" | C6-C1
|-
! style="background: #0D4F8B; color: white;"| Reactants
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|style="text-align: center;"| -
|-
! style="background: #0D4F8B; color: white;"| Transition State
|style="text-align: center;"| 1.38
|style="text-align: center;"| 1.41
|style="text-align: center;"| 1.38
|style="text-align: center;"| 2.11
|style="text-align: center;"| 1.38
|style="text-align: center;"| 2.11
|-
! style="background: #0D4F8B; color: white;"| Product
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}

As the reaction progresses, C1-C2, C3-C4 and C5-C6 elongate as the double bond breaks to form single carbon-carbon bonds, while C2-C3 shortens to form carbon-carbon double bond. Simultaneously, C4-C5 and C6-C1 decrease in distance and ultimately single carbon-carbon bonds are formed. A more detailed overview of how the internuclear distances change over the course of the reaction is shown on the graph on the right.

A typical carbon-carbon single bond length is 1.54 Å and a typical carbon-carbon double bond length is 1.34 Å. <ref name="OrganicChemistryJoseph" />

The Van der Waals radius of one carbon atom is 1.70 Å. <ref name="TheMoleculesofLife" /> The length of the partly formed carbon-carbon bonds in the transition state is about 2.11 Å. This distance is shorter than twice the Van der Waals radius of carbon atom (3.40 Å), indicating bonding interactions are occuring.
<br style="clear:right">

=== Vibration and Reaction Path ===

[[File:exercisa1imaginaryfrequency.jpg]]

The vibration that corresponds to the reaction path at the transition state is illustrated above. This vibration has an imaginary frequency that occurs at 948.97i cm<sup>-1</sup>.

The formation of the two bonds are synchronous as shown below. This means that the two sigma bonds are formed simultaneously. hence, the reaction between butadiene and ethylene goes by a concerted synchronous mechanism.

[[File:IRCgif.jpg]]

=== Calculation Files ===

[[File:TP1414 Exercise 1 Ethylene.log]]

[[File:TP1414 Exercise 1 Butadiene.log]]

[[File:TP1414 Exercise 1 Product.log]]

[[File:TP1414 Exercise 1 Transition State.log]]

[[File:TP1414 Exercise 1 IRC.log]]

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

[[File:exercise 2 reaction schemetp1414.jpg|center]]

=== Molecular Orbital Diagram ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|style="text-align: center;"| [[File:ex 2 MO diagram for exo TS TP1414.jpg|500px]]
Molecular orbital (MO) diagram for the reaction of cyclohexadiene and 1,3-dioxole (exo).
|style="text-align: center;"| [[File:ex 2 MO diagram for endo TS TP1414.jpg|500px]]
Molecular orbital (MO) diagram for the reaction of cyclohexadiene and 1,3-dioxole (endo)
|-
|}

<br style="clear:left">

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Image
! style="background: #0D4F8B; color: white;" | Symmetry
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Image
! style="background: #0D4F8B; color: white;" | Symmetry
|-
! rowspan="4" style="background: #0D4F8B; color: white;"| Exo
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex2exoMO4tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO3 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
! rowspan="4" style="background: #0D4F8B; color: white;"| Endo
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex2endoMO4tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO4 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
|-
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex2exoMO3tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO4 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex2endoMO3tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO3 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex2exoMO2tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO2 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex2endoMO2tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO2 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex2exoMO1tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO1 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex2endoMO1tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO1 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
|-
|}

The exo and endo Diels-Alder between cyclohexadiene and 1,3-dioxole proceed in a similar fashion as the Diels-Alder between butadiene and ethylene in Exercise 1. However, unlike in Exercise 1, the dienophile, 1,3-dioxole, contains two pi electron donating oxygen adjacent to the C-C double bond. This increases the energy of the molecular orbitals of the dienophile, resulting in higher energies HOMO and LUMO of the dienophile relative to neutral ethylene in Exercise 1. As a consequence, the HOMO of the dienophile and the LUMO of the diene are much closer in energy and thus, interact more strongly. This reaction between cyclohexadiene and 1,3-dioxole is said to proceed via inverse electron demand Diels-Alder. The stronger interaction between the HOMO and LUMO results in a faster and more favourable reaction as compared to the neutral electron demand Diels-Alder between butadiene and ethylene in Exercise 1.

=== Thermochemistry ===
[[File:ex2energyprofiletp1414.jpeg|600px|thumb|Energy profile diagram for the reactions between cyclohexadiene and 1,3-dioxole]]
The energies of the reactants, transition state and product for both the exo and endo reactions are tabulated below. These are obtained from optimization at B3LYP/6-31G(d) level.

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;"| Exo
|style="text-align: center;"|-612591.48
|style="text-align: center;"|-701187.43
|style="text-align: center;"|-1313778.91
|style="text-align: center;"|-1313614.33
|style="text-align: center;"|-1313845.77
|style="text-align: center;"|164.58
|style="text-align: center;"|-66.86
|-
!style="background: #0D4F8B; color: white;"| Endo
|style="text-align: center;"|-612591.48
|style="text-align: center;"|-701187.43
|style="text-align: center;"|-1313778.91
|style="text-align: center;"|-1313622.15
|style="text-align: center;"|-1313849.37
|style="text-align: center;"|156.76
|style="text-align: center;"|-70.46
|-
|}

Both the exo and endo reactions are exothermic. However, it can be seen that the energy of the endo product is lower (or more negative) than the energy of the exo product, and the endo reaction also has a lower reaction barrier as compared to the exo reaction. This means that the endo product is both the thermodynamically and kinetically favourable product. This can be explained by considering both electronic and steric factors

[[File:seondaryorbitalinteractionstp1414.png|500px|thumb|left|Secondary orbital interactions in endo transition state]] Secondary orbital interactions stabilize the endo transition state, reducing the reaction barrier. On the left is the HOMO of the endo transition state in which there are obvious secondary orbital interactions between the oxygen p orbitals of the 1,3-dioxole and the p orbitals of the diene. An MO representation of this HOMO is shown below.
[[File:secondaryorbitalinteractionMOrepresentationtp1414.jpeg|350px]]
<br style="clear:left">

[[File:stericclashtp1414.png|500px|thumb|left|Steric clash in exo product]] Steric clash between the sp<sup>3</sup> CH<sub>2</sub> of the dioxole ring and the sp<sup>3</sup> CH<sub>2</sub>'s of the cyclohexadiene destabilize both the exo transition state and the exo product.
<br style="clear:left">

=== Vibration and Reaction Path ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
! style="background: #0D4F8B; color: white;"| Vibration
|style="text-align: center;"| [[File:exercise2 exo vibration tp1414.gif]]
|style="text-align: center;"| [[File:exercise2 endo vibration tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Vibrational Frequency
|style="text-align: center;"| 520.90i cm<sup>-1</sup>
|style="text-align: center;"| 528.85i cm<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| Reaction Pathway
|style="text-align: center;"| [[File:exercise2 exo reaction path tp1414.gif]]
|style="text-align: center;"| [[File:exercise2 endo reaction path tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Mechanism
|style="text-align: center;"| Synchronous concerted
|style="text-align: center;"| Synchronous concerted
|-
|}

=== Calculation Files ===

[[File:TP1414 Exercise 2 Cyclohexadiene 631Gd.log]]

[[File:TP1414 Exercise 2 1,2-Dioxole 631Gd.log]]

[[File:TP1414 Exercise 2 Exo Product 631Gd.log]]

[[File:TP1414 Exercise 2 Endo Product 631Gd.log]]

[[File:TP1414 Exercise 2 Exo Transition State 631Gd.log]]

[[File:TP1414 Exercise 2 Endo Transition State 631Gd.log]]

[[File:TP1414 Exercise 2 Exo IRC 631Gd.log]]

[[File:TP1414 Exercise 2 Endo IRC 631Gd.log]]

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

[[File:exercise3reactionschemetp1414.jpg|center]]

=== Molecular Orbital Diagram ===

The exo and endo Diels-Alder reaction between o-xylylene and SO<sub>2</sub> proceed in a similar fashion as the reactions in Exercise 1 and 2. However, in this case, the dienophile, SO<sub>2</sub>, is electron-deficient and has lower energies HOMO and LUMO compared to the dienophiles in Exercise 1 and 2. As a result, the most significant frontier orbital interaction is between the HOMO of o-xylylene and the LUMO of SO<sub>2</sub>. The Diels-Alder reaction between o-xylylene and SO<sub>2</sub> proceeds via normal electron demand.

The exo and endo Diels-Alder reaction between o-xylylene and SO<sub>2</sub> have another competing pericyclic reaction - cheletropic reaction. Woodward Hoffmann defines cheletropic reactions as pericyclic reactions in which two sigma bonds are formed or broken in a single atom. It is sometimes considered to be a subclass of cycloadditions. <ref name="Cheletropic"/> The MO diagram for the cheletropic reaction is shown below.

[[File:tp1414cheletropicMOdiagram.jpg|500px|thumb|center|Molecular orbital (MO) diagram for the cheletropic reaction between o-xylylene and SO<sub>2</sub> <ref name="OrganicReactions"/>]]

=== Thermochemistry ===
[[File:ex3energyprofiletp1414.jpg|600px|thumb|Energy profile diagram for the reactions between o-xylylene and SO<sub>2</sub>]]
The energies of the reactants, transition state and product for the exo, endo and cheletropic reactions are tabulated below. These are obtained from optimization at PM6 level.

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | o-Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;"| Exo
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|241.75
|style="text-align: center;"|56.31
|style="text-align: center;"|85.18
|style="text-align: center;"|-100.26
|-
!style="background: #0D4F8B; color: white;"| Endo
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|237.77
|style="text-align: center;"|56.98
|style="text-align: center;"|81.20
|style="text-align: center;"|-99.59
|-
!style="background: #0D4F8B; color: white;"| Cheletropic
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|260.09
|style="text-align: center;"|-0.01
|style="text-align: center;"|103.52
|style="text-align: center;"|-156.58
|-
|}

All three reactions are exothermic. The endo product is the kinetically favourable product as it has the lowest reaction barrier, while the cheletropic product is the thermodynamically favourable product as it has the lowest energy. This is consistent with experimental works that have been conducted in which a Diels-Alder adduct is observed to be the kinetic product and cheletropic adduct is observed to be the thermodynamic product. Experimental work shows that the Diels-Alder adduct is thermally unstable and will undergo a retro-Diels-Alder reaction to form back the starting materials, before forming the more stable five membered ring cheletropic product. <ref name="Cheletropic"/>
<br style="clear:right">

=== Vibration and Reaction Path ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
! style="background: #0D4F8B; color: white;" | Cheletropic
|-
! style="background: #0D4F8B; color: white;"| Vibration
|style="text-align: center;"| [[File:ex3 exo vibration tp1414.gif]]
|style="text-align: center;"| [[File:ex3 endo vibration tp1414.gif]]
|style="text-align: center;"| [[File:cheletropic vibration tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Vibrational Frequency
|style="text-align: center;"| 351.78i cm<sup>-1</sup>
|style="text-align: center;"| 334.38i cm<sup>-1</sup>
|style="text-align: center;"| 486.58i cm<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| Reaction Pathway
|style="text-align: center;"| [[File:exo IRC tp1414.gif]]
|style="text-align: center;"| [[File:endo IRC tp1414.gif]]
|style="text-align: center;"| [[File:cheletropic IRC tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Mechanism
|style="text-align: center;"| Asynchronous concerted
|style="text-align: center;"| Asynchronous concerted
|style="text-align: center;"| Synchronous concerted
|-
! style="background: #0D4F8B; color: white;"| IRC
|style="text-align: center;"| [[File:exoIRCtp1414.png]]
|style="text-align: center;"| [[File:endoIRCtp1414.png]]
|style="text-align: center;"| [[File:cheletropicIRCtp1414energy.png]]
|-
|}

It is interesting to note that the exo and endo reactions proceed via asynchronous mechanism in which the C-O bond is formed first before the C-S bond, while the cheletropic reaction proceeds via synchronous mechanism in which the two C-S bonds are formed simultaneously. However, even though the formation of the two bonds are asynchronous in the exo and endo reactions, the total energy along IRC tells us that both reactions are concerted as the reactions do not have any intermediate steps.

In all three reaction pathways, the steepest part on the the total energy versus IRC graph corresponds to the re-aromatisation of the 6-membered ring on the o-xylylene, giving these reactions an aromatic driving force. This also shows the instability of the o-xylylene molecule. O-Xylylene is highly unstable as it is antiaromatic (planar and 4n electrons), and it will undergo an electrocyclic ring closure to form the stable aromatic isomer, benzocyclobutene as shown below.<ref name="Benzocyclobutene"/>

[[File:xylyleneelectrocyclicreactionscheme.jpg|centre]]

A quick transition state optimisation followed by IRC calculation of the above reaction on Gaussian gives the total energy along IRC graph below.

[[File:xylyleneelectrocyclicIRCtp1414.jpg|500px|centre]]

[[File:xylyleneelectrocyclicIRC.gif|500px|centre]]

=== Alternate Diels-Alder Reaction ===

There is a second cis-butadiene fragment in o-xylylene that can undergo a Diels-Alder reaction. This second cis-butadiene is part of the cyclohexadiene ring. The exo and endo for this alternate Diels-Alder reaction proceed as follow:

[[File:alternatedielsalderexotp1414.gif]] [[File:alternatedielsalderendotp1414.gif]]

Both reactions proceed via an asynchronous mechanism.

[[File:energyprofilewithalternatedielsaldertp1414.jpg|600px|thumb|Energy profile diagram for the reactions between o-xylylene and SO<sub>2</sub>]]
The thermochemistry for this alternate Diels-Alder reaction is as follows:

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | o-Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;" | Exo
| style="text-align: center;" |467.99
| style="text-align: center;" |-311.42
| style="text-align: center;" |156.57
| style="text-align: center;" |275.82
| style="text-align: center;" |176.71
| style="text-align: center;" |119.25
| style="text-align: center;" |20.14
|-
! style="background: #0D4F8B; color: white;" | Endo
| style="text-align: center;" |467.99
| style="text-align: center;" |-311.42
| style="text-align: center;" |156.57
| style="text-align: center;" |267.98
| style="text-align: center;" |172.26
| style="text-align: center;" |111.41
| style="text-align: center;" |15.96
|-
|}

Comparing the energies for this alternate Diels-Alder reaction with the energies for the normal Diels-Alder and the cheletropic reactions, it can be seen that both the exo and endo alternate Diels-Alder reactoions are kinetically and thermodynamically unfavourable. The products are also higher in energies than the reactants, making the reactions endothermic.
<br style="clear:right">

=== Calculation Files ===

[[File:TP1414 Exercise 3 Xylylene.log]]

[[File:TP1414 Exercise 3 SO2.log]]

[[File:TP1414 Exercise 3 Exo Product.log]]

[[File:TP1414 Exercise 3 Endo Product.log]]

[[File:TP1414 Exercise 3 Cheletropic Product.log]]

[[File:TP1414 Exercise 3 Exo Transition State.log]]

[[File:TP1414 Exercise 3 Endo Transition State.log]]

[[File:TP1414 Exercise 3 Cheletropic Transition State.log]]

[[File:TP1414 Exercise 3 Exo IRC.log]]

[[File:TP1414 Exercise 3 Endo IRC.log]]

[[File:TP1414 Exercise 3 Cheletropic IRC.log]]

[[File:TP1414 Exercise 3 Xylylene Electrocyclic Transition State.log]]

[[File:TP1414 Exercise 3 Xylylene Electrocyclic IRC.log]]

[[File:TP1414 Exercise 3 Alternate Exo Product.log]]

[[File:TP1414 Exercise 3 Alternate Endo Product.log]]

[[File:TP1414 Exercise 3 Alternate Exo Transition State.log]]

[[File:TP1414 Exercise 3 Alternate Endo Transition State.log]]

[[File:TP1414 Exercise 3 Alternate Exo IRC.log]]

[[File:TP1414 Exercise 3 Alternate Endo IRC.log]]

== Conclusion ==

Two calculation methods were used to study three different Diels-Alder reactions. The semi-empirical method PM6 was used to calculate the geometries of the transition state and product of the reactions in all three exercises for faster calculations. In exercise 2, the geometries were further optimised by the DFT method B3LYP at 6-31G(d) level for better accuracy.

Exercises 1 to 3 illustrate the three different ways in which Diels-Alder reaction can proceed: neutral electron demand, inverse electron demand and normal electron demand respectively. In exercise 1, the frontier orbital interactions of the simplest Diels-Alder reaction was studied and it shows that only orbitals of the same symmetry can interact. Exercise 1 also illustrates how internuclear distances vary as a Diels-Alder reaction proceeds, and how these compare with the Van der Waals radii of the atoms. Exercise 2 presents a more complex Diels-Alder reaction which can proceed in two different orientations - endo and exo. It demonstrates how secondary orbital interactions and steric factors could affect the energies of the transition states and products, and hence, determine the kinetically and thermodynamically favourable reactions. Exercise 3 illustrates an even more complex system where there are two diene functional groups and in which another competing pericyclic cheletropic reaction is possible. It also demonstrates that pericyclic reactions can proceed via synchronous concerted or asynchronous concerted mechanisms depending on the symmetry of the interacting molecules.

In conclusion, Gaussian proves to be a useful molecular modelling software to investigate the molecules and their reactions. Transition states were located and characterized, and frontier orbital interactions and thermochemistry were analysed. Results obtained from these calculations also proved to be consistent with theory and experimental observations.

== References ==

<references>
<ref name="ComputationalChemistry"> Lecture notes: ''Quantum Mechanics 3/3rd Year Computational Chemistry Laboratory'', Michael Bearpark, Imperial College. </ref>
<ref name="OrganicChemistryJoseph"> J. M. Hornback, ''Organic Chemistry'', Thomson Learning. Inc., Belmont, Second., 2006.</ref>
<ref name="TheMoleculesofLife"> J. Kuriyan, B. Konforti and D. Wemmer, ''The Molecules of Life: Physical and Chemical Principles'', Garland Science, New York, 2013.</ref>
<ref name="InverseElectronDemand"> A.-C. Knall and C. Slugovc, ''Chem Soc Rev'', 2013, '''42''', 5131–5142.</ref>
<ref name="TransitionsofElectronDemand"> E. Eibler, P. Hocht, B. Prantl, H. Rormaier, H. M. Schuhbauer and H. Wiest, ''Liebigs Ann.lRemei'', 1997, '''1997''', 2471–2484.</ref>
<ref name="Benzocyclobutene"> G. Mehta and S. Kotha, ''Tetrahedron'', 2001, '''57''', 626.</ref>
<ref name="ManyParticlePhysics"> H. Fehske, R. Schneider and A. Weiβe, Eds., ''Computational Many-Particle Physics'', Springer, Berlin, 2008.</ref>
<ref name="Cheletropic"> D. Suarez, T. L. Sordo and A. Sordo, ''J. Org. Chem.'', 1995, '''60''', 2848–2852.</ref>
<ref name="OrganicReactions"> P. S. Kalsi, ''Organic Reactions Stereochemistry and Mechanism'', New Age International Publishers, New Delhi, Fourth., 2006, pp. 550.</ref>
</references>

File:Tp1414cheletropicMOdiagram.jpg

2017-03-20T14:51:06Z

Tp1414:

Rep:Mod:TP1414

2017-03-20T14:49:55Z

Tp1414: /* Molecular Orbital Diagram */

== Introduction ==

=== Gaussian and Transition State Characterization ===

[[File:Energy surface TP1414.jpg|500px|thumb| Energy surface showing the locations of transition state (TS), local minimum (LM) and global minimum (GM).<ref name="ManyParticlePhysics"/>]]

Gaussian is a molecular modelling software that allows researchers to carry out extensive investigation of molecules and their reactions. In these exercises, the transition states of several Diels-Alder reactions are located and characterized using Gaussian. A transition state is a first order saddle point on a potential energy surface (PES). It is the maximum along the minimum energy path (or reaction path) between two minima (the reactants and the products). ''Geometry optimization'' to find the minimum energy structure will usually lead to a stationary point that is closest to the initial geometry. The stationary point, where the first derivative of energy is zero, can be a global minimum, a local minimum or a saddle point. In a reaction path, the minima (global or local) correspond to the reactants and the products, while the saddle point corresponds to the transition state. To differentiate between a minimum and a saddle point, the second derivatives of energy will have to be analysed. For global or local minima, where energy rises in all directions, the second derivative of energy is positive. In contrast, for transition state, where the energy decreases in one direction (reaction path), the second derivative of energy along the reaction coordinate is negative. The analysis of the second derivatives of energy can be done by a ''frequency calculation'' of the optimized structure. If the structure corresponds to the reactants or products, all the vibrational frequencies (''v'') are real. In contrast, if the structure corresponds to a transition state, there will be one imaginary frequency. This imaginary frequency indicates that the force constant (k), which is given by the second derivative, is negative. <ref name="ComputationalChemistry"/>

<center> <math>\textit{v}=\frac{1}{2\pi }\cdot \sqrt{\frac{k}{\mu }}</math> where <math>k=\frac{\partial ^{2}E}{\partial q^{2}}</math> </center>

Following a successful frequency calculation (one imaginary frequency) of the transition state, an ''Intrinsic Reaction Coordinate (IRC) calculation'' may be set up to examine the transition state along the minimum energy path more closely. The reaction path, or minimum energy path, can be defined as the steepest descent path from the transition state to the reactions and products.

In this exercise, two calculation methods are used. The first is the semi-empirical method PM6, a fitted method used to obtain the initial geometry of the molecule or transition state so as to save time during calculations. The second is the Density Functional Theory (DFT) method B3LYP, a method that is capable of reproducing chemical data and is used to further optimise the geometry obtained from the PM6 method.

=== Diels-Alder Reactions ===

A Diels-Alder reaction is a [4+2] cycloadditon between a conjugated s-cis diene (4π-electron system) and a dienophile (2π-electron system). The reaction has a cyclic transition state with 6π-electrons, is concerted, and results in the formation of two new sigma bonds. According to the Woodward-Hoffmann Rules, the Diels-Alder reaction is thermally allowed and is an orbital-controlled reaction, in which the six electrons are interacting suprafacially. The reaction can mainly proceed in two ways:

# Normal electron demand: HOMO of diene overlaps with LUMO of dienophile
# Inverse electron demand: LUMO of diene overlaps with HOMO of dienophile

Several papers divide the Diels-Alder reactions into three categories instead of two <ref name="InverseElectronDemand"/> <ref name="TransitionsofElectronDemand"/>, the third being a neutral electron demand Diels-Alder, in which the energy separation between the HOMO and LUMO of both reactants is similar. <ref name="InverseElectronDemand"/> Neutral electron demand Diels-Alder reactions are seldom observed and believed to be a transition between normal electron demand and inverse electron demand Diels Alder reactions.<ref name="TransitionsofElectronDemand"/>

[[File:normalinverseneutral.jpeg|center|500px]]

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

The reaction between butadiene and ethylene presents the simplest type of Diels-Alder reaction, in which butadiene is the diene and ethylene is the dienophile. This reaction yields cyclohexene as the product, and the reaction scheme is as follow:

[[File:exercise 1 reaction scheme.jpg|center]]

=== Molecular Orbital Diagram ===

[[File:MO diagram for exercise 1 TP1414.jpg|500px|thumb|center|Molecular orbital (MO) diagram for the reaction of butadiene with ethylene]]
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Jmol
! style="background: #0D4F8B; color: white;" | Symmetry
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Jmol
! style="background: #0D4F8B; color: white;" | Symmetry
|-
! rowspan="2" style="background: #0D4F8B; color: white;"| Butadiene
! style="background: #0D4F8B; color: white;"| LUMO
|style="text-align: center;"| [[File:ex1butadieneLUMOtp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 BUTADIENE BREAK SYMMETRY JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 22; rotate x -90; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
! rowspan="4" style="background: #0D4F8B; color: white;"| Transition State
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex1mo4tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
|-
! style="background: #0D4F8B; color: white;"| HOMO
|style="text-align: center;"| [[File:ex1butadieneHOMOtp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 BUTADIENE BREAK SYMMETRY JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 22; rotate x -90; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex1mo3tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
|-
! rowspan="2" style="background: #0D4F8B; color: white;"| Ethylene
! style="background: #0D4F8B; color: white;"| LUMO
|style="text-align: center;"| [[File:ex1ethyleneLUMOtp1414.png|100px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 ETHYLENE JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 14; rotate z 90; rotate x 90; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex1mo2tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| HOMO
|style="text-align: center;"| [[File:ex1ethyleneHOMOtp1414.png|100px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 ETHYLENE JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 14; rotate z 90; rotate x 90; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex1mo1tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
|-
|}

<br style="clear:right">

Only orbitals of the same symmetry can interact to form molecular orbitals. This means that only symmetric-symmetric interactions and antisymmetric-antisymmetric interactions are allowed. Symmetric-antisymmetric interactions, on the other hand, are forbidden. This is because the orbital overlap integral is non-zero for interactions between orbitals of the same symmetry and zero for interactions between orbitals of different symmetry.

As shown on the MO diagram above, both interactions (between the HOMO of butadiene and the LUMO of ethylene, and between the LUMO of butadiene and the HOMO of ethylene) occur, generating four molecular orbitals for the transition state. As the energy separation for the two interactions is similar, the reaction between butadiene and ethylene progress with aspects of both normal electron demand and inverse electron demand. This is because both butadiene and ethylene are neutral molecules without any obvious nucleophilic or electrophilic reacting centrers. Both molecules are neither electron-rich nor electron-poor. As a result, orbital overlap is possible for both HOMO-LUMO sets. Several papers classify this reaction as a neutral electron demand Diels-Alder. <ref name="InverseElectronDemand"/> <ref name="TransitionsofElectronDemand"/> This particular Diels-Alder reaction between butadiene and ethylene is well-known for its poor yield.

<br style="clear:left">

=== Internuclear Distances ===

[[File:internuclear distance.pdf|600px|thumb|right|Internuclear distances for the reaction of butadiene with ethylene to form cyclohexene.]]

[[File:butadiene and ethylene.jpg]]

{| class="wikitable"
|+ Internuclear Distances (Å)
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | C1-C2
! style="background: #0D4F8B; color: white;" | C2-C3
! style="background: #0D4F8B; color: white;" | C3-C4
! style="background: #0D4F8B; color: white;" | C4-C5
! style="background: #0D4F8B; color: white;" | C5-C6
! style="background: #0D4F8B; color: white;" | C6-C1
|-
! style="background: #0D4F8B; color: white;"| Reactants
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|style="text-align: center;"| -
|-
! style="background: #0D4F8B; color: white;"| Transition State
|style="text-align: center;"| 1.38
|style="text-align: center;"| 1.41
|style="text-align: center;"| 1.38
|style="text-align: center;"| 2.11
|style="text-align: center;"| 1.38
|style="text-align: center;"| 2.11
|-
! style="background: #0D4F8B; color: white;"| Product
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}

As the reaction progresses, C1-C2, C3-C4 and C5-C6 elongate as the double bond breaks to form single carbon-carbon bonds, while C2-C3 shortens to form carbon-carbon double bond. Simultaneously, C4-C5 and C6-C1 decrease in distance and ultimately single carbon-carbon bonds are formed. A more detailed overview of how the internuclear distances change over the course of the reaction is shown on the graph on the right.

A typical carbon-carbon single bond length is 1.54 Å and a typical carbon-carbon double bond length is 1.34 Å. <ref name="OrganicChemistryJoseph" />

The Van der Waals radius of one carbon atom is 1.70 Å. <ref name="TheMoleculesofLife" /> The length of the partly formed carbon-carbon bonds in the transition state is about 2.11 Å. This distance is shorter than twice the Van der Waals radius of carbon atom (3.40 Å), indicating bonding interactions are occuring.
<br style="clear:right">

=== Vibration and Reaction Path ===

[[File:exercisa1imaginaryfrequency.jpg]]

The vibration that corresponds to the reaction path at the transition state is illustrated above. This vibration has an imaginary frequency that occurs at 948.97i cm<sup>-1</sup>.

The formation of the two bonds are synchronous as shown below. This means that the two sigma bonds are formed simultaneously. hence, the reaction between butadiene and ethylene goes by a concerted synchronous mechanism.

[[File:IRCgif.jpg]]

=== Calculation Files ===

[[File:TP1414 Exercise 1 Ethylene.log]]

[[File:TP1414 Exercise 1 Butadiene.log]]

[[File:TP1414 Exercise 1 Product.log]]

[[File:TP1414 Exercise 1 Transition State.log]]

[[File:TP1414 Exercise 1 IRC.log]]

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

[[File:exercise 2 reaction schemetp1414.jpg|center]]

=== Molecular Orbital Diagram ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|style="text-align: center;"| [[File:ex 2 MO diagram for exo TS TP1414.jpg|500px]]
Molecular orbital (MO) diagram for the reaction of cyclohexadiene and 1,3-dioxole (exo).
|style="text-align: center;"| [[File:ex 2 MO diagram for endo TS TP1414.jpg|500px]]
Molecular orbital (MO) diagram for the reaction of cyclohexadiene and 1,3-dioxole (endo)
|-
|}

<br style="clear:left">

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Image
! style="background: #0D4F8B; color: white;" | Symmetry
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Image
! style="background: #0D4F8B; color: white;" | Symmetry
|-
! rowspan="4" style="background: #0D4F8B; color: white;"| Exo
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex2exoMO4tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO3 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
! rowspan="4" style="background: #0D4F8B; color: white;"| Endo
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex2endoMO4tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO4 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
|-
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex2exoMO3tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO4 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex2endoMO3tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO3 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex2exoMO2tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO2 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex2endoMO2tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO2 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex2exoMO1tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO1 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex2endoMO1tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO1 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
|-
|}

The exo and endo Diels-Alder between cyclohexadiene and 1,3-dioxole proceed in a similar fashion as the Diels-Alder between butadiene and ethylene in Exercise 1. However, unlike in Exercise 1, the dienophile, 1,3-dioxole, contains two pi electron donating oxygen adjacent to the C-C double bond. This increases the energy of the molecular orbitals of the dienophile, resulting in higher energies HOMO and LUMO of the dienophile relative to neutral ethylene in Exercise 1. As a consequence, the HOMO of the dienophile and the LUMO of the diene are much closer in energy and thus, interact more strongly. This reaction between cyclohexadiene and 1,3-dioxole is said to proceed via inverse electron demand Diels-Alder. The stronger interaction between the HOMO and LUMO results in a faster and more favourable reaction as compared to the neutral electron demand Diels-Alder between butadiene and ethylene in Exercise 1.

=== Thermochemistry ===
[[File:ex2energyprofiletp1414.jpeg|600px|thumb|Energy profile diagram for the reactions between cyclohexadiene and 1,3-dioxole]]
The energies of the reactants, transition state and product for both the exo and endo reactions are tabulated below. These are obtained from optimization at B3LYP/6-31G(d) level.

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;"| Exo
|style="text-align: center;"|-612591.48
|style="text-align: center;"|-701187.43
|style="text-align: center;"|-1313778.91
|style="text-align: center;"|-1313614.33
|style="text-align: center;"|-1313845.77
|style="text-align: center;"|164.58
|style="text-align: center;"|-66.86
|-
!style="background: #0D4F8B; color: white;"| Endo
|style="text-align: center;"|-612591.48
|style="text-align: center;"|-701187.43
|style="text-align: center;"|-1313778.91
|style="text-align: center;"|-1313622.15
|style="text-align: center;"|-1313849.37
|style="text-align: center;"|156.76
|style="text-align: center;"|-70.46
|-
|}

Both the exo and endo reactions are exothermic. However, it can be seen that the energy of the endo product is lower (or more negative) than the energy of the exo product, and the endo reaction also has a lower reaction barrier as compared to the exo reaction. This means that the endo product is both the thermodynamically and kinetically favourable product. This can be explained by considering both electronic and steric factors

[[File:seondaryorbitalinteractionstp1414.png|500px|thumb|left|Secondary orbital interactions in endo transition state]] Secondary orbital interactions stabilize the endo transition state, reducing the reaction barrier. On the left is the HOMO of the endo transition state in which there are obvious secondary orbital interactions between the oxygen p orbitals of the 1,3-dioxole and the p orbitals of the diene. An MO representation of this HOMO is shown below.
[[File:secondaryorbitalinteractionMOrepresentationtp1414.jpeg|350px]]
<br style="clear:left">

[[File:stericclashtp1414.png|500px|thumb|left|Steric clash in exo product]] Steric clash between the sp<sup>3</sup> CH<sub>2</sub> of the dioxole ring and the sp<sup>3</sup> CH<sub>2</sub>'s of the cyclohexadiene destabilize both the exo transition state and the exo product.
<br style="clear:left">

=== Vibration and Reaction Path ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
! style="background: #0D4F8B; color: white;"| Vibration
|style="text-align: center;"| [[File:exercise2 exo vibration tp1414.gif]]
|style="text-align: center;"| [[File:exercise2 endo vibration tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Vibrational Frequency
|style="text-align: center;"| 520.90i cm<sup>-1</sup>
|style="text-align: center;"| 528.85i cm<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| Reaction Pathway
|style="text-align: center;"| [[File:exercise2 exo reaction path tp1414.gif]]
|style="text-align: center;"| [[File:exercise2 endo reaction path tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Mechanism
|style="text-align: center;"| Synchronous concerted
|style="text-align: center;"| Synchronous concerted
|-
|}

=== Calculation Files ===

[[File:TP1414 Exercise 2 Cyclohexadiene 631Gd.log]]

[[File:TP1414 Exercise 2 1,2-Dioxole 631Gd.log]]

[[File:TP1414 Exercise 2 Exo Product 631Gd.log]]

[[File:TP1414 Exercise 2 Endo Product 631Gd.log]]

[[File:TP1414 Exercise 2 Exo Transition State 631Gd.log]]

[[File:TP1414 Exercise 2 Endo Transition State 631Gd.log]]

[[File:TP1414 Exercise 2 Exo IRC 631Gd.log]]

[[File:TP1414 Exercise 2 Endo IRC 631Gd.log]]

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

[[File:exercise3reactionschemetp1414.jpg|center]]

=== Molecular Orbital Diagram ===

The exo and endo Diels-Alder reaction between o-xylylene and SO<sub>2</sub> proceed in a similar fashion as the reactions in Exercise 1 and 2. However, in this case, the dienophile, SO<sub>2</sub>, is electron-deficient and has lower energies HOMO and LUMO compared to the dienophiles in Exercise 1 and 2. As a result, the most significant frontier orbital interaction is between the HOMO of o-xylylene and the LUMO of SO<sub>2</sub>. The Diels-Alder reaction between o-xylylene and SO<sub>2</sub> proceeds via normal electron demand.

The exo and endo Diels-Alder reaction between o-xylylene and SO<sub>2</sub> have another competing pericyclic reaction - cheletropic reaction. Woodward Hoffmann defines cheletropic reactions as pericyclic reactions in which two sigma bonds are formed or broken in a single atom. It is sometimes considered to be a subclass of cycloadditions. <ref name="Cheletropic"/> The MO diagram for the cheletropic reaction is shown below.

[[File:tp1414cheletropicMOdiagram.jpg|500px|thumb|center|Molecular orbital (MO) diagram for the cheletropic reaction between o-xylylene and SO<sub>2</sub>]]

=== Thermochemistry ===
[[File:ex3energyprofiletp1414.jpg|600px|thumb|Energy profile diagram for the reactions between o-xylylene and SO<sub>2</sub>]]
The energies of the reactants, transition state and product for the exo, endo and cheletropic reactions are tabulated below. These are obtained from optimization at PM6 level.

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | o-Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;"| Exo
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|241.75
|style="text-align: center;"|56.31
|style="text-align: center;"|85.18
|style="text-align: center;"|-100.26
|-
!style="background: #0D4F8B; color: white;"| Endo
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|237.77
|style="text-align: center;"|56.98
|style="text-align: center;"|81.20
|style="text-align: center;"|-99.59
|-
!style="background: #0D4F8B; color: white;"| Cheletropic
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|260.09
|style="text-align: center;"|-0.01
|style="text-align: center;"|103.52
|style="text-align: center;"|-156.58
|-
|}

All three reactions are exothermic. The endo product is the kinetically favourable product as it has the lowest reaction barrier, while the cheletropic product is the thermodynamically favourable product as it has the lowest energy. This is consistent with experimental works that have been conducted in which a Diels-Alder adduct is observed to be the kinetic product and cheletropic adduct is observed to be the thermodynamic product. Experimental work shows that the Diels-Alder adduct is thermally unstable and will undergo a retro-Diels-Alder reaction to form back the starting materials, before forming the more stable five membered ring cheletropic product. <ref name="Cheletropic"/>
<br style="clear:right">

=== Vibration and Reaction Path ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
! style="background: #0D4F8B; color: white;" | Cheletropic
|-
! style="background: #0D4F8B; color: white;"| Vibration
|style="text-align: center;"| [[File:ex3 exo vibration tp1414.gif]]
|style="text-align: center;"| [[File:ex3 endo vibration tp1414.gif]]
|style="text-align: center;"| [[File:cheletropic vibration tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Vibrational Frequency
|style="text-align: center;"| 351.78i cm<sup>-1</sup>
|style="text-align: center;"| 334.38i cm<sup>-1</sup>
|style="text-align: center;"| 486.58i cm<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| Reaction Pathway
|style="text-align: center;"| [[File:exo IRC tp1414.gif]]
|style="text-align: center;"| [[File:endo IRC tp1414.gif]]
|style="text-align: center;"| [[File:cheletropic IRC tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Mechanism
|style="text-align: center;"| Asynchronous concerted
|style="text-align: center;"| Asynchronous concerted
|style="text-align: center;"| Synchronous concerted
|-
! style="background: #0D4F8B; color: white;"| IRC
|style="text-align: center;"| [[File:exoIRCtp1414.png]]
|style="text-align: center;"| [[File:endoIRCtp1414.png]]
|style="text-align: center;"| [[File:cheletropicIRCtp1414energy.png]]
|-
|}

It is interesting to note that the exo and endo reactions proceed via asynchronous mechanism in which the C-O bond is formed first before the C-S bond, while the cheletropic reaction proceeds via synchronous mechanism in which the two C-S bonds are formed simultaneously. However, even though the formation of the two bonds are asynchronous in the exo and endo reactions, the total energy along IRC tells us that both reactions are concerted as the reactions do not have any intermediate steps.

In all three reaction pathways, the steepest part on the the total energy versus IRC graph corresponds to the re-aromatisation of the 6-membered ring on the o-xylylene, giving these reactions an aromatic driving force. This also shows the instability of the o-xylylene molecule. O-Xylylene is highly unstable as it is antiaromatic (planar and 4n electrons), and it will undergo an electrocyclic ring closure to form the stable aromatic isomer, benzocyclobutene as shown below.<ref name="Benzocyclobutene"/>

[[File:xylyleneelectrocyclicreactionscheme.jpg|centre]]

A quick transition state optimisation followed by IRC calculation of the above reaction on Gaussian gives the total energy along IRC graph below.

[[File:xylyleneelectrocyclicIRCtp1414.jpg|500px|centre]]

[[File:xylyleneelectrocyclicIRC.gif|500px|centre]]

=== Alternate Diels-Alder Reaction ===

There is a second cis-butadiene fragment in o-xylylene that can undergo a Diels-Alder reaction. This second cis-butadiene is part of the cyclohexadiene ring. The exo and endo for this alternate Diels-Alder reaction proceed as follow:

[[File:alternatedielsalderexotp1414.gif]] [[File:alternatedielsalderendotp1414.gif]]

Both reactions proceed via an asynchronous mechanism.

[[File:energyprofilewithalternatedielsaldertp1414.jpg|600px|thumb|Energy profile diagram for the reactions between o-xylylene and SO<sub>2</sub>]]
The thermochemistry for this alternate Diels-Alder reaction is as follows:

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | o-Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;" | Exo
| style="text-align: center;" |467.99
| style="text-align: center;" |-311.42
| style="text-align: center;" |156.57
| style="text-align: center;" |275.82
| style="text-align: center;" |176.71
| style="text-align: center;" |119.25
| style="text-align: center;" |20.14
|-
! style="background: #0D4F8B; color: white;" | Endo
| style="text-align: center;" |467.99
| style="text-align: center;" |-311.42
| style="text-align: center;" |156.57
| style="text-align: center;" |267.98
| style="text-align: center;" |172.26
| style="text-align: center;" |111.41
| style="text-align: center;" |15.96
|-
|}

Comparing the energies for this alternate Diels-Alder reaction with the energies for the normal Diels-Alder and the cheletropic reactions, it can be seen that both the exo and endo alternate Diels-Alder reactoions are kinetically and thermodynamically unfavourable. The products are also higher in energies than the reactants, making the reactions endothermic.
<br style="clear:right">

=== Calculation Files ===

[[File:TP1414 Exercise 3 Xylylene.log]]

[[File:TP1414 Exercise 3 SO2.log]]

[[File:TP1414 Exercise 3 Exo Product.log]]

[[File:TP1414 Exercise 3 Endo Product.log]]

[[File:TP1414 Exercise 3 Cheletropic Product.log]]

[[File:TP1414 Exercise 3 Exo Transition State.log]]

[[File:TP1414 Exercise 3 Endo Transition State.log]]

[[File:TP1414 Exercise 3 Cheletropic Transition State.log]]

[[File:TP1414 Exercise 3 Exo IRC.log]]

[[File:TP1414 Exercise 3 Endo IRC.log]]

[[File:TP1414 Exercise 3 Cheletropic IRC.log]]

[[File:TP1414 Exercise 3 Xylylene Electrocyclic Transition State.log]]

[[File:TP1414 Exercise 3 Xylylene Electrocyclic IRC.log]]

[[File:TP1414 Exercise 3 Alternate Exo Product.log]]

[[File:TP1414 Exercise 3 Alternate Endo Product.log]]

[[File:TP1414 Exercise 3 Alternate Exo Transition State.log]]

[[File:TP1414 Exercise 3 Alternate Endo Transition State.log]]

[[File:TP1414 Exercise 3 Alternate Exo IRC.log]]

[[File:TP1414 Exercise 3 Alternate Endo IRC.log]]

== Conclusion ==

Two calculation methods were used to study three different Diels-Alder reactions. The semi-empirical method PM6 was used to calculate the geometries of the transition state and product of the reactions in all three exercises for faster calculations. In exercise 2, the geometries were further optimised by the DFT method B3LYP at 6-31G(d) level for better accuracy.

Exercises 1 to 3 illustrate the three different ways in which Diels-Alder reaction can proceed: neutral electron demand, inverse electron demand and normal electron demand respectively. In exercise 1, the frontier orbital interactions of the simplest Diels-Alder reaction was studied and it shows that only orbitals of the same symmetry can interact. Exercise 1 also illustrates how internuclear distances vary as a Diels-Alder reaction proceeds, and how these compare with the Van der Waals radii of the atoms. Exercise 2 presents a more complex Diels-Alder reaction which can proceed in two different orientations - endo and exo. It demonstrates how secondary orbital interactions and steric factors could affect the energies of the transition states and products, and hence, determine the kinetically and thermodynamically favourable reactions. Exercise 3 illustrates an even more complex system where there are two diene functional groups and in which another competing pericyclic cheletropic reaction is possible. It also demonstrates that pericyclic reactions can proceed via synchronous concerted or asynchronous concerted mechanisms depending on the symmetry of the interacting molecules.

In conclusion, Gaussian proves to be a useful molecular modelling software to investigate the molecules and their reactions. Transition states were located and characterized, and frontier orbital interactions and thermochemistry were analysed. Results obtained from these calculations also proved to be consistent with theory and experimental observations.

== References ==

<references>
<ref name="ComputationalChemistry"> Lecture notes: ''Quantum Mechanics 3/3rd Year Computational Chemistry Laboratory'', Michael Bearpark, Imperial College. </ref>
<ref name="OrganicChemistryJoseph"> J. M. Hornback, ''Organic Chemistry'', Thomson Learning. Inc., Belmont, Second., 2006.</ref>
<ref name="TheMoleculesofLife"> J. Kuriyan, B. Konforti and D. Wemmer, ''The Molecules of Life: Physical and Chemical Principles'', Garland Science, New York, 2013.</ref>
<ref name="InverseElectronDemand"> A.-C. Knall and C. Slugovc, ''Chem Soc Rev'', 2013, '''42''', 5131–5142.</ref>
<ref name="TransitionsofElectronDemand"> E. Eibler, P. Hocht, B. Prantl, H. Rormaier, H. M. Schuhbauer and H. Wiest, ''Liebigs Ann.lRemei'', 1997, '''1997''', 2471–2484.</ref>
<ref name="Benzocyclobutene"> G. Mehta and S. Kotha, ''Tetrahedron'', 2001, '''57''', 626.</ref>
<ref name="ManyParticlePhysics"> H. Fehske, R. Schneider and A. Weiβe, Eds., ''Computational Many-Particle Physics'', Springer, Berlin, 2008.</ref>
<ref name="Cheletropic"> D. Suarez, T. L. Sordo and A. Sordo, ''J. Org. Chem.'', 1995, '''60''', 2848–2852.</ref>
</references>

Rep:Mod:TP1414

2017-03-20T14:46:24Z

Tp1414:

== Introduction ==

=== Gaussian and Transition State Characterization ===

[[File:Energy surface TP1414.jpg|500px|thumb| Energy surface showing the locations of transition state (TS), local minimum (LM) and global minimum (GM).<ref name="ManyParticlePhysics"/>]]

Gaussian is a molecular modelling software that allows researchers to carry out extensive investigation of molecules and their reactions. In these exercises, the transition states of several Diels-Alder reactions are located and characterized using Gaussian. A transition state is a first order saddle point on a potential energy surface (PES). It is the maximum along the minimum energy path (or reaction path) between two minima (the reactants and the products). ''Geometry optimization'' to find the minimum energy structure will usually lead to a stationary point that is closest to the initial geometry. The stationary point, where the first derivative of energy is zero, can be a global minimum, a local minimum or a saddle point. In a reaction path, the minima (global or local) correspond to the reactants and the products, while the saddle point corresponds to the transition state. To differentiate between a minimum and a saddle point, the second derivatives of energy will have to be analysed. For global or local minima, where energy rises in all directions, the second derivative of energy is positive. In contrast, for transition state, where the energy decreases in one direction (reaction path), the second derivative of energy along the reaction coordinate is negative. The analysis of the second derivatives of energy can be done by a ''frequency calculation'' of the optimized structure. If the structure corresponds to the reactants or products, all the vibrational frequencies (''v'') are real. In contrast, if the structure corresponds to a transition state, there will be one imaginary frequency. This imaginary frequency indicates that the force constant (k), which is given by the second derivative, is negative. <ref name="ComputationalChemistry"/>

<center> <math>\textit{v}=\frac{1}{2\pi }\cdot \sqrt{\frac{k}{\mu }}</math> where <math>k=\frac{\partial ^{2}E}{\partial q^{2}}</math> </center>

Following a successful frequency calculation (one imaginary frequency) of the transition state, an ''Intrinsic Reaction Coordinate (IRC) calculation'' may be set up to examine the transition state along the minimum energy path more closely. The reaction path, or minimum energy path, can be defined as the steepest descent path from the transition state to the reactions and products.

In this exercise, two calculation methods are used. The first is the semi-empirical method PM6, a fitted method used to obtain the initial geometry of the molecule or transition state so as to save time during calculations. The second is the Density Functional Theory (DFT) method B3LYP, a method that is capable of reproducing chemical data and is used to further optimise the geometry obtained from the PM6 method.

=== Diels-Alder Reactions ===

A Diels-Alder reaction is a [4+2] cycloadditon between a conjugated s-cis diene (4π-electron system) and a dienophile (2π-electron system). The reaction has a cyclic transition state with 6π-electrons, is concerted, and results in the formation of two new sigma bonds. According to the Woodward-Hoffmann Rules, the Diels-Alder reaction is thermally allowed and is an orbital-controlled reaction, in which the six electrons are interacting suprafacially. The reaction can mainly proceed in two ways:

# Normal electron demand: HOMO of diene overlaps with LUMO of dienophile
# Inverse electron demand: LUMO of diene overlaps with HOMO of dienophile

Several papers divide the Diels-Alder reactions into three categories instead of two <ref name="InverseElectronDemand"/> <ref name="TransitionsofElectronDemand"/>, the third being a neutral electron demand Diels-Alder, in which the energy separation between the HOMO and LUMO of both reactants is similar. <ref name="InverseElectronDemand"/> Neutral electron demand Diels-Alder reactions are seldom observed and believed to be a transition between normal electron demand and inverse electron demand Diels Alder reactions.<ref name="TransitionsofElectronDemand"/>

[[File:normalinverseneutral.jpeg|center|500px]]

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

The reaction between butadiene and ethylene presents the simplest type of Diels-Alder reaction, in which butadiene is the diene and ethylene is the dienophile. This reaction yields cyclohexene as the product, and the reaction scheme is as follow:

[[File:exercise 1 reaction scheme.jpg|center]]

=== Molecular Orbital Diagram ===

[[File:MO diagram for exercise 1 TP1414.jpg|500px|thumb|center|Molecular orbital (MO) diagram for the reaction of butadiene with ethylene]]
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Jmol
! style="background: #0D4F8B; color: white;" | Symmetry
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Jmol
! style="background: #0D4F8B; color: white;" | Symmetry
|-
! rowspan="2" style="background: #0D4F8B; color: white;"| Butadiene
! style="background: #0D4F8B; color: white;"| LUMO
|style="text-align: center;"| [[File:ex1butadieneLUMOtp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 BUTADIENE BREAK SYMMETRY JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 22; rotate x -90; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
! rowspan="4" style="background: #0D4F8B; color: white;"| Transition State
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex1mo4tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
|-
! style="background: #0D4F8B; color: white;"| HOMO
|style="text-align: center;"| [[File:ex1butadieneHOMOtp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 BUTADIENE BREAK SYMMETRY JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 22; rotate x -90; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex1mo3tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
|-
! rowspan="2" style="background: #0D4F8B; color: white;"| Ethylene
! style="background: #0D4F8B; color: white;"| LUMO
|style="text-align: center;"| [[File:ex1ethyleneLUMOtp1414.png|100px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 ETHYLENE JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 14; rotate z 90; rotate x 90; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex1mo2tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| HOMO
|style="text-align: center;"| [[File:ex1ethyleneHOMOtp1414.png|100px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 ETHYLENE JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 14; rotate z 90; rotate x 90; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex1mo1tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
|-
|}

<br style="clear:right">

Only orbitals of the same symmetry can interact to form molecular orbitals. This means that only symmetric-symmetric interactions and antisymmetric-antisymmetric interactions are allowed. Symmetric-antisymmetric interactions, on the other hand, are forbidden. This is because the orbital overlap integral is non-zero for interactions between orbitals of the same symmetry and zero for interactions between orbitals of different symmetry.

As shown on the MO diagram above, both interactions (between the HOMO of butadiene and the LUMO of ethylene, and between the LUMO of butadiene and the HOMO of ethylene) occur, generating four molecular orbitals for the transition state. As the energy separation for the two interactions is similar, the reaction between butadiene and ethylene progress with aspects of both normal electron demand and inverse electron demand. This is because both butadiene and ethylene are neutral molecules without any obvious nucleophilic or electrophilic reacting centrers. Both molecules are neither electron-rich nor electron-poor. As a result, orbital overlap is possible for both HOMO-LUMO sets. Several papers classify this reaction as a neutral electron demand Diels-Alder. <ref name="InverseElectronDemand"/> <ref name="TransitionsofElectronDemand"/> This particular Diels-Alder reaction between butadiene and ethylene is well-known for its poor yield.

<br style="clear:left">

=== Internuclear Distances ===

[[File:internuclear distance.pdf|600px|thumb|right|Internuclear distances for the reaction of butadiene with ethylene to form cyclohexene.]]

[[File:butadiene and ethylene.jpg]]

{| class="wikitable"
|+ Internuclear Distances (Å)
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | C1-C2
! style="background: #0D4F8B; color: white;" | C2-C3
! style="background: #0D4F8B; color: white;" | C3-C4
! style="background: #0D4F8B; color: white;" | C4-C5
! style="background: #0D4F8B; color: white;" | C5-C6
! style="background: #0D4F8B; color: white;" | C6-C1
|-
! style="background: #0D4F8B; color: white;"| Reactants
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|style="text-align: center;"| -
|-
! style="background: #0D4F8B; color: white;"| Transition State
|style="text-align: center;"| 1.38
|style="text-align: center;"| 1.41
|style="text-align: center;"| 1.38
|style="text-align: center;"| 2.11
|style="text-align: center;"| 1.38
|style="text-align: center;"| 2.11
|-
! style="background: #0D4F8B; color: white;"| Product
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}

As the reaction progresses, C1-C2, C3-C4 and C5-C6 elongate as the double bond breaks to form single carbon-carbon bonds, while C2-C3 shortens to form carbon-carbon double bond. Simultaneously, C4-C5 and C6-C1 decrease in distance and ultimately single carbon-carbon bonds are formed. A more detailed overview of how the internuclear distances change over the course of the reaction is shown on the graph on the right.

A typical carbon-carbon single bond length is 1.54 Å and a typical carbon-carbon double bond length is 1.34 Å. <ref name="OrganicChemistryJoseph" />

The Van der Waals radius of one carbon atom is 1.70 Å. <ref name="TheMoleculesofLife" /> The length of the partly formed carbon-carbon bonds in the transition state is about 2.11 Å. This distance is shorter than twice the Van der Waals radius of carbon atom (3.40 Å), indicating bonding interactions are occuring.
<br style="clear:right">

=== Vibration and Reaction Path ===

[[File:exercisa1imaginaryfrequency.jpg]]

The vibration that corresponds to the reaction path at the transition state is illustrated above. This vibration has an imaginary frequency that occurs at 948.97i cm<sup>-1</sup>.

The formation of the two bonds are synchronous as shown below. This means that the two sigma bonds are formed simultaneously. hence, the reaction between butadiene and ethylene goes by a concerted synchronous mechanism.

[[File:IRCgif.jpg]]

=== Calculation Files ===

[[File:TP1414 Exercise 1 Ethylene.log]]

[[File:TP1414 Exercise 1 Butadiene.log]]

[[File:TP1414 Exercise 1 Product.log]]

[[File:TP1414 Exercise 1 Transition State.log]]

[[File:TP1414 Exercise 1 IRC.log]]

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

[[File:exercise 2 reaction schemetp1414.jpg|center]]

=== Molecular Orbital Diagram ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|style="text-align: center;"| [[File:ex 2 MO diagram for exo TS TP1414.jpg|500px]]
Molecular orbital (MO) diagram for the reaction of cyclohexadiene and 1,3-dioxole (exo).
|style="text-align: center;"| [[File:ex 2 MO diagram for endo TS TP1414.jpg|500px]]
Molecular orbital (MO) diagram for the reaction of cyclohexadiene and 1,3-dioxole (endo)
|-
|}

<br style="clear:left">

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Image
! style="background: #0D4F8B; color: white;" | Symmetry
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Image
! style="background: #0D4F8B; color: white;" | Symmetry
|-
! rowspan="4" style="background: #0D4F8B; color: white;"| Exo
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex2exoMO4tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO3 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
! rowspan="4" style="background: #0D4F8B; color: white;"| Endo
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex2endoMO4tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO4 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
|-
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex2exoMO3tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO4 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex2endoMO3tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO3 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex2exoMO2tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO2 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex2endoMO2tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO2 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex2exoMO1tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO1 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex2endoMO1tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO1 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
|-
|}

The exo and endo Diels-Alder between cyclohexadiene and 1,3-dioxole proceed in a similar fashion as the Diels-Alder between butadiene and ethylene in Exercise 1. However, unlike in Exercise 1, the dienophile, 1,3-dioxole, contains two pi electron donating oxygen adjacent to the C-C double bond. This increases the energy of the molecular orbitals of the dienophile, resulting in higher energies HOMO and LUMO of the dienophile relative to neutral ethylene in Exercise 1. As a consequence, the HOMO of the dienophile and the LUMO of the diene are much closer in energy and thus, interact more strongly. This reaction between cyclohexadiene and 1,3-dioxole is said to proceed via inverse electron demand Diels-Alder. The stronger interaction between the HOMO and LUMO results in a faster and more favourable reaction as compared to the neutral electron demand Diels-Alder between butadiene and ethylene in Exercise 1.

=== Thermochemistry ===
[[File:ex2energyprofiletp1414.jpeg|600px|thumb|Energy profile diagram for the reactions between cyclohexadiene and 1,3-dioxole]]
The energies of the reactants, transition state and product for both the exo and endo reactions are tabulated below. These are obtained from optimization at B3LYP/6-31G(d) level.

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;"| Exo
|style="text-align: center;"|-612591.48
|style="text-align: center;"|-701187.43
|style="text-align: center;"|-1313778.91
|style="text-align: center;"|-1313614.33
|style="text-align: center;"|-1313845.77
|style="text-align: center;"|164.58
|style="text-align: center;"|-66.86
|-
!style="background: #0D4F8B; color: white;"| Endo
|style="text-align: center;"|-612591.48
|style="text-align: center;"|-701187.43
|style="text-align: center;"|-1313778.91
|style="text-align: center;"|-1313622.15
|style="text-align: center;"|-1313849.37
|style="text-align: center;"|156.76
|style="text-align: center;"|-70.46
|-
|}

Both the exo and endo reactions are exothermic. However, it can be seen that the energy of the endo product is lower (or more negative) than the energy of the exo product, and the endo reaction also has a lower reaction barrier as compared to the exo reaction. This means that the endo product is both the thermodynamically and kinetically favourable product. This can be explained by considering both electronic and steric factors

[[File:seondaryorbitalinteractionstp1414.png|500px|thumb|left|Secondary orbital interactions in endo transition state]] Secondary orbital interactions stabilize the endo transition state, reducing the reaction barrier. On the left is the HOMO of the endo transition state in which there are obvious secondary orbital interactions between the oxygen p orbitals of the 1,3-dioxole and the p orbitals of the diene. An MO representation of this HOMO is shown below.
[[File:secondaryorbitalinteractionMOrepresentationtp1414.jpeg|350px]]
<br style="clear:left">

[[File:stericclashtp1414.png|500px|thumb|left|Steric clash in exo product]] Steric clash between the sp<sup>3</sup> CH<sub>2</sub> of the dioxole ring and the sp<sup>3</sup> CH<sub>2</sub>'s of the cyclohexadiene destabilize both the exo transition state and the exo product.
<br style="clear:left">

=== Vibration and Reaction Path ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
! style="background: #0D4F8B; color: white;"| Vibration
|style="text-align: center;"| [[File:exercise2 exo vibration tp1414.gif]]
|style="text-align: center;"| [[File:exercise2 endo vibration tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Vibrational Frequency
|style="text-align: center;"| 520.90i cm<sup>-1</sup>
|style="text-align: center;"| 528.85i cm<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| Reaction Pathway
|style="text-align: center;"| [[File:exercise2 exo reaction path tp1414.gif]]
|style="text-align: center;"| [[File:exercise2 endo reaction path tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Mechanism
|style="text-align: center;"| Synchronous concerted
|style="text-align: center;"| Synchronous concerted
|-
|}

=== Calculation Files ===

[[File:TP1414 Exercise 2 Cyclohexadiene 631Gd.log]]

[[File:TP1414 Exercise 2 1,2-Dioxole 631Gd.log]]

[[File:TP1414 Exercise 2 Exo Product 631Gd.log]]

[[File:TP1414 Exercise 2 Endo Product 631Gd.log]]

[[File:TP1414 Exercise 2 Exo Transition State 631Gd.log]]

[[File:TP1414 Exercise 2 Endo Transition State 631Gd.log]]

[[File:TP1414 Exercise 2 Exo IRC 631Gd.log]]

[[File:TP1414 Exercise 2 Endo IRC 631Gd.log]]

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

[[File:exercise3reactionschemetp1414.jpg|center]]

=== Molecular Orbital Diagram ===

The exo and endo Diels-Alder reaction between o-xylylene and SO<sub>2</sub> proceed in a similar fashion as the reactions in Exercise 1 and 2. However, in this case, the dienophile, SO<sub>2</sub>, is electron-deficient and has lower energies HOMO and LUMO compared to the dienophiles in Exercise 1 and 2. As a result, the most significant frontier orbital interaction is between the HOMO of o-xylylene and the LUMO of SO<sub>2</sub>. The Diels-Alder reaction between o-xylylene and SO<sub>2</sub> proceeds via normal electron demand.

The exo and endo Diels-Alder reaction between o-xylylene and SO<sub>2</sub> have another competing pericyclic reaction - cheletropic reaction. Woodward Hoffmann defines cheletropic reactions as pericyclic reactions in which two sigma bonds are formed or broken in a single atom. It is sometimes considered to be a subclass of cycloadditions. <ref name="Cheletropic"/> The MO diagram for the cheletropic reaction is shown below.

[[File:tp1414cheletropicMO.jpg|500px|thumb|center|Molecular orbital (MO) diagram for the cheletropic reaction between o-xylylene and SO<sub>2</sub>]]

=== Thermochemistry ===
[[File:ex3energyprofiletp1414.jpg|600px|thumb|Energy profile diagram for the reactions between o-xylylene and SO<sub>2</sub>]]
The energies of the reactants, transition state and product for the exo, endo and cheletropic reactions are tabulated below. These are obtained from optimization at PM6 level.

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | o-Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;"| Exo
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|241.75
|style="text-align: center;"|56.31
|style="text-align: center;"|85.18
|style="text-align: center;"|-100.26
|-
!style="background: #0D4F8B; color: white;"| Endo
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|237.77
|style="text-align: center;"|56.98
|style="text-align: center;"|81.20
|style="text-align: center;"|-99.59
|-
!style="background: #0D4F8B; color: white;"| Cheletropic
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|260.09
|style="text-align: center;"|-0.01
|style="text-align: center;"|103.52
|style="text-align: center;"|-156.58
|-
|}

All three reactions are exothermic. The endo product is the kinetically favourable product as it has the lowest reaction barrier, while the cheletropic product is the thermodynamically favourable product as it has the lowest energy. This is consistent with experimental works that have been conducted in which a Diels-Alder adduct is observed to be the kinetic product and cheletropic adduct is observed to be the thermodynamic product. Experimental work shows that the Diels-Alder adduct is thermally unstable and will undergo a retro-Diels-Alder reaction to form back the starting materials, before forming the more stable five membered ring cheletropic product. <ref name="Cheletropic"/>
<br style="clear:right">

=== Vibration and Reaction Path ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
! style="background: #0D4F8B; color: white;" | Cheletropic
|-
! style="background: #0D4F8B; color: white;"| Vibration
|style="text-align: center;"| [[File:ex3 exo vibration tp1414.gif]]
|style="text-align: center;"| [[File:ex3 endo vibration tp1414.gif]]
|style="text-align: center;"| [[File:cheletropic vibration tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Vibrational Frequency
|style="text-align: center;"| 351.78i cm<sup>-1</sup>
|style="text-align: center;"| 334.38i cm<sup>-1</sup>
|style="text-align: center;"| 486.58i cm<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| Reaction Pathway
|style="text-align: center;"| [[File:exo IRC tp1414.gif]]
|style="text-align: center;"| [[File:endo IRC tp1414.gif]]
|style="text-align: center;"| [[File:cheletropic IRC tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Mechanism
|style="text-align: center;"| Asynchronous concerted
|style="text-align: center;"| Asynchronous concerted
|style="text-align: center;"| Synchronous concerted
|-
! style="background: #0D4F8B; color: white;"| IRC
|style="text-align: center;"| [[File:exoIRCtp1414.png]]
|style="text-align: center;"| [[File:endoIRCtp1414.png]]
|style="text-align: center;"| [[File:cheletropicIRCtp1414energy.png]]
|-
|}

It is interesting to note that the exo and endo reactions proceed via asynchronous mechanism in which the C-O bond is formed first before the C-S bond, while the cheletropic reaction proceeds via synchronous mechanism in which the two C-S bonds are formed simultaneously. However, even though the formation of the two bonds are asynchronous in the exo and endo reactions, the total energy along IRC tells us that both reactions are concerted as the reactions do not have any intermediate steps.

In all three reaction pathways, the steepest part on the the total energy versus IRC graph corresponds to the re-aromatisation of the 6-membered ring on the o-xylylene, giving these reactions an aromatic driving force. This also shows the instability of the o-xylylene molecule. O-Xylylene is highly unstable as it is antiaromatic (planar and 4n electrons), and it will undergo an electrocyclic ring closure to form the stable aromatic isomer, benzocyclobutene as shown below.<ref name="Benzocyclobutene"/>

[[File:xylyleneelectrocyclicreactionscheme.jpg|centre]]

A quick transition state optimisation followed by IRC calculation of the above reaction on Gaussian gives the total energy along IRC graph below.

[[File:xylyleneelectrocyclicIRCtp1414.jpg|500px|centre]]

[[File:xylyleneelectrocyclicIRC.gif|500px|centre]]

=== Alternate Diels-Alder Reaction ===

There is a second cis-butadiene fragment in o-xylylene that can undergo a Diels-Alder reaction. This second cis-butadiene is part of the cyclohexadiene ring. The exo and endo for this alternate Diels-Alder reaction proceed as follow:

[[File:alternatedielsalderexotp1414.gif]] [[File:alternatedielsalderendotp1414.gif]]

Both reactions proceed via an asynchronous mechanism.

[[File:energyprofilewithalternatedielsaldertp1414.jpg|600px|thumb|Energy profile diagram for the reactions between o-xylylene and SO<sub>2</sub>]]
The thermochemistry for this alternate Diels-Alder reaction is as follows:

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | o-Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;" | Exo
| style="text-align: center;" |467.99
| style="text-align: center;" |-311.42
| style="text-align: center;" |156.57
| style="text-align: center;" |275.82
| style="text-align: center;" |176.71
| style="text-align: center;" |119.25
| style="text-align: center;" |20.14
|-
! style="background: #0D4F8B; color: white;" | Endo
| style="text-align: center;" |467.99
| style="text-align: center;" |-311.42
| style="text-align: center;" |156.57
| style="text-align: center;" |267.98
| style="text-align: center;" |172.26
| style="text-align: center;" |111.41
| style="text-align: center;" |15.96
|-
|}

Comparing the energies for this alternate Diels-Alder reaction with the energies for the normal Diels-Alder and the cheletropic reactions, it can be seen that both the exo and endo alternate Diels-Alder reactoions are kinetically and thermodynamically unfavourable. The products are also higher in energies than the reactants, making the reactions endothermic.
<br style="clear:right">

=== Calculation Files ===

[[File:TP1414 Exercise 3 Xylylene.log]]

[[File:TP1414 Exercise 3 SO2.log]]

[[File:TP1414 Exercise 3 Exo Product.log]]

[[File:TP1414 Exercise 3 Endo Product.log]]

[[File:TP1414 Exercise 3 Cheletropic Product.log]]

[[File:TP1414 Exercise 3 Exo Transition State.log]]

[[File:TP1414 Exercise 3 Endo Transition State.log]]

[[File:TP1414 Exercise 3 Cheletropic Transition State.log]]

[[File:TP1414 Exercise 3 Exo IRC.log]]

[[File:TP1414 Exercise 3 Endo IRC.log]]

[[File:TP1414 Exercise 3 Cheletropic IRC.log]]

[[File:TP1414 Exercise 3 Xylylene Electrocyclic Transition State.log]]

[[File:TP1414 Exercise 3 Xylylene Electrocyclic IRC.log]]

[[File:TP1414 Exercise 3 Alternate Exo Product.log]]

[[File:TP1414 Exercise 3 Alternate Endo Product.log]]

[[File:TP1414 Exercise 3 Alternate Exo Transition State.log]]

[[File:TP1414 Exercise 3 Alternate Endo Transition State.log]]

[[File:TP1414 Exercise 3 Alternate Exo IRC.log]]

[[File:TP1414 Exercise 3 Alternate Endo IRC.log]]

== Conclusion ==

Two calculation methods were used to study three different Diels-Alder reactions. The semi-empirical method PM6 was used to calculate the geometries of the transition state and product of the reactions in all three exercises for faster calculations. In exercise 2, the geometries were further optimised by the DFT method B3LYP at 6-31G(d) level for better accuracy.

Exercises 1 to 3 illustrate the three different ways in which Diels-Alder reaction can proceed: neutral electron demand, inverse electron demand and normal electron demand respectively. In exercise 1, the frontier orbital interactions of the simplest Diels-Alder reaction was studied and it shows that only orbitals of the same symmetry can interact. Exercise 1 also illustrates how internuclear distances vary as a Diels-Alder reaction proceeds, and how these compare with the Van der Waals radii of the atoms. Exercise 2 presents a more complex Diels-Alder reaction which can proceed in two different orientations - endo and exo. It demonstrates how secondary orbital interactions and steric factors could affect the energies of the transition states and products, and hence, determine the kinetically and thermodynamically favourable reactions. Exercise 3 illustrates an even more complex system where there are two diene functional groups and in which another competing pericyclic cheletropic reaction is possible. It also demonstrates that pericyclic reactions can proceed via synchronous concerted or asynchronous concerted mechanisms depending on the symmetry of the interacting molecules.

In conclusion, Gaussian proves to be a useful molecular modelling software to investigate the molecules and their reactions. Transition states were located and characterized, and frontier orbital interactions and thermochemistry were analysed. Results obtained from these calculations also proved to be consistent with theory and experimental observations.

== References ==

<references>
<ref name="ComputationalChemistry"> Lecture notes: ''Quantum Mechanics 3/3rd Year Computational Chemistry Laboratory'', Michael Bearpark, Imperial College. </ref>
<ref name="OrganicChemistryJoseph"> J. M. Hornback, ''Organic Chemistry'', Thomson Learning. Inc., Belmont, Second., 2006.</ref>
<ref name="TheMoleculesofLife"> J. Kuriyan, B. Konforti and D. Wemmer, ''The Molecules of Life: Physical and Chemical Principles'', Garland Science, New York, 2013.</ref>
<ref name="InverseElectronDemand"> A.-C. Knall and C. Slugovc, ''Chem Soc Rev'', 2013, '''42''', 5131–5142.</ref>
<ref name="TransitionsofElectronDemand"> E. Eibler, P. Hocht, B. Prantl, H. Rormaier, H. M. Schuhbauer and H. Wiest, ''Liebigs Ann.lRemei'', 1997, '''1997''', 2471–2484.</ref>
<ref name="Benzocyclobutene"> G. Mehta and S. Kotha, ''Tetrahedron'', 2001, '''57''', 626.</ref>
<ref name="ManyParticlePhysics"> H. Fehske, R. Schneider and A. Weiβe, Eds., ''Computational Many-Particle Physics'', Springer, Berlin, 2008.</ref>
<ref name="Cheletropic"> D. Suarez, T. L. Sordo and A. Sordo, ''J. Org. Chem.'', 1995, '''60''', 2848–2852.</ref>
</references>

2017-03-18T21:11:26Z

Tp1414: /* Introduction */

== Introduction ==

=== Gaussian and Transition State Characterization ===

[[File:Energy surface TP1414.jpg|500px|thumb| Energy surface showing the locations of transition state (TS), local minimum (LM) and global minimum (GM).<ref name="ManyParticlePhysics"/>]]

Gaussian is a molecular modelling software that allows researchers to carry out extensive investigation of molecules and their reactions. In these exercises, the transition states of several Diels-Alder reactions are located and characterized using Gaussian. A transition state is a first order saddle point on a potential energy surface (PES). It is the maximum along the minimum energy path (or reaction path) between two minima (the reactants and the products). ''Geometry optimization'' to find the minimum energy structure will usually lead to a stationary point that is closest to the initial geometry. The stationary point, where the first derivative of energy is zero, can be a global minimum, a local minimum or a saddle point. In a reaction path, the minima (global or local) correspond to the reactants and the products, while the saddle point corresponds to the transition state. To differentiate between a minimum and a saddle point, the second derivatives of energy will have to be analysed. For global or local minima, where energy rises in all directions, the second derivative of energy is positive. In contrast, for transition state, where the energy decreases in one direction (reaction path), the second derivative of energy along the reaction coordinate is negative. The analysis of the second derivatives of energy can be done by a ''frequency calculation'' of the optimized structure. If the structure corresponds to the reactants or products, all the vibrational frequencies (''v'') are real. In contrast, if the structure corresponds to a transition state, there will be one imaginary frequency. This imaginary frequency indicates that the force constant (k), which is given by the second derivative, is negative. <ref name="ComputationalChemistry"/>

<center> <math>\textit{v}=\frac{1}{2\pi }\cdot \sqrt{\frac{k}{\mu }}</math> where <math>k=\frac{\partial ^{2}E}{\partial q^{2}}</math> </center>

Following a successful frequency calculation (one imaginary frequency) of the transition state, an ''Intrinsic Reaction Coordinate (IRC) calculation'' may be set up to examine the transition state along the minimum energy path more closely. The reaction path, or minimum energy path, can be defined as the steepest descent path from the transition state to the reactions and products.

In this exercise, two calculation methods are used. The first is the semi-empirical method PM6, a fitted method used to obtain the initial geometry of the molecule or transition state so as to save time during calculations. The second is the Density Functional Theory (DFT) method B3LYP, a method that is capable of reproducing chemical data and is used to further optimise the geometry obtained from the PM6 method.

=== Diels-Alder Reactions ===

A Diels-Alder reaction is a [4+2] cycloadditon between a conjugated s-cis diene (4π-electron system) and a dienophile (2π-electron system). The reaction has a cyclic transition state with 6π-electrons, is concerted, and results in the formation of two new sigma bonds. According to the Woodward-Hoffmann Rules, the Diels-Alder reaction is thermally allowed and is an orbital-controlled reaction, in which the six electrons are interacting suprafacially. The reaction can mainly proceed in two ways:

# Normal electron demand: HOMO of diene overlaps with LUMO of dienophile
# Inverse electron demand: LUMO of diene overlaps with HOMO of dienophile

Several papers divide the Diels-Alder reactions into three categories instead of two <ref name="InverseElectronDemand"/> <ref name="TransitionsofElectronDemand"/>, the third being a neutral electron demand Diels-Alder, in which the energy separation between the HOMO and LUMO of both reactants is similar. <ref name="InverseElectronDemand"/> Neutral electron demand Diels-Alder reactions are seldom observed and believed to be a transition between normal electron demand and inverse electron demand Diels Alder reactions.<ref name="TransitionsofElectronDemand"/>

[[File:normalinverseneutral.jpeg|center|500px]]

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

The reaction between butadiene and ethylene presents the simplest type of Diels-Alder reaction, in which butadiene is the diene and ethylene is the dienophile. This reaction yields cyclohexene as the product, and the reaction scheme is as follow:

[[File:exercise 1 reaction scheme.jpg|center]]

=== Molecular Orbital Diagram ===

[[File:MO diagram for exercise 1 TP1414.jpg|500px|thumb|center|Molecular orbital (MO) diagram for the reaction of butadiene with ethylene]]
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Jmol
! style="background: #0D4F8B; color: white;" | Symmetry
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Jmol
! style="background: #0D4F8B; color: white;" | Symmetry
|-
! rowspan="2" style="background: #0D4F8B; color: white;"| Butadiene
! style="background: #0D4F8B; color: white;"| LUMO
|style="text-align: center;"| [[File:ex1butadieneLUMOtp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 BUTADIENE BREAK SYMMETRY JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 22; rotate x -90; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
! rowspan="4" style="background: #0D4F8B; color: white;"| Transition State
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex1mo4tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
|-
! style="background: #0D4F8B; color: white;"| HOMO
|style="text-align: center;"| [[File:ex1butadieneHOMOtp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 BUTADIENE BREAK SYMMETRY JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 22; rotate x -90; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex1mo3tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
|-
! rowspan="2" style="background: #0D4F8B; color: white;"| Ethylene
! style="background: #0D4F8B; color: white;"| LUMO
|style="text-align: center;"| [[File:ex1ethyleneLUMOtp1414.png|100px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 ETHYLENE JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 14; rotate z 90; rotate x 90; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex1mo2tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| HOMO
|style="text-align: center;"| [[File:ex1ethyleneHOMOtp1414.png|100px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 ETHYLENE JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 14; rotate z 90; rotate x 90; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex1mo1tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
|-
|}

<br style="clear:right">

Only orbitals of the same symmetry can interact to form molecular orbitals. This means that only symmetric-symmetric interactions and antisymmetric-antisymmetric interactions are allowed. Symmetric-antisymmetric interactions, on the other hand, are forbidden. This is because the orbital overlap integral is non-zero for interactions between orbitals of the same symmetry and zero for interactions between orbitals of different symmetry.

As shown on the MO diagram above, both interactions (between the HOMO of butadiene and the LUMO of ethylene, and between the LUMO of butadiene and the HOMO of ethylene) occur, generating four molecular orbitals for the transition state. As the energy separation for the two interactions is similar, the reaction between butadiene and ethylene progress with aspects of both normal electron demand and inverse electron demand. This is because both butadiene and ethylene are neutral molecules without any obvious nucleophilic or electrophilic reacting centrers. Both molecules are neither electron-rich nor electron-poor. As a result, orbital overlap is possible for both HOMO-LUMO sets. Several papers classify this reaction as a neutral electron demand Diels-Alder. <ref name="InverseElectronDemand"/> <ref name="TransitionsofElectronDemand"/> This particular Diels-Alder reaction between butadiene and ethylene is well-known for its poor yield.

<br style="clear:left">

=== Internuclear Distances ===

[[File:internuclear distance.pdf|600px|thumb|right|Internuclear distances for the reaction of butadiene with ethylene to form cyclohexene.]]

[[File:butadiene and ethylene.jpg]]

{| class="wikitable"
|+ Internuclear Distances (Å)
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | C1-C2
! style="background: #0D4F8B; color: white;" | C2-C3
! style="background: #0D4F8B; color: white;" | C3-C4
! style="background: #0D4F8B; color: white;" | C4-C5
! style="background: #0D4F8B; color: white;" | C5-C6
! style="background: #0D4F8B; color: white;" | C6-C1
|-
! style="background: #0D4F8B; color: white;"| Reactants
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|style="text-align: center;"| -
|-
! style="background: #0D4F8B; color: white;"| Transition State
|style="text-align: center;"| 1.38
|style="text-align: center;"| 1.41
|style="text-align: center;"| 1.38
|style="text-align: center;"| 2.11
|style="text-align: center;"| 1.38
|style="text-align: center;"| 2.11
|-
! style="background: #0D4F8B; color: white;"| Product
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}

As the reaction progresses, C1-C2, C3-C4 and C5-C6 elongate as the double bond breaks to form single carbon-carbon bonds, while C2-C3 shortens to form carbon-carbon double bond. Simultaneously, C4-C5 and C6-C1 decrease in distance and ultimately single carbon-carbon bonds are formed. A more detailed overview of how the internuclear distances change over the course of the reaction is shown on the graph on the right.

A typical carbon-carbon single bond length is 1.54 Å and a typical carbon-carbon double bond length is 1.34 Å. <ref name="OrganicChemistryJoseph" />

The Van der Waals radius of one carbon atom is 1.70 Å. <ref name="TheMoleculesofLife" /> The length of the partly formed carbon-carbon bonds in the transition state is about 2.11 Å. This distance is shorter than twice the Van der Waals radius of carbon atom (3.40 Å), indicating bonding interactions are occuring.
<br style="clear:right">

=== Vibration and Reaction Path ===

[[File:exercisa1imaginaryfrequency.jpg]]

The vibration that corresponds to the reaction path at the transition state is illustrated above. This vibration has an imaginary frequency that occurs at 948.97i cm<sup>-1</sup>.

The formation of the two bonds are synchronous as shown below. This means that the two sigma bonds are formed simultaneously. hence, the reaction between butadiene and ethylene goes by a concerted synchronous mechanism.

[[File:IRCgif.jpg]]

=== Calculation Files ===

[[File:TP1414 Exercise 1 Ethylene.log]]

[[File:TP1414 Exercise 1 Butadiene.log]]

[[File:TP1414 Exercise 1 Product.log]]

[[File:TP1414 Exercise 1 Transition State.log]]

[[File:TP1414 Exercise 1 IRC.log]]

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

[[File:exercise 2 reaction schemetp1414.jpg|center]]

=== Molecular Orbital Diagram ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|style="text-align: center;"| [[File:ex 2 MO diagram for exo TS TP1414.jpg|500px]]
Molecular orbital (MO) diagram for the reaction of cyclohexadiene and 1,3-dioxole (exo).
|style="text-align: center;"| [[File:ex 2 MO diagram for endo TS TP1414.jpg|500px]]
Molecular orbital (MO) diagram for the reaction of cyclohexadiene and 1,3-dioxole (endo)
|-
|}

<br style="clear:left">

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Image
! style="background: #0D4F8B; color: white;" | Symmetry
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Image
! style="background: #0D4F8B; color: white;" | Symmetry
|-
! rowspan="4" style="background: #0D4F8B; color: white;"| Exo
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex2exoMO4tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO3 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
! rowspan="4" style="background: #0D4F8B; color: white;"| Endo
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex2endoMO4tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO4 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
|-
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex2exoMO3tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO4 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex2endoMO3tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO3 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex2exoMO2tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO2 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex2endoMO2tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO2 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex2exoMO1tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO1 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex2endoMO1tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO1 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
|-
|}

The exo and endo Diels-Alder between cyclohexadiene and 1,3-dioxole proceed in a similar fashion as the Diels-Alder between butadiene and ethylene in Exercise 1. However, unlike in Exercise 1, the dienophile, 1,3-dioxole, contains two pi electron donating oxygen adjacent to the C-C double bond. This increases the energy of the molecular orbitals of the dienophile, resulting in higher energies HOMO and LUMO of the dienophile relative to neutral ethylene in Exercise 1. As a consequence, the HOMO of the dienophile and the LUMO of the diene are much closer in energy and thus, interact more strongly. This reaction between cyclohexadiene and 1,3-dioxole is said to proceed via inverse electron demand Diels-Alder. The stronger interaction between the HOMO and LUMO results in a faster and more favourable reaction as compared to the neutral electron demand Diels-Alder between butadiene and ethylene in Exercise 1.

=== Thermochemistry ===
[[File:ex2energyprofiletp1414.jpeg|600px|thumb|Energy profile diagram for the reactions between cyclohexadiene and 1,3-dioxole]]
The energies of the reactants, transition state and product for both the exo and endo reactions are tabulated below. These are obtained from optimization at B3LYP/6-31G(d) level.

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;"| Exo
|style="text-align: center;"|-612591.48
|style="text-align: center;"|-701187.43
|style="text-align: center;"|-1313778.91
|style="text-align: center;"|-1313614.33
|style="text-align: center;"|-1313845.77
|style="text-align: center;"|164.58
|style="text-align: center;"|-66.86
|-
!style="background: #0D4F8B; color: white;"| Endo
|style="text-align: center;"|-612591.48
|style="text-align: center;"|-701187.43
|style="text-align: center;"|-1313778.91
|style="text-align: center;"|-1313622.15
|style="text-align: center;"|-1313849.37
|style="text-align: center;"|156.76
|style="text-align: center;"|-70.46
|-
|}

Both the exo and endo reactions are exothermic. However, it can be seen that the energy of the endo product is lower (or more negative) than the energy of the exo product, and the endo reaction also has a lower reaction barrier as compared to the exo reaction. This means that the endo product is both the thermodynamically and kinetically favourable product. This can be explained by considering both electronic and steric factors

[[File:seondaryorbitalinteractionstp1414.png|500px|thumb|left|Secondary orbital interactions in endo transition state]] Secondary orbital interactions stabilize the endo transition state, reducing the reaction barrier. On the left is the HOMO of the endo transition state in which there are obvious secondary orbital interactions between the oxygen p orbitals of the 1,3-dioxole and the p orbitals of the diene. An MO representation of this HOMO is shown below.
[[File:secondaryorbitalinteractionMOrepresentationtp1414.jpeg|350px]]
<br style="clear:left">

[[File:stericclashtp1414.png|500px|thumb|left|Steric clash in exo product]] Steric clash between the sp<sup>3</sup> CH<sub>2</sub> of the dioxole ring and the sp<sup>3</sup> CH<sub>2</sub>'s of the cyclohexadiene destabilize both the exo transition state and the exo product.
<br style="clear:left">

=== Vibration and Reaction Path ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
! style="background: #0D4F8B; color: white;"| Vibration
|style="text-align: center;"| [[File:exercise2 exo vibration tp1414.gif]]
|style="text-align: center;"| [[File:exercise2 endo vibration tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Vibrational Frequency
|style="text-align: center;"| 520.90i cm<sup>-1</sup>
|style="text-align: center;"| 528.85i cm<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| Reaction Pathway
|style="text-align: center;"| [[File:exercise2 exo reaction path tp1414.gif]]
|style="text-align: center;"| [[File:exercise2 endo reaction path tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Mechanism
|style="text-align: center;"| Synchronous concerted
|style="text-align: center;"| Synchronous concerted
|-
|}

=== Calculation Files ===

[[File:TP1414 Exercise 2 Cyclohexadiene 631Gd.log]]

[[File:TP1414 Exercise 2 1,2-Dioxole 631Gd.log]]

[[File:TP1414 Exercise 2 Exo Product 631Gd.log]]

[[File:TP1414 Exercise 2 Endo Product 631Gd.log]]

[[File:TP1414 Exercise 2 Exo Transition State 631Gd.log]]

[[File:TP1414 Exercise 2 Endo Transition State 631Gd.log]]

[[File:TP1414 Exercise 2 Exo IRC 631Gd.log]]

[[File:TP1414 Exercise 2 Endo IRC 631Gd.log]]

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

[[File:exercise3reactionschemetp1414.jpg|center]]

=== Thermochemistry ===
[[File:ex3energyprofiletp1414.jpg|600px|thumb|Energy profile diagram for the reactions between o-xylylene and SO<sub>2</sub>]]
The energies of the reactants, transition state and product for the exo, endo and cheletropic reactions are tabulated below. These are obtained from optimization at PM6 level.

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | o-Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;"| Exo
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|241.75
|style="text-align: center;"|56.31
|style="text-align: center;"|85.18
|style="text-align: center;"|-100.26
|-
!style="background: #0D4F8B; color: white;"| Endo
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|237.77
|style="text-align: center;"|56.98
|style="text-align: center;"|81.20
|style="text-align: center;"|-99.59
|-
!style="background: #0D4F8B; color: white;"| Cheletropic
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|260.09
|style="text-align: center;"|-0.01
|style="text-align: center;"|103.52
|style="text-align: center;"|-156.58
|-
|}

All three reactions are exothermic. The endo product is the kinetically favourable product as it has the lowest reaction barrier, while the cheletropic product is the thermodynamically favourable product as it has the lowest energy.
<br style="clear:right">

=== Vibration and Reaction Path ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
! style="background: #0D4F8B; color: white;" | Cheletropic
|-
! style="background: #0D4F8B; color: white;"| Vibration
|style="text-align: center;"| [[File:ex3 exo vibration tp1414.gif]]
|style="text-align: center;"| [[File:ex3 endo vibration tp1414.gif]]
|style="text-align: center;"| [[File:cheletropic vibration tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Vibrational Frequency
|style="text-align: center;"| 351.78i cm<sup>-1</sup>
|style="text-align: center;"| 334.38i cm<sup>-1</sup>
|style="text-align: center;"| 486.58i cm<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| Reaction Pathway
|style="text-align: center;"| [[File:exo IRC tp1414.gif]]
|style="text-align: center;"| [[File:endo IRC tp1414.gif]]
|style="text-align: center;"| [[File:cheletropic IRC tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Mechanism
|style="text-align: center;"| Asynchronous concerted
|style="text-align: center;"| Asynchronous concerted
|style="text-align: center;"| Synchronous concerted
|-
! style="background: #0D4F8B; color: white;"| IRC
|style="text-align: center;"| [[File:exoIRCtp1414.png]]
|style="text-align: center;"| [[File:endoIRCtp1414.png]]
|style="text-align: center;"| [[File:cheletropicIRCtp1414energy.png]]
|-
|}

It is interesting to note that the exo and endo reactions proceed via asynchronous mechanism in which the C-O bond is formed first before the C-S bond, while the cheletropic reaction proceeds via synchronous mechanism in which the two C-S bonds are formed simultaneously. However, even though the formation of the two bonds are asynchronous in the exo and endo reactions, the total energy along IRC tells us that both reactions are concerted as the reactions do not have any intermediate steps.

In all three reaction pathways, the steepest part on the the total energy versus IRC graph corresponds to the re-aromatisation of the 6-membered ring on the o-xylylene, giving these reactions an aromatic driving force. This also shows the instability of the o-xylylene molecule. O-Xylylene is highly unstable as it is antiaromatic (planar and 4n electrons), and it will undergo an electrocyclic ring closure to form the stable aromatic isomer, benzocyclobutene as shown below.<ref name="Benzocyclobutene"/>

[[File:xylyleneelectrocyclicreactionscheme.jpg|centre]]

A quick transition state optimisation followed by IRC calculation of the above reaction on Gaussian gives the total energy along IRC graph below.

[[File:xylyleneelectrocyclicIRCtp1414.jpg|500px|centre]]

[[File:xylyleneelectrocyclicIRC.gif|500px|centre]]

=== Alternate Diels-Alder Reaction ===

There is a second cis-butadiene fragment in o-xylylene that can undergo a Diels-Alder reaction. This second cis-butadiene is part of the cyclohexadiene ring. The exo and endo for this alternate Diels-Alder reaction proceed as follow:

[[File:alternatedielsalderexotp1414.gif]] [[File:alternatedielsalderendotp1414.gif]]

Both reactions proceed via an asynchronous mechanism.

[[File:energyprofilewithalternatedielsaldertp1414.jpg|600px|thumb|Energy profile diagram for the reactions between o-xylylene and SO<sub>2</sub>]]
The thermochemistry for this alternate Diels-Alder reaction is as follows:

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | o-Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;" | Exo
| style="text-align: center;" |467.99
| style="text-align: center;" |-311.42
| style="text-align: center;" |156.57
| style="text-align: center;" |275.82
| style="text-align: center;" |176.71
| style="text-align: center;" |119.25
| style="text-align: center;" |20.14
|-
! style="background: #0D4F8B; color: white;" | Endo
| style="text-align: center;" |467.99
| style="text-align: center;" |-311.42
| style="text-align: center;" |156.57
| style="text-align: center;" |267.98
| style="text-align: center;" |172.26
| style="text-align: center;" |111.41
| style="text-align: center;" |15.96
|-
|}

Comparing the energies for this alternate Diels-Alder reaction with the energies for the normal Diels-Alder and the cheletropic reactions, it can be seen that both the exo and endo alternate Diels-Alder reactoions are kinetically and thermodynamically unfavourable. The products are also higher in energies than the reactants, making the reactions endothermic.
<br style="clear:right">

=== Calculation Files ===

[[File:TP1414 Exercise 3 Xylylene.log]]

[[File:TP1414 Exercise 3 SO2.log]]

[[File:TP1414 Exercise 3 Exo Product.log]]

[[File:TP1414 Exercise 3 Endo Product.log]]

[[File:TP1414 Exercise 3 Cheletropic Product.log]]

[[File:TP1414 Exercise 3 Exo Transition State.log]]

[[File:TP1414 Exercise 3 Endo Transition State.log]]

[[File:TP1414 Exercise 3 Cheletropic Transition State.log]]

[[File:TP1414 Exercise 3 Exo IRC.log]]

[[File:TP1414 Exercise 3 Endo IRC.log]]

[[File:TP1414 Exercise 3 Cheletropic IRC.log]]

[[File:TP1414 Exercise 3 Xylylene Electrocyclic Transition State.log]]

[[File:TP1414 Exercise 3 Xylylene Electrocyclic IRC.log]]

[[File:TP1414 Exercise 3 Alternate Exo Product.log]]

[[File:TP1414 Exercise 3 Alternate Endo Product.log]]

[[File:TP1414 Exercise 3 Alternate Exo Transition State.log]]

[[File:TP1414 Exercise 3 Alternate Endo Transition State.log]]

[[File:TP1414 Exercise 3 Alternate Exo IRC.log]]

[[File:TP1414 Exercise 3 Alternate Endo IRC.log]]

== Conclusion ==
Synchronous and asynchronous mechanism. Symmetrical molecules?

== References ==

<references>
<ref name="ComputationalChemistry"> Lecture notes: ''Quantum Mechanics 3/3rd Year Computational Chemistry Laboratory'', Michael Bearpark, Imperial College. </ref>
<ref name="OrganicChemistryJoseph"> J. M. Hornback, ''Organic Chemistry'', Thomson Learning. Inc., Belmont, Second., 2006.</ref>
<ref name="TheMoleculesofLife"> J. Kuriyan, B. Konforti and D. Wemmer, ''The Molecules of Life: Physical and Chemical Principles'', Garland Science, New York, 2013.</ref>
<ref name="InverseElectronDemand"> A.-C. Knall and C. Slugovc, ''Chem Soc Rev'', 2013, '''42''', 5131–5142.</ref>
<ref name="TransitionsofElectronDemand"> E. Eibler, P. Hocht, B. Prantl, H. Rormaier, H. M. Schuhbauer and H. Wiest, ''Liebigs Ann.lRemei'', 1997, '''1997''', 2471–2484.</ref>
<ref name="Benzocyclobutene"> G. Mehta and S. Kotha, ''Tetrahedron'', 2001, '''57''', 626.</ref>
<ref name="ManyParticlePhysics"> H. Fehske, R. Schneider and A. Weiβe, Eds., ''Computational Many-Particle Physics'', Springer, Berlin, 2008.</ref>
</references>

2017-03-14T16:20:21Z

Tp1414:

Rep:Mod:TP1414

2017-03-14T16:19:51Z

Tp1414: /* Vibration and Reaction Path */

== Introduction ==

=== Gaussian and Transition State Characterization ===

Gaussian is a molecular modelling software that allows researchers to carry out extensive investigation of molecules and their reactions. In these exercises, the transition states of several Diels-Alder reactions are located and characterized using Gaussian. A transition state is a first order saddle point on a potential energy surface (PES). It is the maximum along the minimum energy path (or reaction path) between two minima (the reactants and the products). ''Geometry optimization'' to find the minimum energy structure will usually lead to a stationary point that is closest to the initial geometry. The stationary point, where the first derivative of energy is zero, can be a global minimum, a local minimum or a saddle point. In a reaction path, the minima (global or local) correspond to the reactants and the products, while the saddle point corresponds to the transition state. To differentiate between a minimum and a saddle point, the second derivatives of energy will have to be analysed. For global or local minima, where energy rises in all directions, the second derivative of energy is positive. In contrast, for transition state, where the energy decreases in one direction (reaction path), the second derivative of energy along the reaction coordinate is negative. The analysis of the second derivatives of energy can be done by a ''frequency calculation'' of the optimized structure. If the structure corresponds to the reactants or products, all the vibrational frequencies are real. In contrast, if the structure corresponds to a transition state, there will be one imaginary frequency. This imaginary frequency indicates that the force constant (k), which is given by the second derivative, is negative.

[[File:frequencyequation.png|center]]

[[File:forceconstantequation.png|center]]

Following a successful frequency calculation (one imaginary frequency) of the transition state, an ''Intrinsic Reaction Coordinate (IRC) calculation'' may be set up to examine the transition state along the minimum energy path more closely. The reaction path, or minimum energy path, can be defined as the steepest descent path from the transition state to the reactions and products.

=== Diels-Alder Reactions ===

A Diels-Alder reaction is a [4+2] cycloadditon between a conjugated s-cis diene (4π-electron system) and a dienophile (2π-electron system). The reaction has a cyclic transition state with 6π-electrons, is concerted, and results in the formation of two new sigma bonds. According to the Woodward-Hoffmann Rules, the Diels-Alder reaction is thermally allowed and is an orbital-controlled reaction, in which the six electrons are interacting suprafacially. The reaction can mainly proceed in two ways:

# Normal electron demand: HOMO of diene overlaps with LUMO of dienophile
# Inverse electron demand: LUMO of diene overlaps with HOMO of dienophile

Several papers divide the Diels-Alder reactions into three categories instead of two <ref name="InverseElectronDemand"/> <ref name="TransitionsofElectronDemand"/>, the third being a neutral electron demand Diels-Alder, in which the energy separation between the HOMO and LUMO of both reactants is similar. <ref name="InverseElectronDemand"/> Neutral electron demand Diels-Alder reactions are seldom observed and believed to be a transition between normal electron demand and inverse electron demand Diels Alder reactions.<ref name="TransitionsofElectronDemand"/>

[[File:normalinverseneutral.jpeg|center|500px]]

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

The reaction between butadiene and ethylene presents the simplest type of Diels-Alder reaction, in which butadiene is the diene and ethylene is the dienophile. This reaction yields cyclohexene as the product, and the reaction scheme is as follow:

[[File:exercise 1 reaction scheme.jpg|center]]

=== Molecular Orbital Diagram ===

[[File:MO diagram for exercise 1 TP1414.jpg|500px|thumb|center|Molecular orbital (MO) diagram for the reaction of butadiene with ethylene]]
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Jmol
! style="background: #0D4F8B; color: white;" | Symmetry
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Jmol
! style="background: #0D4F8B; color: white;" | Symmetry
|-
! rowspan="2" style="background: #0D4F8B; color: white;"| Butadiene
! style="background: #0D4F8B; color: white;"| LUMO
|style="text-align: center;"| [[File:ex1butadieneLUMOtp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 BUTADIENE BREAK SYMMETRY JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 22; rotate x -90; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
! rowspan="4" style="background: #0D4F8B; color: white;"| Transition State
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex1mo4tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
|-
! style="background: #0D4F8B; color: white;"| HOMO
|style="text-align: center;"| [[File:ex1butadieneHOMOtp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 BUTADIENE BREAK SYMMETRY JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 22; rotate x -90; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex1mo3tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
|-
! rowspan="2" style="background: #0D4F8B; color: white;"| Ethylene
! style="background: #0D4F8B; color: white;"| LUMO
|style="text-align: center;"| [[File:ex1ethyleneLUMOtp1414.png|100px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 ETHYLENE JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 14; rotate z 90; rotate x 90; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex1mo2tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| HOMO
|style="text-align: center;"| [[File:ex1ethyleneHOMOtp1414.png|100px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 ETHYLENE JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 14; rotate z 90; rotate x 90; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex1mo1tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
|-
|}

<br style="clear:right">

Only orbitals of the same symmetry can interact to form molecular orbitals. This means that only symmetric-symmetric interactions and antisymmetric-antisymmetric interactions are allowed. Symmetric-antisymmetric interactions, on the other hand, are forbidden. This is because the orbital overlap integral is non-zero for interactions between orbitals of the same symmetry and zero for interactions between orbitals of different symmetry.

As shown on the MO diagram above, both interactions (between the HOMO of butadiene and the LUMO of ethylene, and between the LUMO of butadiene and the HOMO of ethylene) occur, generating four molecular orbitals for the transition state. As the energy separation for the two interactions is similar, the reaction between butadiene and ethylene progress with aspects of both normal electron demand and inverse electron demand. This is because both butadiene and ethylene are neutral molecules without any obvious nucleophilic or electrophilic reacting centrers. Both molecules are neither electron-rich nor electron-poor. As a result, orbital overlap is possible for both HOMO-LUMO sets. Several papers classify this reaction as a neutral electron demand Diels-Alder. <ref name="InverseElectronDemand"/> <ref name="TransitionsofElectronDemand"/> This particular Diels-Alder reaction between butadiene and ethylene is well-known for its poor yield.

<br style="clear:left">

=== Internuclear Distances ===

[[File:internuclear distance.pdf|600px|thumb|right|Internuclear distances for the reaction of butadiene with ethylene to form cyclohexene.]]

[[File:butadiene and ethylene.jpg]]

{| class="wikitable"
|+ Internuclear Distances (Å)
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | C1-C2
! style="background: #0D4F8B; color: white;" | C2-C3
! style="background: #0D4F8B; color: white;" | C3-C4
! style="background: #0D4F8B; color: white;" | C4-C5
! style="background: #0D4F8B; color: white;" | C5-C6
! style="background: #0D4F8B; color: white;" | C6-C1
|-
! style="background: #0D4F8B; color: white;"| Reactants
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|style="text-align: center;"| -
|-
! style="background: #0D4F8B; color: white;"| Transition State
|style="text-align: center;"| 1.38
|style="text-align: center;"| 1.41
|style="text-align: center;"| 1.38
|style="text-align: center;"| 2.11
|style="text-align: center;"| 1.38
|style="text-align: center;"| 2.11
|-
! style="background: #0D4F8B; color: white;"| Product
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}

As the reaction progresses, C1-C2, C3-C4 and C5-C6 elongate as the double bond breaks to form single carbon-carbon bonds, while C2-C3 shortens to form carbon-carbon double bond. Simultaneously, C4-C5 and C6-C1 decrease in distance and ultimately single carbon-carbon bonds are formed. A more detailed overview of how the internuclear distances change over the course of the reaction is shown on the graph on the right.

A typical carbon-carbon single bond length is 1.54 Å and a typical carbon-carbon double bond length is 1.34 Å. <ref name="OrganicChemistryJoseph" />

The Van der Waals radius of one carbon atom is 1.70 Å. <ref name="TheMoleculesofLife" /> The length of the partly formed carbon-carbon bonds in the transition state is about 2.11 Å. This distance is shorter than twice the Van der Waals radius of carbon atom (3.40 Å), indicating bonding interactions are occuring.
<br style="clear:right">

=== Vibration and Reaction Path ===

[[File:exercisa1imaginaryfrequency.jpg]]

The vibration that corresponds to the reaction path at the transition state is illustrated above. This vibration has an imaginary frequency that occurs at 948.97i cm<sup>-1</sup>.

The formation of the two bonds are synchronous as shown below. This means that the two sigma bonds are formed simultaneously. hence, the reaction between butadiene and ethylene goes by a concerted synchronous mechanism.

[[File:IRCgif.jpg]]

=== Calculation Files ===

[[File:TP1414 Exercise 1 Ethylene.log]]

[[File:TP1414 Exercise 1 Butadiene.log]]

[[File:TP1414 Exercise 1 Product.log]]

[[File:TP1414 Exercise 1 Transition State.log]]

[[File:TP1414 Exercise 1 IRC.log]]

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

[[File:exercise 2 reaction schemetp1414.jpg|center]]

=== Molecular Orbital Diagram ===

[[File:ex 2 MO diagram for exo TS TP1414.jpg|left|500px|thumb|Molecular orbital (MO) diagram for the reaction of cyclohexadiene and 1,3-dioxole (exo).]]

[[File:ex 2 MO diagram for endo TS TP1414.jpg|500px|thumb|Molecular orbital (MO) diagram for the reaction of cyclohexadiene and 1,3-dioxole (endo).]]

<br style="clear:left">

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Image
! style="background: #0D4F8B; color: white;" | Symmetry
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Image
! style="background: #0D4F8B; color: white;" | Symmetry
|-
! rowspan="4" style="background: #0D4F8B; color: white;"| Exo
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex2exoMO4tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO4 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
! rowspan="4" style="background: #0D4F8B; color: white;"| Endo
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex2endoMO4tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO4 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
|-
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex2exoMO3tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO3 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex2endoMO3tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO3 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex2exoMO2tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO2 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex2endoMO2tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO2 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex2exoMO1tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO1 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex2endoMO1tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO1 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
|-
|}

Inverse electron demand Diels-Alder

=== Thermochemistry ===
[[File:ex2energyprofiletp1414.jpeg|600px|thumb|Energy profile diagram for the reactions between cyclohexadiene and 1,3-dioxole]]
The energies of the reactants, transition state and product for both the exo and endo reactions are tabulated below. These are obtained from optimization at B3LYP/6-31G(d) level.

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;"| Exo
|style="text-align: center;"|-612591.48
|style="text-align: center;"|-701187.43
|style="text-align: center;"|-1313778.91
|style="text-align: center;"|-1313614.33
|style="text-align: center;"|-1313845.77
|style="text-align: center;"|164.58
|style="text-align: center;"|-66.86
|-
!style="background: #0D4F8B; color: white;"| Endo
|style="text-align: center;"|-612591.48
|style="text-align: center;"|-701187.43
|style="text-align: center;"|-1313778.91
|style="text-align: center;"|-1313622.15
|style="text-align: center;"|-1313849.37
|style="text-align: center;"|156.76
|style="text-align: center;"|-70.46
|-
|}

Both the exo and endo reactions are exothermic. However, it can be seen that the energy of the endo product is lower (or more negative) than the energy of the exo product, and the endo reaction also has a lower reaction barrier as compared to the exo reaction. This means that the endo product is both the thermodynamically and kinetically favourable product. This can be explained by considering both electronic and steric factors

[[File:seondaryorbitalinteractionstp1414.png|500px|thumb|left|Secondary orbital interactions in endo transition state]] Secondary orbital interactions stabilize the endo transition state, reducing the reaction barrier. On the left is the HOMO of the endo transition state in which there are obvious secondary orbital interactions between the oxygen p orbitals of the 1,3-dioxole and the p orbitals of the diene. An MO representation of this HOMO is shown below.
[[File:secondaryorbitalinteractionMOrepresentationtp1414.jpeg|350px]]
<br style="clear:left">

[[File:stericclashtp1414.png|500px|thumb|left|Steric clash in exo product]] Steric clash between the sp<sup>3</sup> CH<sub>2</sub> of the dioxole ring and the sp<sup>3</sup> CH<sub>2</sub>'s of the cyclohexadiene destabilize both the exo transition state and the exo product.
<br style="clear:left">

=== Vibration and Reaction Path ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
! style="background: #0D4F8B; color: white;"| Vibration
|style="text-align: center;"| [[File:exercise2 exo vibration tp1414.gif]]
|style="text-align: center;"| [[File:exercise2 endo vibration tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Vibrational Frequency
|style="text-align: center;"| 520.90i cm<sup>-1</sup>
|style="text-align: center;"| 528.85i cm<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| Reaction Pathway
|style="text-align: center;"| [[File:exercise2 exo reaction path tp1414.gif]]
|style="text-align: center;"| [[File:exercise2 endo reaction path tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Mechanism
|style="text-align: center;"| Synchronous concerted
|style="text-align: center;"| Synchronous concerted
|-
|}

=== Calculation Files ===

[[File:TP1414 Exercise 2 Cyclohexadiene 631Gd.log]]

[[File:TP1414 Exercise 2 1,2-Dioxole 631Gd.log]]

[[File:TP1414 Exercise 2 Exo Product 631Gd.log]]

[[File:TP1414 Exercise 2 Endo Product 631Gd.log]]

[[File:TP1414 Exercise 2 Exo Transition State 631Gd.log]]

[[File:TP1414 Exercise 2 Endo Transition State 631Gd.log]]

[[File:TP1414 Exercise 2 Exo IRC 631Gd.log]]

[[File:TP1414 Exercise 2 Endo IRC 631Gd.log]]

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

[[File:exercise3reactionschemetp1414.jpg|center]]

=== Thermochemistry ===
[[File:ex3energyprofiletp1414.jpg|600px|thumb|Energy profile diagram for the reactions between o-xylylene and SO<sub>2</sub>]]
The energies of the reactants, transition state and product for the exo, endo and cheletropic reactions are tabulated below. These are obtained from optimization at PM6 level.

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | o-Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;"| Exo
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|241.75
|style="text-align: center;"|56.31
|style="text-align: center;"|85.18
|style="text-align: center;"|-71.39
|-
!style="background: #0D4F8B; color: white;"| Endo
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|237.77
|style="text-align: center;"|56.98
|style="text-align: center;"|81.20
|style="text-align: center;"|-75.37
|-
!style="background: #0D4F8B; color: white;"| Cheletropic
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|260.09
|style="text-align: center;"|-0.01
|style="text-align: center;"|103.52
|style="text-align: center;"|-53.05
|-
|}

All three reactions are exothermic. The endo product is the kinetically favourable product as it has the lowest reaction barrier, while the cheletropic product is the thermodynamically favourable product as it has the lowest energy.
<br style="clear:right">

=== Vibration and Reaction Path ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
! style="background: #0D4F8B; color: white;" | Cheletropic
|-
! style="background: #0D4F8B; color: white;"| Vibration
|style="text-align: center;"| [[File:ex3 exo vibration tp1414.gif]]
|style="text-align: center;"| [[File:ex3 endo vibration tp1414.gif]]
|style="text-align: center;"| [[File:cheletropic vibration tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Vibrational Frequency
|style="text-align: center;"| 351.78i cm<sup>-1</sup>
|style="text-align: center;"| 334.38i cm<sup>-1</sup>
|style="text-align: center;"| 486.58i cm<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| Reaction Pathway
|style="text-align: center;"| [[File:exo IRC tp1414.gif]]
|style="text-align: center;"| [[File:endo IRC tp1414.gif]]
|style="text-align: center;"| [[File:cheletropic IRC tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Mechanism
|style="text-align: center;"| Asynchronous concerted
|style="text-align: center;"| Asynchronous concerted
|style="text-align: center;"| Synchronous concerted
|-
! style="background: #0D4F8B; color: white;"| IRC
|style="text-align: center;"| [[File:exoIRCtp1414.png]]
|style="text-align: center;"| [[File:endoIRCtp1414.png]]
|style="text-align: center;"| [[File:cheletropicIRCtp1414energy.png]]
|-
|}

It is interesting to note that the exo and endo reactions proceed via asynchronous mechanism in which the C-O bond is formed first before the C-S bond, while the cheletropic reaction proceeds via synchronous mechanism in which the two C-S bonds are formed simultaneously. However, even though the formation of the two bonds are asynchronous in the exo and endo reactions, the total energy along IRC tells us that both reactions are concerted as the reactions do not have any intermediate steps.

In all three reaction pathways, the steepest part on the the total energy versus IRC graph corresponds to the re-aromatisation of the 6-membered ring on the o-xylylene, giving these reactions an aromatic driving force. This also shows the instability of the o-xylylene molecule. O-Xylylene is highly unstable as it is antiaromatic (planar and 4n electrons), and it will undergo an electrocyclic ring closure to form the stable aromatic isomer, benzocyclobutene as shown below.

[[File:xylyleneelectrocyclicreactionscheme.jpg|centre]]

A quick transition state optimisation followed by IRC calculation of the above reaction on Gaussian gives the total energy along IRC graph below.

[[File:xylyleneelectrocyclicIRCtp1414.jpg|centre]]

[[File:xylyleneelectrocyclicIRC.gif|centre]]

=== Alternate Diels-Alder Reaction ===

There is a second cis-butadiene fragment in o-xylylene that can undergo a Diels-Alder reaction. This second cis-butadiene is part of the cyclohexadiene ring. The exo and endo for this alternate Diels-Alder reaction proceed as follow:

[[File:alternatedielsalderexotp1414.gif]] [[File:alternatedielsalderendotp1414.gif]]

Both reactions proceed via an asynchronous mechanism.

[[File:energyprofilewithalternatedielsaldertp1414.jpg|600px|thumb|Energy profile diagram for the reactions between o-xylylene and SO<sub>2</sub>]]
The thermochemistry for this alternate Diels-Alder reaction is as follows:

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | o-Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;" | Exo
| style="text-align: center;" |467.99
| style="text-align: center;" |-311.42
| style="text-align: center;" |156.57
| style="text-align: center;" |275.82
| style="text-align: center;" |176.71
| style="text-align: center;" |119.25
| style="text-align: center;" |20.14
|-
! style="background: #0D4F8B; color: white;" | Endo
| style="text-align: center;" |467.99
| style="text-align: center;" |-311.42
| style="text-align: center;" |156.57
| style="text-align: center;" |267.98
| style="text-align: center;" |172.26
| style="text-align: center;" |111.41
| style="text-align: center;" |15.96
|-
|}

Comparing the energies for this alternate Diels-Alder reaction with the energies for the normal Diels-Alder and the cheletropic reactions, it can be seen that both the exo and endo alternate Diels-Alder reactoions are kinetically and thermodynamically unfavourable. The products are also higher in energies than the reactants, making the reactions endothermic.
<br style="clear:right">

=== Calculation Files ===

[[File:TP1414 Exercise 3 Xylylene.log]]

[[File:TP1414 Exercise 3 SO2.log]]

[[File:TP1414 Exercise 3 Exo Product.log]]

[[File:TP1414 Exercise 3 Endo Product.log]]

[[File:TP1414 Exercise 3 Cheletropic Product.log]]

[[File:TP1414 Exercise 3 Exo Transition State.log]]

[[File:TP1414 Exercise 3 Endo Transition State.log]]

[[File:TP1414 Exercise 3 Cheletropic Transition State.log]]

[[File:TP1414 Exercise 3 Exo IRC.log]]

[[File:TP1414 Exercise 3 Endo IRC.log]]

[[File:TP1414 Exercise 3 Cheletropic IRC.log]]

[[File:TP1414 Exercise 3 Xylylene Electrocyclic Transition State.log]]

[[File:TP1414 Exercise 3 Xylylene Electrocyclic IRC.log]]

[[File:TP1414 Exercise 3 Alternate Exo Product.log]]

[[File:TP1414 Exercise 3 Alternate Endo Product.log]]

[[File:TP1414 Exercise 3 Alternate Exo Transition State.log]]

[[File:TP1414 Exercise 3 Alternate Endo Transition State.log]]

[[File:TP1414 Exercise 3 Alternate Exo IRC.log]]

[[File:TP1414 Exercise 3 Alternate Endo IRC.log]]

== Conclusion ==
Synchronous and asynchronous mechanism. Symmetrical molecules?

== References ==

<references>
<ref name="OrganicChemistryJoseph"> J. M. Hornback, ''Organic Chemistry'', Thomson Learning. Inc., Belmont, Second., 2006.</ref>
<ref name="TheMoleculesofLife"> J. Kuriyan, B. Konforti and D. Wemmer, ''The Molecules of Life: Physical and Chemical Principles'', Garland Science, New York, 2013.</ref>
<ref name="InverseElectronDemand"> A.-C. Knall and C. Slugovc, ''Chem Soc Rev'', 2013, '''42''', 5131–5142.</ref>
<ref name="TransitionsofElectronDemand"> E. Eibler, P. Hocht, B. Prantl, H. Rormaier, H. M. Schuhbauer and H. Wiest, ''Liebigs Ann.lRemei'', 1997, '''1997''', 2471–2484.</ref>
</references>

File:XylyleneelectrocyclicIRCtp1414.jpg

2017-03-14T16:16:59Z

Tp1414:

File:TP1414 Exercise 3 Xylylene Electrocyclic IRC.log

2017-03-14T16:16:42Z

Tp1414:

Rep:Mod:TP1414

2017-03-14T16:16:03Z

Tp1414: /* Vibration and Reaction Path */

== Introduction ==

=== Gaussian and Transition State Characterization ===

Gaussian is a molecular modelling software that allows researchers to carry out extensive investigation of molecules and their reactions. In these exercises, the transition states of several Diels-Alder reactions are located and characterized using Gaussian. A transition state is a first order saddle point on a potential energy surface (PES). It is the maximum along the minimum energy path (or reaction path) between two minima (the reactants and the products). ''Geometry optimization'' to find the minimum energy structure will usually lead to a stationary point that is closest to the initial geometry. The stationary point, where the first derivative of energy is zero, can be a global minimum, a local minimum or a saddle point. In a reaction path, the minima (global or local) correspond to the reactants and the products, while the saddle point corresponds to the transition state. To differentiate between a minimum and a saddle point, the second derivatives of energy will have to be analysed. For global or local minima, where energy rises in all directions, the second derivative of energy is positive. In contrast, for transition state, where the energy decreases in one direction (reaction path), the second derivative of energy along the reaction coordinate is negative. The analysis of the second derivatives of energy can be done by a ''frequency calculation'' of the optimized structure. If the structure corresponds to the reactants or products, all the vibrational frequencies are real. In contrast, if the structure corresponds to a transition state, there will be one imaginary frequency. This imaginary frequency indicates that the force constant (k), which is given by the second derivative, is negative.

[[File:frequencyequation.png|center]]

[[File:forceconstantequation.png|center]]

Following a successful frequency calculation (one imaginary frequency) of the transition state, an ''Intrinsic Reaction Coordinate (IRC) calculation'' may be set up to examine the transition state along the minimum energy path more closely. The reaction path, or minimum energy path, can be defined as the steepest descent path from the transition state to the reactions and products.

=== Diels-Alder Reactions ===

A Diels-Alder reaction is a [4+2] cycloadditon between a conjugated s-cis diene (4π-electron system) and a dienophile (2π-electron system). The reaction has a cyclic transition state with 6π-electrons, is concerted, and results in the formation of two new sigma bonds. According to the Woodward-Hoffmann Rules, the Diels-Alder reaction is thermally allowed and is an orbital-controlled reaction, in which the six electrons are interacting suprafacially. The reaction can mainly proceed in two ways:

# Normal electron demand: HOMO of diene overlaps with LUMO of dienophile
# Inverse electron demand: LUMO of diene overlaps with HOMO of dienophile

Several papers divide the Diels-Alder reactions into three categories instead of two <ref name="InverseElectronDemand"/> <ref name="TransitionsofElectronDemand"/>, the third being a neutral electron demand Diels-Alder, in which the energy separation between the HOMO and LUMO of both reactants is similar. <ref name="InverseElectronDemand"/> Neutral electron demand Diels-Alder reactions are seldom observed and believed to be a transition between normal electron demand and inverse electron demand Diels Alder reactions.<ref name="TransitionsofElectronDemand"/>

[[File:normalinverseneutral.jpeg|center|500px]]

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

The reaction between butadiene and ethylene presents the simplest type of Diels-Alder reaction, in which butadiene is the diene and ethylene is the dienophile. This reaction yields cyclohexene as the product, and the reaction scheme is as follow:

[[File:exercise 1 reaction scheme.jpg|center]]

=== Molecular Orbital Diagram ===

[[File:MO diagram for exercise 1 TP1414.jpg|500px|thumb|center|Molecular orbital (MO) diagram for the reaction of butadiene with ethylene]]
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Jmol
! style="background: #0D4F8B; color: white;" | Symmetry
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Jmol
! style="background: #0D4F8B; color: white;" | Symmetry
|-
! rowspan="2" style="background: #0D4F8B; color: white;"| Butadiene
! style="background: #0D4F8B; color: white;"| LUMO
|style="text-align: center;"| [[File:ex1butadieneLUMOtp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 BUTADIENE BREAK SYMMETRY JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 22; rotate x -90; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
! rowspan="4" style="background: #0D4F8B; color: white;"| Transition State
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex1mo4tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
|-
! style="background: #0D4F8B; color: white;"| HOMO
|style="text-align: center;"| [[File:ex1butadieneHOMOtp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 BUTADIENE BREAK SYMMETRY JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 22; rotate x -90; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex1mo3tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
|-
! rowspan="2" style="background: #0D4F8B; color: white;"| Ethylene
! style="background: #0D4F8B; color: white;"| LUMO
|style="text-align: center;"| [[File:ex1ethyleneLUMOtp1414.png|100px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 ETHYLENE JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 14; rotate z 90; rotate x 90; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex1mo2tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| HOMO
|style="text-align: center;"| [[File:ex1ethyleneHOMOtp1414.png|100px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 ETHYLENE JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 14; rotate z 90; rotate x 90; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex1mo1tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
|-
|}

<br style="clear:right">

Only orbitals of the same symmetry can interact to form molecular orbitals. This means that only symmetric-symmetric interactions and antisymmetric-antisymmetric interactions are allowed. Symmetric-antisymmetric interactions, on the other hand, are forbidden. This is because the orbital overlap integral is non-zero for interactions between orbitals of the same symmetry and zero for interactions between orbitals of different symmetry.

As shown on the MO diagram above, both interactions (between the HOMO of butadiene and the LUMO of ethylene, and between the LUMO of butadiene and the HOMO of ethylene) occur, generating four molecular orbitals for the transition state. As the energy separation for the two interactions is similar, the reaction between butadiene and ethylene progress with aspects of both normal electron demand and inverse electron demand. This is because both butadiene and ethylene are neutral molecules without any obvious nucleophilic or electrophilic reacting centrers. Both molecules are neither electron-rich nor electron-poor. As a result, orbital overlap is possible for both HOMO-LUMO sets. Several papers classify this reaction as a neutral electron demand Diels-Alder. <ref name="InverseElectronDemand"/> <ref name="TransitionsofElectronDemand"/> This particular Diels-Alder reaction between butadiene and ethylene is well-known for its poor yield.

<br style="clear:left">

=== Internuclear Distances ===

[[File:internuclear distance.pdf|600px|thumb|right|Internuclear distances for the reaction of butadiene with ethylene to form cyclohexene.]]

[[File:butadiene and ethylene.jpg]]

{| class="wikitable"
|+ Internuclear Distances (Å)
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | C1-C2
! style="background: #0D4F8B; color: white;" | C2-C3
! style="background: #0D4F8B; color: white;" | C3-C4
! style="background: #0D4F8B; color: white;" | C4-C5
! style="background: #0D4F8B; color: white;" | C5-C6
! style="background: #0D4F8B; color: white;" | C6-C1
|-
! style="background: #0D4F8B; color: white;"| Reactants
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|style="text-align: center;"| -
|-
! style="background: #0D4F8B; color: white;"| Transition State
|style="text-align: center;"| 1.38
|style="text-align: center;"| 1.41
|style="text-align: center;"| 1.38
|style="text-align: center;"| 2.11
|style="text-align: center;"| 1.38
|style="text-align: center;"| 2.11
|-
! style="background: #0D4F8B; color: white;"| Product
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}

As the reaction progresses, C1-C2, C3-C4 and C5-C6 elongate as the double bond breaks to form single carbon-carbon bonds, while C2-C3 shortens to form carbon-carbon double bond. Simultaneously, C4-C5 and C6-C1 decrease in distance and ultimately single carbon-carbon bonds are formed. A more detailed overview of how the internuclear distances change over the course of the reaction is shown on the graph on the right.

A typical carbon-carbon single bond length is 1.54 Å and a typical carbon-carbon double bond length is 1.34 Å. <ref name="OrganicChemistryJoseph" />

The Van der Waals radius of one carbon atom is 1.70 Å. <ref name="TheMoleculesofLife" /> The length of the partly formed carbon-carbon bonds in the transition state is about 2.11 Å. This distance is shorter than twice the Van der Waals radius of carbon atom (3.40 Å), indicating bonding interactions are occuring.
<br style="clear:right">

=== Vibration and Reaction Path ===

[[File:exercisa1imaginaryfrequency.jpg]]

The vibration that corresponds to the reaction path at the transition state is illustrated above. This vibration has an imaginary frequency that occurs at 948.97i cm<sup>-1</sup>.

The formation of the two bonds are synchronous as shown below. This means that the two sigma bonds are formed simultaneously. hence, the reaction between butadiene and ethylene goes by a concerted synchronous mechanism.

[[File:IRCgif.jpg]]

=== Calculation Files ===

[[File:TP1414 Exercise 1 Ethylene.log]]

[[File:TP1414 Exercise 1 Butadiene.log]]

[[File:TP1414 Exercise 1 Product.log]]

[[File:TP1414 Exercise 1 Transition State.log]]

[[File:TP1414 Exercise 1 IRC.log]]

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

[[File:exercise 2 reaction schemetp1414.jpg|center]]

=== Molecular Orbital Diagram ===

[[File:ex 2 MO diagram for exo TS TP1414.jpg|left|500px|thumb|Molecular orbital (MO) diagram for the reaction of cyclohexadiene and 1,3-dioxole (exo).]]

[[File:ex 2 MO diagram for endo TS TP1414.jpg|500px|thumb|Molecular orbital (MO) diagram for the reaction of cyclohexadiene and 1,3-dioxole (endo).]]

<br style="clear:left">

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Image
! style="background: #0D4F8B; color: white;" | Symmetry
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Image
! style="background: #0D4F8B; color: white;" | Symmetry
|-
! rowspan="4" style="background: #0D4F8B; color: white;"| Exo
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex2exoMO4tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO4 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
! rowspan="4" style="background: #0D4F8B; color: white;"| Endo
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex2endoMO4tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO4 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
|-
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex2exoMO3tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO3 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex2endoMO3tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO3 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex2exoMO2tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO2 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex2endoMO2tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO2 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex2exoMO1tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO1 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex2endoMO1tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO1 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
|-
|}

Inverse electron demand Diels-Alder

=== Thermochemistry ===
[[File:ex2energyprofiletp1414.jpeg|600px|thumb|Energy profile diagram for the reactions between cyclohexadiene and 1,3-dioxole]]
The energies of the reactants, transition state and product for both the exo and endo reactions are tabulated below. These are obtained from optimization at B3LYP/6-31G(d) level.

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;"| Exo
|style="text-align: center;"|-612591.48
|style="text-align: center;"|-701187.43
|style="text-align: center;"|-1313778.91
|style="text-align: center;"|-1313614.33
|style="text-align: center;"|-1313845.77
|style="text-align: center;"|164.58
|style="text-align: center;"|-66.86
|-
!style="background: #0D4F8B; color: white;"| Endo
|style="text-align: center;"|-612591.48
|style="text-align: center;"|-701187.43
|style="text-align: center;"|-1313778.91
|style="text-align: center;"|-1313622.15
|style="text-align: center;"|-1313849.37
|style="text-align: center;"|156.76
|style="text-align: center;"|-70.46
|-
|}

Both the exo and endo reactions are exothermic. However, it can be seen that the energy of the endo product is lower (or more negative) than the energy of the exo product, and the endo reaction also has a lower reaction barrier as compared to the exo reaction. This means that the endo product is both the thermodynamically and kinetically favourable product. This can be explained by considering both electronic and steric factors

[[File:seondaryorbitalinteractionstp1414.png|500px|thumb|left|Secondary orbital interactions in endo transition state]] Secondary orbital interactions stabilize the endo transition state, reducing the reaction barrier. On the left is the HOMO of the endo transition state in which there are obvious secondary orbital interactions between the oxygen p orbitals of the 1,3-dioxole and the p orbitals of the diene. An MO representation of this HOMO is shown below.
[[File:secondaryorbitalinteractionMOrepresentationtp1414.jpeg|350px]]
<br style="clear:left">

[[File:stericclashtp1414.png|500px|thumb|left|Steric clash in exo product]] Steric clash between the sp<sup>3</sup> CH<sub>2</sub> of the dioxole ring and the sp<sup>3</sup> CH<sub>2</sub>'s of the cyclohexadiene destabilize both the exo transition state and the exo product.
<br style="clear:left">

=== Vibration and Reaction Path ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
! style="background: #0D4F8B; color: white;"| Vibration
|style="text-align: center;"| [[File:exercise2 exo vibration tp1414.gif]]
|style="text-align: center;"| [[File:exercise2 endo vibration tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Vibrational Frequency
|style="text-align: center;"| 520.90i cm<sup>-1</sup>
|style="text-align: center;"| 528.85i cm<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| Reaction Pathway
|style="text-align: center;"| [[File:exercise2 exo reaction path tp1414.gif]]
|style="text-align: center;"| [[File:exercise2 endo reaction path tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Mechanism
|style="text-align: center;"| Synchronous concerted
|style="text-align: center;"| Synchronous concerted
|-
|}

=== Calculation Files ===

[[File:TP1414 Exercise 2 Cyclohexadiene 631Gd.log]]

[[File:TP1414 Exercise 2 1,2-Dioxole 631Gd.log]]

[[File:TP1414 Exercise 2 Exo Product 631Gd.log]]

[[File:TP1414 Exercise 2 Endo Product 631Gd.log]]

[[File:TP1414 Exercise 2 Exo Transition State 631Gd.log]]

[[File:TP1414 Exercise 2 Endo Transition State 631Gd.log]]

[[File:TP1414 Exercise 2 Exo IRC 631Gd.log]]

[[File:TP1414 Exercise 2 Endo IRC 631Gd.log]]

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

[[File:exercise3reactionschemetp1414.jpg|center]]

=== Thermochemistry ===
[[File:ex3energyprofiletp1414.jpg|600px|thumb|Energy profile diagram for the reactions between o-xylylene and SO<sub>2</sub>]]
The energies of the reactants, transition state and product for the exo, endo and cheletropic reactions are tabulated below. These are obtained from optimization at PM6 level.

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | o-Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;"| Exo
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|241.75
|style="text-align: center;"|56.31
|style="text-align: center;"|85.18
|style="text-align: center;"|-71.39
|-
!style="background: #0D4F8B; color: white;"| Endo
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|237.77
|style="text-align: center;"|56.98
|style="text-align: center;"|81.20
|style="text-align: center;"|-75.37
|-
!style="background: #0D4F8B; color: white;"| Cheletropic
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|260.09
|style="text-align: center;"|-0.01
|style="text-align: center;"|103.52
|style="text-align: center;"|-53.05
|-
|}

All three reactions are exothermic. The endo product is the kinetically favourable product as it has the lowest reaction barrier, while the cheletropic product is the thermodynamically favourable product as it has the lowest energy.
<br style="clear:right">

=== Vibration and Reaction Path ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
! style="background: #0D4F8B; color: white;" | Cheletropic
|-
! style="background: #0D4F8B; color: white;"| Vibration
|style="text-align: center;"| [[File:ex3 exo vibration tp1414.gif]]
|style="text-align: center;"| [[File:ex3 endo vibration tp1414.gif]]
|style="text-align: center;"| [[File:cheletropic vibration tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Vibrational Frequency
|style="text-align: center;"| 351.78i cm<sup>-1</sup>
|style="text-align: center;"| 334.38i cm<sup>-1</sup>
|style="text-align: center;"| 486.58i cm<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| Reaction Pathway
|style="text-align: center;"| [[File:exo IRC tp1414.gif]]
|style="text-align: center;"| [[File:endo IRC tp1414.gif]]
|style="text-align: center;"| [[File:cheletropic IRC tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Mechanism
|style="text-align: center;"| Asynchronous concerted
|style="text-align: center;"| Asynchronous concerted
|style="text-align: center;"| Synchronous concerted
|-
! style="background: #0D4F8B; color: white;"| IRC
|style="text-align: center;"| [[File:exoIRCtp1414.png]]
|style="text-align: center;"| [[File:endoIRCtp1414.png]]
|style="text-align: center;"| [[File:cheletropicIRCtp1414energy.png]]
|-
|}

It is interesting to note that the exo and endo reactions proceed via asynchronous mechanism in which the C-O bond is formed first before the C-S bond, while the cheletropic reaction proceeds via synchronous mechanism in which the two C-S bonds are formed simultaneously. However, even though the formation of the two bonds are asynchronous in the exo and endo reactions, the total energy along IRC tells us that both reactions are concerted as the reactions do not have any intermediate steps.

In all three reaction pathways, the steepest part on the the total energy versus IRC graph corresponds to the re-aromatisation of the 6-membered ring on the o-xylylene, giving these reactions an aromatic driving force. This also shows the instability of the o-xylylene molecule. O-Xylylene is highly unstable as it is antiaromatic (planar and 4n electrons), and it will undergo an electrocyclic ring closure to form the stable aromatic isomer, benzocyclobutene as shown below.

[[File:xylyleneelectrocyclicreactionscheme.jpg|centre]]

A quick transition state optimisation followed by IRC calculation of the above reaction on Gaussian gives the total energy along IRC graph below.

[[File:xylyleneelectrocyclicIRCtp1414.jpg|centre]]

=== Alternate Diels-Alder Reaction ===

There is a second cis-butadiene fragment in o-xylylene that can undergo a Diels-Alder reaction. This second cis-butadiene is part of the cyclohexadiene ring. The exo and endo for this alternate Diels-Alder reaction proceed as follow:

[[File:alternatedielsalderexotp1414.gif]] [[File:alternatedielsalderendotp1414.gif]]

Both reactions proceed via an asynchronous mechanism.

[[File:energyprofilewithalternatedielsaldertp1414.jpg|600px|thumb|Energy profile diagram for the reactions between o-xylylene and SO<sub>2</sub>]]
The thermochemistry for this alternate Diels-Alder reaction is as follows:

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | o-Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;" | Exo
| style="text-align: center;" |467.99
| style="text-align: center;" |-311.42
| style="text-align: center;" |156.57
| style="text-align: center;" |275.82
| style="text-align: center;" |176.71
| style="text-align: center;" |119.25
| style="text-align: center;" |20.14
|-
! style="background: #0D4F8B; color: white;" | Endo
| style="text-align: center;" |467.99
| style="text-align: center;" |-311.42
| style="text-align: center;" |156.57
| style="text-align: center;" |267.98
| style="text-align: center;" |172.26
| style="text-align: center;" |111.41
| style="text-align: center;" |15.96
|-
|}

Comparing the energies for this alternate Diels-Alder reaction with the energies for the normal Diels-Alder and the cheletropic reactions, it can be seen that both the exo and endo alternate Diels-Alder reactoions are kinetically and thermodynamically unfavourable. The products are also higher in energies than the reactants, making the reactions endothermic.
<br style="clear:right">

=== Calculation Files ===

[[File:TP1414 Exercise 3 Xylylene.log]]

[[File:TP1414 Exercise 3 SO2.log]]

[[File:TP1414 Exercise 3 Exo Product.log]]

[[File:TP1414 Exercise 3 Endo Product.log]]

[[File:TP1414 Exercise 3 Cheletropic Product.log]]

[[File:TP1414 Exercise 3 Exo Transition State.log]]

[[File:TP1414 Exercise 3 Endo Transition State.log]]

[[File:TP1414 Exercise 3 Cheletropic Transition State.log]]

[[File:TP1414 Exercise 3 Exo IRC.log]]

[[File:TP1414 Exercise 3 Endo IRC.log]]

[[File:TP1414 Exercise 3 Cheletropic IRC.log]]

[[File:TP1414 Exercise 3 Xylylene Electrocyclic Transition State.log]]

[[File:TP1414 Exercise 3 Xylylene Electrocyclic IRC.log]]

[[File:TP1414 Exercise 3 Alternate Exo Product.log]]

[[File:TP1414 Exercise 3 Alternate Endo Product.log]]

[[File:TP1414 Exercise 3 Alternate Exo Transition State.log]]

[[File:TP1414 Exercise 3 Alternate Endo Transition State.log]]

[[File:TP1414 Exercise 3 Alternate Exo IRC.log]]

[[File:TP1414 Exercise 3 Alternate Endo IRC.log]]

== Conclusion ==
Synchronous and asynchronous mechanism. Symmetrical molecules?

== References ==

<references>
<ref name="OrganicChemistryJoseph"> J. M. Hornback, ''Organic Chemistry'', Thomson Learning. Inc., Belmont, Second., 2006.</ref>
<ref name="TheMoleculesofLife"> J. Kuriyan, B. Konforti and D. Wemmer, ''The Molecules of Life: Physical and Chemical Principles'', Garland Science, New York, 2013.</ref>
<ref name="InverseElectronDemand"> A.-C. Knall and C. Slugovc, ''Chem Soc Rev'', 2013, '''42''', 5131–5142.</ref>
<ref name="TransitionsofElectronDemand"> E. Eibler, P. Hocht, B. Prantl, H. Rormaier, H. M. Schuhbauer and H. Wiest, ''Liebigs Ann.lRemei'', 1997, '''1997''', 2471–2484.</ref>
</references>

File:TP1414 Exercise 3 Xylylene Electrocyclic Transition State.log

2017-03-14T16:10:54Z

Tp1414:

Rep:Mod:TP1414

2017-03-14T16:09:56Z

Tp1414: /* Calculation Files */

== Introduction ==

=== Gaussian and Transition State Characterization ===

Gaussian is a molecular modelling software that allows researchers to carry out extensive investigation of molecules and their reactions. In these exercises, the transition states of several Diels-Alder reactions are located and characterized using Gaussian. A transition state is a first order saddle point on a potential energy surface (PES). It is the maximum along the minimum energy path (or reaction path) between two minima (the reactants and the products). ''Geometry optimization'' to find the minimum energy structure will usually lead to a stationary point that is closest to the initial geometry. The stationary point, where the first derivative of energy is zero, can be a global minimum, a local minimum or a saddle point. In a reaction path, the minima (global or local) correspond to the reactants and the products, while the saddle point corresponds to the transition state. To differentiate between a minimum and a saddle point, the second derivatives of energy will have to be analysed. For global or local minima, where energy rises in all directions, the second derivative of energy is positive. In contrast, for transition state, where the energy decreases in one direction (reaction path), the second derivative of energy along the reaction coordinate is negative. The analysis of the second derivatives of energy can be done by a ''frequency calculation'' of the optimized structure. If the structure corresponds to the reactants or products, all the vibrational frequencies are real. In contrast, if the structure corresponds to a transition state, there will be one imaginary frequency. This imaginary frequency indicates that the force constant (k), which is given by the second derivative, is negative.

[[File:frequencyequation.png|center]]

[[File:forceconstantequation.png|center]]

Following a successful frequency calculation (one imaginary frequency) of the transition state, an ''Intrinsic Reaction Coordinate (IRC) calculation'' may be set up to examine the transition state along the minimum energy path more closely. The reaction path, or minimum energy path, can be defined as the steepest descent path from the transition state to the reactions and products.

=== Diels-Alder Reactions ===

A Diels-Alder reaction is a [4+2] cycloadditon between a conjugated s-cis diene (4π-electron system) and a dienophile (2π-electron system). The reaction has a cyclic transition state with 6π-electrons, is concerted, and results in the formation of two new sigma bonds. According to the Woodward-Hoffmann Rules, the Diels-Alder reaction is thermally allowed and is an orbital-controlled reaction, in which the six electrons are interacting suprafacially. The reaction can mainly proceed in two ways:

# Normal electron demand: HOMO of diene overlaps with LUMO of dienophile
# Inverse electron demand: LUMO of diene overlaps with HOMO of dienophile

Several papers divide the Diels-Alder reactions into three categories instead of two <ref name="InverseElectronDemand"/> <ref name="TransitionsofElectronDemand"/>, the third being a neutral electron demand Diels-Alder, in which the energy separation between the HOMO and LUMO of both reactants is similar. <ref name="InverseElectronDemand"/> Neutral electron demand Diels-Alder reactions are seldom observed and believed to be a transition between normal electron demand and inverse electron demand Diels Alder reactions.<ref name="TransitionsofElectronDemand"/>

[[File:normalinverseneutral.jpeg|center|500px]]

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

The reaction between butadiene and ethylene presents the simplest type of Diels-Alder reaction, in which butadiene is the diene and ethylene is the dienophile. This reaction yields cyclohexene as the product, and the reaction scheme is as follow:

[[File:exercise 1 reaction scheme.jpg|center]]

=== Molecular Orbital Diagram ===

[[File:MO diagram for exercise 1 TP1414.jpg|500px|thumb|center|Molecular orbital (MO) diagram for the reaction of butadiene with ethylene]]
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Jmol
! style="background: #0D4F8B; color: white;" | Symmetry
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Jmol
! style="background: #0D4F8B; color: white;" | Symmetry
|-
! rowspan="2" style="background: #0D4F8B; color: white;"| Butadiene
! style="background: #0D4F8B; color: white;"| LUMO
|style="text-align: center;"| [[File:ex1butadieneLUMOtp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 BUTADIENE BREAK SYMMETRY JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 22; rotate x -90; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
! rowspan="4" style="background: #0D4F8B; color: white;"| Transition State
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex1mo4tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
|-
! style="background: #0D4F8B; color: white;"| HOMO
|style="text-align: center;"| [[File:ex1butadieneHOMOtp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 BUTADIENE BREAK SYMMETRY JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 22; rotate x -90; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex1mo3tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
|-
! rowspan="2" style="background: #0D4F8B; color: white;"| Ethylene
! style="background: #0D4F8B; color: white;"| LUMO
|style="text-align: center;"| [[File:ex1ethyleneLUMOtp1414.png|100px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 ETHYLENE JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 14; rotate z 90; rotate x 90; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex1mo2tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| HOMO
|style="text-align: center;"| [[File:ex1ethyleneHOMOtp1414.png|100px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 ETHYLENE JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 14; rotate z 90; rotate x 90; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex1mo1tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
|-
|}

<br style="clear:right">

Only orbitals of the same symmetry can interact to form molecular orbitals. This means that only symmetric-symmetric interactions and antisymmetric-antisymmetric interactions are allowed. Symmetric-antisymmetric interactions, on the other hand, are forbidden. This is because the orbital overlap integral is non-zero for interactions between orbitals of the same symmetry and zero for interactions between orbitals of different symmetry.

As shown on the MO diagram above, both interactions (between the HOMO of butadiene and the LUMO of ethylene, and between the LUMO of butadiene and the HOMO of ethylene) occur, generating four molecular orbitals for the transition state. As the energy separation for the two interactions is similar, the reaction between butadiene and ethylene progress with aspects of both normal electron demand and inverse electron demand. This is because both butadiene and ethylene are neutral molecules without any obvious nucleophilic or electrophilic reacting centrers. Both molecules are neither electron-rich nor electron-poor. As a result, orbital overlap is possible for both HOMO-LUMO sets. Several papers classify this reaction as a neutral electron demand Diels-Alder. <ref name="InverseElectronDemand"/> <ref name="TransitionsofElectronDemand"/> This particular Diels-Alder reaction between butadiene and ethylene is well-known for its poor yield.

<br style="clear:left">

=== Internuclear Distances ===

[[File:internuclear distance.pdf|600px|thumb|right|Internuclear distances for the reaction of butadiene with ethylene to form cyclohexene.]]

[[File:butadiene and ethylene.jpg]]

{| class="wikitable"
|+ Internuclear Distances (Å)
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | C1-C2
! style="background: #0D4F8B; color: white;" | C2-C3
! style="background: #0D4F8B; color: white;" | C3-C4
! style="background: #0D4F8B; color: white;" | C4-C5
! style="background: #0D4F8B; color: white;" | C5-C6
! style="background: #0D4F8B; color: white;" | C6-C1
|-
! style="background: #0D4F8B; color: white;"| Reactants
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|style="text-align: center;"| -
|-
! style="background: #0D4F8B; color: white;"| Transition State
|style="text-align: center;"| 1.38
|style="text-align: center;"| 1.41
|style="text-align: center;"| 1.38
|style="text-align: center;"| 2.11
|style="text-align: center;"| 1.38
|style="text-align: center;"| 2.11
|-
! style="background: #0D4F8B; color: white;"| Product
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}

As the reaction progresses, C1-C2, C3-C4 and C5-C6 elongate as the double bond breaks to form single carbon-carbon bonds, while C2-C3 shortens to form carbon-carbon double bond. Simultaneously, C4-C5 and C6-C1 decrease in distance and ultimately single carbon-carbon bonds are formed. A more detailed overview of how the internuclear distances change over the course of the reaction is shown on the graph on the right.

A typical carbon-carbon single bond length is 1.54 Å and a typical carbon-carbon double bond length is 1.34 Å. <ref name="OrganicChemistryJoseph" />

The Van der Waals radius of one carbon atom is 1.70 Å. <ref name="TheMoleculesofLife" /> The length of the partly formed carbon-carbon bonds in the transition state is about 2.11 Å. This distance is shorter than twice the Van der Waals radius of carbon atom (3.40 Å), indicating bonding interactions are occuring.
<br style="clear:right">

=== Vibration and Reaction Path ===

[[File:exercisa1imaginaryfrequency.jpg]]

The vibration that corresponds to the reaction path at the transition state is illustrated above. This vibration has an imaginary frequency that occurs at 948.97i cm<sup>-1</sup>.

The formation of the two bonds are synchronous as shown below. This means that the two sigma bonds are formed simultaneously. hence, the reaction between butadiene and ethylene goes by a concerted synchronous mechanism.

[[File:IRCgif.jpg]]

=== Calculation Files ===

[[File:TP1414 Exercise 1 Ethylene.log]]

[[File:TP1414 Exercise 1 Butadiene.log]]

[[File:TP1414 Exercise 1 Product.log]]

[[File:TP1414 Exercise 1 Transition State.log]]

[[File:TP1414 Exercise 1 IRC.log]]

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

[[File:exercise 2 reaction schemetp1414.jpg|center]]

=== Molecular Orbital Diagram ===

[[File:ex 2 MO diagram for exo TS TP1414.jpg|left|500px|thumb|Molecular orbital (MO) diagram for the reaction of cyclohexadiene and 1,3-dioxole (exo).]]

[[File:ex 2 MO diagram for endo TS TP1414.jpg|500px|thumb|Molecular orbital (MO) diagram for the reaction of cyclohexadiene and 1,3-dioxole (endo).]]

<br style="clear:left">

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Image
! style="background: #0D4F8B; color: white;" | Symmetry
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Image
! style="background: #0D4F8B; color: white;" | Symmetry
|-
! rowspan="4" style="background: #0D4F8B; color: white;"| Exo
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex2exoMO4tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO4 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
! rowspan="4" style="background: #0D4F8B; color: white;"| Endo
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex2endoMO4tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO4 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
|-
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex2exoMO3tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO3 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex2endoMO3tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO3 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex2exoMO2tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO2 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex2endoMO2tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO2 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex2exoMO1tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO1 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex2endoMO1tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO1 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
|-
|}

Inverse electron demand Diels-Alder

=== Thermochemistry ===
[[File:ex2energyprofiletp1414.jpeg|600px|thumb|Energy profile diagram for the reactions between cyclohexadiene and 1,3-dioxole]]
The energies of the reactants, transition state and product for both the exo and endo reactions are tabulated below. These are obtained from optimization at B3LYP/6-31G(d) level.

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;"| Exo
|style="text-align: center;"|-612591.48
|style="text-align: center;"|-701187.43
|style="text-align: center;"|-1313778.91
|style="text-align: center;"|-1313614.33
|style="text-align: center;"|-1313845.77
|style="text-align: center;"|164.58
|style="text-align: center;"|-66.86
|-
!style="background: #0D4F8B; color: white;"| Endo
|style="text-align: center;"|-612591.48
|style="text-align: center;"|-701187.43
|style="text-align: center;"|-1313778.91
|style="text-align: center;"|-1313622.15
|style="text-align: center;"|-1313849.37
|style="text-align: center;"|156.76
|style="text-align: center;"|-70.46
|-
|}

Both the exo and endo reactions are exothermic. However, it can be seen that the energy of the endo product is lower (or more negative) than the energy of the exo product, and the endo reaction also has a lower reaction barrier as compared to the exo reaction. This means that the endo product is both the thermodynamically and kinetically favourable product. This can be explained by considering both electronic and steric factors

[[File:seondaryorbitalinteractionstp1414.png|500px|thumb|left|Secondary orbital interactions in endo transition state]] Secondary orbital interactions stabilize the endo transition state, reducing the reaction barrier. On the left is the HOMO of the endo transition state in which there are obvious secondary orbital interactions between the oxygen p orbitals of the 1,3-dioxole and the p orbitals of the diene. An MO representation of this HOMO is shown below.
[[File:secondaryorbitalinteractionMOrepresentationtp1414.jpeg|350px]]
<br style="clear:left">

[[File:stericclashtp1414.png|500px|thumb|left|Steric clash in exo product]] Steric clash between the sp<sup>3</sup> CH<sub>2</sub> of the dioxole ring and the sp<sup>3</sup> CH<sub>2</sub>'s of the cyclohexadiene destabilize both the exo transition state and the exo product.
<br style="clear:left">

=== Vibration and Reaction Path ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
! style="background: #0D4F8B; color: white;"| Vibration
|style="text-align: center;"| [[File:exercise2 exo vibration tp1414.gif]]
|style="text-align: center;"| [[File:exercise2 endo vibration tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Vibrational Frequency
|style="text-align: center;"| 520.90i cm<sup>-1</sup>
|style="text-align: center;"| 528.85i cm<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| Reaction Pathway
|style="text-align: center;"| [[File:exercise2 exo reaction path tp1414.gif]]
|style="text-align: center;"| [[File:exercise2 endo reaction path tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Mechanism
|style="text-align: center;"| Synchronous concerted
|style="text-align: center;"| Synchronous concerted
|-
|}

=== Calculation Files ===

[[File:TP1414 Exercise 2 Cyclohexadiene 631Gd.log]]

[[File:TP1414 Exercise 2 1,2-Dioxole 631Gd.log]]

[[File:TP1414 Exercise 2 Exo Product 631Gd.log]]

[[File:TP1414 Exercise 2 Endo Product 631Gd.log]]

[[File:TP1414 Exercise 2 Exo Transition State 631Gd.log]]

[[File:TP1414 Exercise 2 Endo Transition State 631Gd.log]]

[[File:TP1414 Exercise 2 Exo IRC 631Gd.log]]

[[File:TP1414 Exercise 2 Endo IRC 631Gd.log]]

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

[[File:exercise3reactionschemetp1414.jpg|center]]

=== Thermochemistry ===
[[File:ex3energyprofiletp1414.jpg|600px|thumb|Energy profile diagram for the reactions between o-xylylene and SO<sub>2</sub>]]
The energies of the reactants, transition state and product for the exo, endo and cheletropic reactions are tabulated below. These are obtained from optimization at PM6 level.

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | o-Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;"| Exo
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|241.75
|style="text-align: center;"|56.31
|style="text-align: center;"|85.18
|style="text-align: center;"|-71.39
|-
!style="background: #0D4F8B; color: white;"| Endo
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|237.77
|style="text-align: center;"|56.98
|style="text-align: center;"|81.20
|style="text-align: center;"|-75.37
|-
!style="background: #0D4F8B; color: white;"| Cheletropic
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|260.09
|style="text-align: center;"|-0.01
|style="text-align: center;"|103.52
|style="text-align: center;"|-53.05
|-
|}

All three reactions are exothermic. The endo product is the kinetically favourable product as it has the lowest reaction barrier, while the cheletropic product is the thermodynamically favourable product as it has the lowest energy.
<br style="clear:right">

=== Vibration and Reaction Path ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
! style="background: #0D4F8B; color: white;" | Cheletropic
|-
! style="background: #0D4F8B; color: white;"| Vibration
|style="text-align: center;"| [[File:ex3 exo vibration tp1414.gif]]
|style="text-align: center;"| [[File:ex3 endo vibration tp1414.gif]]
|style="text-align: center;"| [[File:cheletropic vibration tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Vibrational Frequency
|style="text-align: center;"| 351.78i cm<sup>-1</sup>
|style="text-align: center;"| 334.38i cm<sup>-1</sup>
|style="text-align: center;"| 486.58i cm<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| Reaction Pathway
|style="text-align: center;"| [[File:exo IRC tp1414.gif]]
|style="text-align: center;"| [[File:endo IRC tp1414.gif]]
|style="text-align: center;"| [[File:cheletropic IRC tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Mechanism
|style="text-align: center;"| Asynchronous concerted
|style="text-align: center;"| Asynchronous concerted
|style="text-align: center;"| Synchronous concerted
|-
! style="background: #0D4F8B; color: white;"| IRC
|style="text-align: center;"| [[File:exoIRCtp1414.png]]
|style="text-align: center;"| [[File:endoIRCtp1414.png]]
|style="text-align: center;"| [[File:cheletropicIRCtp1414energy.png]]
|-
|}

It is interesting to note that the exo and endo reactions proceed via asynchronous mechanism in which the C-O bond is formed first before the C-S bond, while the cheletropic reaction proceeds via synchronous mechanism in which the two C-S bonds are formed simultaneously. However, even though the formation of the two bonds are asynchronous in the exo and endo reactions, the total energy along the IRC tells us that both reactions are concerted as the reactions do not have any intermediate steps.

In all three reaction pathways, the steepest part on the the total energy versus IRC graph corresponds to the re-aromatisation of the 6-membered ring on the o-xylylene, giving these reactions an aromatic driving force. This also shows the instability of the o-xylylene molecule. O-Xylylene is highly unstable as it is antiaromatic (planar and 4n electrons), and it will undergo an electrocyclic ring closure to form the stable aromatic isomer, benzocyclobutene as shown below.

[[File:xylyleneelectrocyclicreactionscheme.jpg|centre]]

=== Alternate Diels-Alder Reaction ===

There is a second cis-butadiene fragment in o-xylylene that can undergo a Diels-Alder reaction. This second cis-butadiene is part of the cyclohexadiene ring. The exo and endo for this alternate Diels-Alder reaction proceed as follow:

[[File:alternatedielsalderexotp1414.gif]] [[File:alternatedielsalderendotp1414.gif]]

Both reactions proceed via an asynchronous mechanism.

[[File:energyprofilewithalternatedielsaldertp1414.jpg|600px|thumb|Energy profile diagram for the reactions between o-xylylene and SO<sub>2</sub>]]
The thermochemistry for this alternate Diels-Alder reaction is as follows:

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | o-Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;" | Exo
| style="text-align: center;" |467.99
| style="text-align: center;" |-311.42
| style="text-align: center;" |156.57
| style="text-align: center;" |275.82
| style="text-align: center;" |176.71
| style="text-align: center;" |119.25
| style="text-align: center;" |20.14
|-
! style="background: #0D4F8B; color: white;" | Endo
| style="text-align: center;" |467.99
| style="text-align: center;" |-311.42
| style="text-align: center;" |156.57
| style="text-align: center;" |267.98
| style="text-align: center;" |172.26
| style="text-align: center;" |111.41
| style="text-align: center;" |15.96
|-
|}

Comparing the energies for this alternate Diels-Alder reaction with the energies for the normal Diels-Alder and the cheletropic reactions, it can be seen that both the exo and endo alternate Diels-Alder reactoions are kinetically and thermodynamically unfavourable. The products are also higher in energies than the reactants, making the reactions endothermic.
<br style="clear:right">

=== Calculation Files ===

[[File:TP1414 Exercise 3 Xylylene.log]]

[[File:TP1414 Exercise 3 SO2.log]]

[[File:TP1414 Exercise 3 Exo Product.log]]

[[File:TP1414 Exercise 3 Endo Product.log]]

[[File:TP1414 Exercise 3 Cheletropic Product.log]]

[[File:TP1414 Exercise 3 Exo Transition State.log]]

[[File:TP1414 Exercise 3 Endo Transition State.log]]

[[File:TP1414 Exercise 3 Cheletropic Transition State.log]]

[[File:TP1414 Exercise 3 Exo IRC.log]]

[[File:TP1414 Exercise 3 Endo IRC.log]]

[[File:TP1414 Exercise 3 Cheletropic IRC.log]]

[[File:TP1414 Exercise 3 Xylylene Electrocyclic Transition State.log]]

[[File:TP1414 Exercise 3 Xylylene Electrocyclic IRC.log]]

[[File:TP1414 Exercise 3 Alternate Exo Product.log]]

[[File:TP1414 Exercise 3 Alternate Endo Product.log]]

[[File:TP1414 Exercise 3 Alternate Exo Transition State.log]]

[[File:TP1414 Exercise 3 Alternate Endo Transition State.log]]

[[File:TP1414 Exercise 3 Alternate Exo IRC.log]]

[[File:TP1414 Exercise 3 Alternate Endo IRC.log]]

== Conclusion ==
Synchronous and asynchronous mechanism. Symmetrical molecules?

== References ==

<references>
<ref name="OrganicChemistryJoseph"> J. M. Hornback, ''Organic Chemistry'', Thomson Learning. Inc., Belmont, Second., 2006.</ref>
<ref name="TheMoleculesofLife"> J. Kuriyan, B. Konforti and D. Wemmer, ''The Molecules of Life: Physical and Chemical Principles'', Garland Science, New York, 2013.</ref>
<ref name="InverseElectronDemand"> A.-C. Knall and C. Slugovc, ''Chem Soc Rev'', 2013, '''42''', 5131–5142.</ref>
<ref name="TransitionsofElectronDemand"> E. Eibler, P. Hocht, B. Prantl, H. Rormaier, H. M. Schuhbauer and H. Wiest, ''Liebigs Ann.lRemei'', 1997, '''1997''', 2471–2484.</ref>
</references>

Rep:Mod:TP1414

2017-03-14T16:03:56Z

Tp1414: /* Vibration and Reaction Path */

== Introduction ==

=== Gaussian and Transition State Characterization ===

Gaussian is a molecular modelling software that allows researchers to carry out extensive investigation of molecules and their reactions. In these exercises, the transition states of several Diels-Alder reactions are located and characterized using Gaussian. A transition state is a first order saddle point on a potential energy surface (PES). It is the maximum along the minimum energy path (or reaction path) between two minima (the reactants and the products). ''Geometry optimization'' to find the minimum energy structure will usually lead to a stationary point that is closest to the initial geometry. The stationary point, where the first derivative of energy is zero, can be a global minimum, a local minimum or a saddle point. In a reaction path, the minima (global or local) correspond to the reactants and the products, while the saddle point corresponds to the transition state. To differentiate between a minimum and a saddle point, the second derivatives of energy will have to be analysed. For global or local minima, where energy rises in all directions, the second derivative of energy is positive. In contrast, for transition state, where the energy decreases in one direction (reaction path), the second derivative of energy along the reaction coordinate is negative. The analysis of the second derivatives of energy can be done by a ''frequency calculation'' of the optimized structure. If the structure corresponds to the reactants or products, all the vibrational frequencies are real. In contrast, if the structure corresponds to a transition state, there will be one imaginary frequency. This imaginary frequency indicates that the force constant (k), which is given by the second derivative, is negative.

[[File:frequencyequation.png|center]]

[[File:forceconstantequation.png|center]]

Following a successful frequency calculation (one imaginary frequency) of the transition state, an ''Intrinsic Reaction Coordinate (IRC) calculation'' may be set up to examine the transition state along the minimum energy path more closely. The reaction path, or minimum energy path, can be defined as the steepest descent path from the transition state to the reactions and products.

=== Diels-Alder Reactions ===

A Diels-Alder reaction is a [4+2] cycloadditon between a conjugated s-cis diene (4π-electron system) and a dienophile (2π-electron system). The reaction has a cyclic transition state with 6π-electrons, is concerted, and results in the formation of two new sigma bonds. According to the Woodward-Hoffmann Rules, the Diels-Alder reaction is thermally allowed and is an orbital-controlled reaction, in which the six electrons are interacting suprafacially. The reaction can mainly proceed in two ways:

# Normal electron demand: HOMO of diene overlaps with LUMO of dienophile
# Inverse electron demand: LUMO of diene overlaps with HOMO of dienophile

Several papers divide the Diels-Alder reactions into three categories instead of two <ref name="InverseElectronDemand"/> <ref name="TransitionsofElectronDemand"/>, the third being a neutral electron demand Diels-Alder, in which the energy separation between the HOMO and LUMO of both reactants is similar. <ref name="InverseElectronDemand"/> Neutral electron demand Diels-Alder reactions are seldom observed and believed to be a transition between normal electron demand and inverse electron demand Diels Alder reactions.<ref name="TransitionsofElectronDemand"/>

[[File:normalinverseneutral.jpeg|center|500px]]

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

The reaction between butadiene and ethylene presents the simplest type of Diels-Alder reaction, in which butadiene is the diene and ethylene is the dienophile. This reaction yields cyclohexene as the product, and the reaction scheme is as follow:

[[File:exercise 1 reaction scheme.jpg|center]]

=== Molecular Orbital Diagram ===

[[File:MO diagram for exercise 1 TP1414.jpg|500px|thumb|center|Molecular orbital (MO) diagram for the reaction of butadiene with ethylene]]
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Jmol
! style="background: #0D4F8B; color: white;" | Symmetry
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Jmol
! style="background: #0D4F8B; color: white;" | Symmetry
|-
! rowspan="2" style="background: #0D4F8B; color: white;"| Butadiene
! style="background: #0D4F8B; color: white;"| LUMO
|style="text-align: center;"| [[File:ex1butadieneLUMOtp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 BUTADIENE BREAK SYMMETRY JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 22; rotate x -90; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
! rowspan="4" style="background: #0D4F8B; color: white;"| Transition State
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex1mo4tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
|-
! style="background: #0D4F8B; color: white;"| HOMO
|style="text-align: center;"| [[File:ex1butadieneHOMOtp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 BUTADIENE BREAK SYMMETRY JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 22; rotate x -90; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex1mo3tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
|-
! rowspan="2" style="background: #0D4F8B; color: white;"| Ethylene
! style="background: #0D4F8B; color: white;"| LUMO
|style="text-align: center;"| [[File:ex1ethyleneLUMOtp1414.png|100px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 ETHYLENE JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 14; rotate z 90; rotate x 90; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex1mo2tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| HOMO
|style="text-align: center;"| [[File:ex1ethyleneHOMOtp1414.png|100px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 ETHYLENE JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 14; rotate z 90; rotate x 90; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex1mo1tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
|-
|}

<br style="clear:right">

Only orbitals of the same symmetry can interact to form molecular orbitals. This means that only symmetric-symmetric interactions and antisymmetric-antisymmetric interactions are allowed. Symmetric-antisymmetric interactions, on the other hand, are forbidden. This is because the orbital overlap integral is non-zero for interactions between orbitals of the same symmetry and zero for interactions between orbitals of different symmetry.

As shown on the MO diagram above, both interactions (between the HOMO of butadiene and the LUMO of ethylene, and between the LUMO of butadiene and the HOMO of ethylene) occur, generating four molecular orbitals for the transition state. As the energy separation for the two interactions is similar, the reaction between butadiene and ethylene progress with aspects of both normal electron demand and inverse electron demand. This is because both butadiene and ethylene are neutral molecules without any obvious nucleophilic or electrophilic reacting centrers. Both molecules are neither electron-rich nor electron-poor. As a result, orbital overlap is possible for both HOMO-LUMO sets. Several papers classify this reaction as a neutral electron demand Diels-Alder. <ref name="InverseElectronDemand"/> <ref name="TransitionsofElectronDemand"/> This particular Diels-Alder reaction between butadiene and ethylene is well-known for its poor yield.

<br style="clear:left">

=== Internuclear Distances ===

[[File:internuclear distance.pdf|600px|thumb|right|Internuclear distances for the reaction of butadiene with ethylene to form cyclohexene.]]

[[File:butadiene and ethylene.jpg]]

{| class="wikitable"
|+ Internuclear Distances (Å)
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | C1-C2
! style="background: #0D4F8B; color: white;" | C2-C3
! style="background: #0D4F8B; color: white;" | C3-C4
! style="background: #0D4F8B; color: white;" | C4-C5
! style="background: #0D4F8B; color: white;" | C5-C6
! style="background: #0D4F8B; color: white;" | C6-C1
|-
! style="background: #0D4F8B; color: white;"| Reactants
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|style="text-align: center;"| -
|-
! style="background: #0D4F8B; color: white;"| Transition State
|style="text-align: center;"| 1.38
|style="text-align: center;"| 1.41
|style="text-align: center;"| 1.38
|style="text-align: center;"| 2.11
|style="text-align: center;"| 1.38
|style="text-align: center;"| 2.11
|-
! style="background: #0D4F8B; color: white;"| Product
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}

As the reaction progresses, C1-C2, C3-C4 and C5-C6 elongate as the double bond breaks to form single carbon-carbon bonds, while C2-C3 shortens to form carbon-carbon double bond. Simultaneously, C4-C5 and C6-C1 decrease in distance and ultimately single carbon-carbon bonds are formed. A more detailed overview of how the internuclear distances change over the course of the reaction is shown on the graph on the right.

A typical carbon-carbon single bond length is 1.54 Å and a typical carbon-carbon double bond length is 1.34 Å. <ref name="OrganicChemistryJoseph" />

The Van der Waals radius of one carbon atom is 1.70 Å. <ref name="TheMoleculesofLife" /> The length of the partly formed carbon-carbon bonds in the transition state is about 2.11 Å. This distance is shorter than twice the Van der Waals radius of carbon atom (3.40 Å), indicating bonding interactions are occuring.
<br style="clear:right">

=== Vibration and Reaction Path ===

[[File:exercisa1imaginaryfrequency.jpg]]

The vibration that corresponds to the reaction path at the transition state is illustrated above. This vibration has an imaginary frequency that occurs at 948.97i cm<sup>-1</sup>.

The formation of the two bonds are synchronous as shown below. This means that the two sigma bonds are formed simultaneously. hence, the reaction between butadiene and ethylene goes by a concerted synchronous mechanism.

[[File:IRCgif.jpg]]

=== Calculation Files ===

[[File:TP1414 Exercise 1 Ethylene.log]]

[[File:TP1414 Exercise 1 Butadiene.log]]

[[File:TP1414 Exercise 1 Product.log]]

[[File:TP1414 Exercise 1 Transition State.log]]

[[File:TP1414 Exercise 1 IRC.log]]

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

[[File:exercise 2 reaction schemetp1414.jpg|center]]

=== Molecular Orbital Diagram ===

[[File:ex 2 MO diagram for exo TS TP1414.jpg|left|500px|thumb|Molecular orbital (MO) diagram for the reaction of cyclohexadiene and 1,3-dioxole (exo).]]

[[File:ex 2 MO diagram for endo TS TP1414.jpg|500px|thumb|Molecular orbital (MO) diagram for the reaction of cyclohexadiene and 1,3-dioxole (endo).]]

<br style="clear:left">

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Image
! style="background: #0D4F8B; color: white;" | Symmetry
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Image
! style="background: #0D4F8B; color: white;" | Symmetry
|-
! rowspan="4" style="background: #0D4F8B; color: white;"| Exo
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex2exoMO4tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO4 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
! rowspan="4" style="background: #0D4F8B; color: white;"| Endo
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex2endoMO4tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO4 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
|-
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex2exoMO3tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO3 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex2endoMO3tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO3 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex2exoMO2tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO2 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex2endoMO2tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO2 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex2exoMO1tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO1 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex2endoMO1tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO1 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
|-
|}

Inverse electron demand Diels-Alder

=== Thermochemistry ===
[[File:ex2energyprofiletp1414.jpeg|600px|thumb|Energy profile diagram for the reactions between cyclohexadiene and 1,3-dioxole]]
The energies of the reactants, transition state and product for both the exo and endo reactions are tabulated below. These are obtained from optimization at B3LYP/6-31G(d) level.

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;"| Exo
|style="text-align: center;"|-612591.48
|style="text-align: center;"|-701187.43
|style="text-align: center;"|-1313778.91
|style="text-align: center;"|-1313614.33
|style="text-align: center;"|-1313845.77
|style="text-align: center;"|164.58
|style="text-align: center;"|-66.86
|-
!style="background: #0D4F8B; color: white;"| Endo
|style="text-align: center;"|-612591.48
|style="text-align: center;"|-701187.43
|style="text-align: center;"|-1313778.91
|style="text-align: center;"|-1313622.15
|style="text-align: center;"|-1313849.37
|style="text-align: center;"|156.76
|style="text-align: center;"|-70.46
|-
|}

Both the exo and endo reactions are exothermic. However, it can be seen that the energy of the endo product is lower (or more negative) than the energy of the exo product, and the endo reaction also has a lower reaction barrier as compared to the exo reaction. This means that the endo product is both the thermodynamically and kinetically favourable product. This can be explained by considering both electronic and steric factors

[[File:seondaryorbitalinteractionstp1414.png|500px|thumb|left|Secondary orbital interactions in endo transition state]] Secondary orbital interactions stabilize the endo transition state, reducing the reaction barrier. On the left is the HOMO of the endo transition state in which there are obvious secondary orbital interactions between the oxygen p orbitals of the 1,3-dioxole and the p orbitals of the diene. An MO representation of this HOMO is shown below.
[[File:secondaryorbitalinteractionMOrepresentationtp1414.jpeg|350px]]
<br style="clear:left">

[[File:stericclashtp1414.png|500px|thumb|left|Steric clash in exo product]] Steric clash between the sp<sup>3</sup> CH<sub>2</sub> of the dioxole ring and the sp<sup>3</sup> CH<sub>2</sub>'s of the cyclohexadiene destabilize both the exo transition state and the exo product.
<br style="clear:left">

=== Vibration and Reaction Path ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
! style="background: #0D4F8B; color: white;"| Vibration
|style="text-align: center;"| [[File:exercise2 exo vibration tp1414.gif]]
|style="text-align: center;"| [[File:exercise2 endo vibration tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Vibrational Frequency
|style="text-align: center;"| 520.90i cm<sup>-1</sup>
|style="text-align: center;"| 528.85i cm<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| Reaction Pathway
|style="text-align: center;"| [[File:exercise2 exo reaction path tp1414.gif]]
|style="text-align: center;"| [[File:exercise2 endo reaction path tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Mechanism
|style="text-align: center;"| Synchronous concerted
|style="text-align: center;"| Synchronous concerted
|-
|}

=== Calculation Files ===

[[File:TP1414 Exercise 2 Cyclohexadiene 631Gd.log]]

[[File:TP1414 Exercise 2 1,2-Dioxole 631Gd.log]]

[[File:TP1414 Exercise 2 Exo Product 631Gd.log]]

[[File:TP1414 Exercise 2 Endo Product 631Gd.log]]

[[File:TP1414 Exercise 2 Exo Transition State 631Gd.log]]

[[File:TP1414 Exercise 2 Endo Transition State 631Gd.log]]

[[File:TP1414 Exercise 2 Exo IRC 631Gd.log]]

[[File:TP1414 Exercise 2 Endo IRC 631Gd.log]]

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

[[File:exercise3reactionschemetp1414.jpg|center]]

=== Thermochemistry ===
[[File:ex3energyprofiletp1414.jpg|600px|thumb|Energy profile diagram for the reactions between o-xylylene and SO<sub>2</sub>]]
The energies of the reactants, transition state and product for the exo, endo and cheletropic reactions are tabulated below. These are obtained from optimization at PM6 level.

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | o-Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;"| Exo
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|241.75
|style="text-align: center;"|56.31
|style="text-align: center;"|85.18
|style="text-align: center;"|-71.39
|-
!style="background: #0D4F8B; color: white;"| Endo
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|237.77
|style="text-align: center;"|56.98
|style="text-align: center;"|81.20
|style="text-align: center;"|-75.37
|-
!style="background: #0D4F8B; color: white;"| Cheletropic
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|260.09
|style="text-align: center;"|-0.01
|style="text-align: center;"|103.52
|style="text-align: center;"|-53.05
|-
|}

All three reactions are exothermic. The endo product is the kinetically favourable product as it has the lowest reaction barrier, while the cheletropic product is the thermodynamically favourable product as it has the lowest energy.
<br style="clear:right">

=== Vibration and Reaction Path ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
! style="background: #0D4F8B; color: white;" | Cheletropic
|-
! style="background: #0D4F8B; color: white;"| Vibration
|style="text-align: center;"| [[File:ex3 exo vibration tp1414.gif]]
|style="text-align: center;"| [[File:ex3 endo vibration tp1414.gif]]
|style="text-align: center;"| [[File:cheletropic vibration tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Vibrational Frequency
|style="text-align: center;"| 351.78i cm<sup>-1</sup>
|style="text-align: center;"| 334.38i cm<sup>-1</sup>
|style="text-align: center;"| 486.58i cm<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| Reaction Pathway
|style="text-align: center;"| [[File:exo IRC tp1414.gif]]
|style="text-align: center;"| [[File:endo IRC tp1414.gif]]
|style="text-align: center;"| [[File:cheletropic IRC tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Mechanism
|style="text-align: center;"| Asynchronous concerted
|style="text-align: center;"| Asynchronous concerted
|style="text-align: center;"| Synchronous concerted
|-
! style="background: #0D4F8B; color: white;"| IRC
|style="text-align: center;"| [[File:exoIRCtp1414.png]]
|style="text-align: center;"| [[File:endoIRCtp1414.png]]
|style="text-align: center;"| [[File:cheletropicIRCtp1414energy.png]]
|-
|}

It is interesting to note that the exo and endo reactions proceed via asynchronous mechanism in which the C-O bond is formed first before the C-S bond, while the cheletropic reaction proceeds via synchronous mechanism in which the two C-S bonds are formed simultaneously. However, even though the formation of the two bonds are asynchronous in the exo and endo reactions, the total energy along the IRC tells us that both reactions are concerted as the reactions do not have any intermediate steps.

In all three reaction pathways, the steepest part on the the total energy versus IRC graph corresponds to the re-aromatisation of the 6-membered ring on the o-xylylene, giving these reactions an aromatic driving force. This also shows the instability of the o-xylylene molecule. O-Xylylene is highly unstable as it is antiaromatic (planar and 4n electrons), and it will undergo an electrocyclic ring closure to form the stable aromatic isomer, benzocyclobutene as shown below.

[[File:xylyleneelectrocyclicreactionscheme.jpg|centre]]

=== Alternate Diels-Alder Reaction ===

There is a second cis-butadiene fragment in o-xylylene that can undergo a Diels-Alder reaction. This second cis-butadiene is part of the cyclohexadiene ring. The exo and endo for this alternate Diels-Alder reaction proceed as follow:

[[File:alternatedielsalderexotp1414.gif]] [[File:alternatedielsalderendotp1414.gif]]

Both reactions proceed via an asynchronous mechanism.

[[File:energyprofilewithalternatedielsaldertp1414.jpg|600px|thumb|Energy profile diagram for the reactions between o-xylylene and SO<sub>2</sub>]]
The thermochemistry for this alternate Diels-Alder reaction is as follows:

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | o-Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;" | Exo
| style="text-align: center;" |467.99
| style="text-align: center;" |-311.42
| style="text-align: center;" |156.57
| style="text-align: center;" |275.82
| style="text-align: center;" |176.71
| style="text-align: center;" |119.25
| style="text-align: center;" |20.14
|-
! style="background: #0D4F8B; color: white;" | Endo
| style="text-align: center;" |467.99
| style="text-align: center;" |-311.42
| style="text-align: center;" |156.57
| style="text-align: center;" |267.98
| style="text-align: center;" |172.26
| style="text-align: center;" |111.41
| style="text-align: center;" |15.96
|-
|}

Comparing the energies for this alternate Diels-Alder reaction with the energies for the normal Diels-Alder and the cheletropic reactions, it can be seen that both the exo and endo alternate Diels-Alder reactoions are kinetically and thermodynamically unfavourable. The products are also higher in energies than the reactants, making the reactions endothermic.
<br style="clear:right">

=== Calculation Files ===

[[File:TP1414 Exercise 3 Xylylene.log]]

[[File:TP1414 Exercise 3 SO2.log]]

[[File:TP1414 Exercise 3 Exo Product.log]]

[[File:TP1414 Exercise 3 Endo Product.log]]

[[File:TP1414 Exercise 3 Cheletropic Product.log]]

[[File:TP1414 Exercise 3 Exo Transition State.log]]

[[File:TP1414 Exercise 3 Endo Transition State.log]]

[[File:TP1414 Exercise 3 Cheletropic Transition State.log]]

[[File:TP1414 Exercise 3 Exo IRC.log]]

[[File:TP1414 Exercise 3 Endo IRC.log]]

[[File:TP1414 Exercise 3 Cheletropic IRC.log]]

[[File:TP1414 Exercise 3 Alternate Exo Product.log]]

[[File:TP1414 Exercise 3 Alternate Endo Product.log]]

[[File:TP1414 Exercise 3 Alternate Exo Transition State.log]]

[[File:TP1414 Exercise 3 Alternate Endo Transition State.log]]

[[File:TP1414 Exercise 3 Alternate Exo IRC.log]]

[[File:TP1414 Exercise 3 Alternate Endo IRC.log]]

== Conclusion ==
Synchronous and asynchronous mechanism. Symmetrical molecules?

== References ==

<references>
<ref name="OrganicChemistryJoseph"> J. M. Hornback, ''Organic Chemistry'', Thomson Learning. Inc., Belmont, Second., 2006.</ref>
<ref name="TheMoleculesofLife"> J. Kuriyan, B. Konforti and D. Wemmer, ''The Molecules of Life: Physical and Chemical Principles'', Garland Science, New York, 2013.</ref>
<ref name="InverseElectronDemand"> A.-C. Knall and C. Slugovc, ''Chem Soc Rev'', 2013, '''42''', 5131–5142.</ref>
<ref name="TransitionsofElectronDemand"> E. Eibler, P. Hocht, B. Prantl, H. Rormaier, H. M. Schuhbauer and H. Wiest, ''Liebigs Ann.lRemei'', 1997, '''1997''', 2471–2484.</ref>
</references>

File:Xylyleneelectrocyclicreactionscheme.jpg

2017-03-14T16:03:28Z

Tp1414:

Rep:Mod:TP1414

2017-03-14T16:02:59Z

Tp1414: /* Vibration and Reaction Path */

== Introduction ==

=== Gaussian and Transition State Characterization ===

Gaussian is a molecular modelling software that allows researchers to carry out extensive investigation of molecules and their reactions. In these exercises, the transition states of several Diels-Alder reactions are located and characterized using Gaussian. A transition state is a first order saddle point on a potential energy surface (PES). It is the maximum along the minimum energy path (or reaction path) between two minima (the reactants and the products). ''Geometry optimization'' to find the minimum energy structure will usually lead to a stationary point that is closest to the initial geometry. The stationary point, where the first derivative of energy is zero, can be a global minimum, a local minimum or a saddle point. In a reaction path, the minima (global or local) correspond to the reactants and the products, while the saddle point corresponds to the transition state. To differentiate between a minimum and a saddle point, the second derivatives of energy will have to be analysed. For global or local minima, where energy rises in all directions, the second derivative of energy is positive. In contrast, for transition state, where the energy decreases in one direction (reaction path), the second derivative of energy along the reaction coordinate is negative. The analysis of the second derivatives of energy can be done by a ''frequency calculation'' of the optimized structure. If the structure corresponds to the reactants or products, all the vibrational frequencies are real. In contrast, if the structure corresponds to a transition state, there will be one imaginary frequency. This imaginary frequency indicates that the force constant (k), which is given by the second derivative, is negative.

[[File:frequencyequation.png|center]]

[[File:forceconstantequation.png|center]]

Following a successful frequency calculation (one imaginary frequency) of the transition state, an ''Intrinsic Reaction Coordinate (IRC) calculation'' may be set up to examine the transition state along the minimum energy path more closely. The reaction path, or minimum energy path, can be defined as the steepest descent path from the transition state to the reactions and products.

=== Diels-Alder Reactions ===

A Diels-Alder reaction is a [4+2] cycloadditon between a conjugated s-cis diene (4π-electron system) and a dienophile (2π-electron system). The reaction has a cyclic transition state with 6π-electrons, is concerted, and results in the formation of two new sigma bonds. According to the Woodward-Hoffmann Rules, the Diels-Alder reaction is thermally allowed and is an orbital-controlled reaction, in which the six electrons are interacting suprafacially. The reaction can mainly proceed in two ways:

# Normal electron demand: HOMO of diene overlaps with LUMO of dienophile
# Inverse electron demand: LUMO of diene overlaps with HOMO of dienophile

Several papers divide the Diels-Alder reactions into three categories instead of two <ref name="InverseElectronDemand"/> <ref name="TransitionsofElectronDemand"/>, the third being a neutral electron demand Diels-Alder, in which the energy separation between the HOMO and LUMO of both reactants is similar. <ref name="InverseElectronDemand"/> Neutral electron demand Diels-Alder reactions are seldom observed and believed to be a transition between normal electron demand and inverse electron demand Diels Alder reactions.<ref name="TransitionsofElectronDemand"/>

[[File:normalinverseneutral.jpeg|center|500px]]

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

The reaction between butadiene and ethylene presents the simplest type of Diels-Alder reaction, in which butadiene is the diene and ethylene is the dienophile. This reaction yields cyclohexene as the product, and the reaction scheme is as follow:

[[File:exercise 1 reaction scheme.jpg|center]]

=== Molecular Orbital Diagram ===

[[File:MO diagram for exercise 1 TP1414.jpg|500px|thumb|center|Molecular orbital (MO) diagram for the reaction of butadiene with ethylene]]
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Jmol
! style="background: #0D4F8B; color: white;" | Symmetry
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Jmol
! style="background: #0D4F8B; color: white;" | Symmetry
|-
! rowspan="2" style="background: #0D4F8B; color: white;"| Butadiene
! style="background: #0D4F8B; color: white;"| LUMO
|style="text-align: center;"| [[File:ex1butadieneLUMOtp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 BUTADIENE BREAK SYMMETRY JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 22; rotate x -90; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
! rowspan="4" style="background: #0D4F8B; color: white;"| Transition State
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex1mo4tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
|-
! style="background: #0D4F8B; color: white;"| HOMO
|style="text-align: center;"| [[File:ex1butadieneHOMOtp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 BUTADIENE BREAK SYMMETRY JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 22; rotate x -90; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex1mo3tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
|-
! rowspan="2" style="background: #0D4F8B; color: white;"| Ethylene
! style="background: #0D4F8B; color: white;"| LUMO
|style="text-align: center;"| [[File:ex1ethyleneLUMOtp1414.png|100px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 ETHYLENE JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 14; rotate z 90; rotate x 90; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex1mo2tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| HOMO
|style="text-align: center;"| [[File:ex1ethyleneHOMOtp1414.png|100px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 ETHYLENE JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 14; rotate z 90; rotate x 90; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex1mo1tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
|-
|}

<br style="clear:right">

Only orbitals of the same symmetry can interact to form molecular orbitals. This means that only symmetric-symmetric interactions and antisymmetric-antisymmetric interactions are allowed. Symmetric-antisymmetric interactions, on the other hand, are forbidden. This is because the orbital overlap integral is non-zero for interactions between orbitals of the same symmetry and zero for interactions between orbitals of different symmetry.

As shown on the MO diagram above, both interactions (between the HOMO of butadiene and the LUMO of ethylene, and between the LUMO of butadiene and the HOMO of ethylene) occur, generating four molecular orbitals for the transition state. As the energy separation for the two interactions is similar, the reaction between butadiene and ethylene progress with aspects of both normal electron demand and inverse electron demand. This is because both butadiene and ethylene are neutral molecules without any obvious nucleophilic or electrophilic reacting centrers. Both molecules are neither electron-rich nor electron-poor. As a result, orbital overlap is possible for both HOMO-LUMO sets. Several papers classify this reaction as a neutral electron demand Diels-Alder. <ref name="InverseElectronDemand"/> <ref name="TransitionsofElectronDemand"/> This particular Diels-Alder reaction between butadiene and ethylene is well-known for its poor yield.

<br style="clear:left">

=== Internuclear Distances ===

[[File:internuclear distance.pdf|600px|thumb|right|Internuclear distances for the reaction of butadiene with ethylene to form cyclohexene.]]

[[File:butadiene and ethylene.jpg]]

{| class="wikitable"
|+ Internuclear Distances (Å)
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | C1-C2
! style="background: #0D4F8B; color: white;" | C2-C3
! style="background: #0D4F8B; color: white;" | C3-C4
! style="background: #0D4F8B; color: white;" | C4-C5
! style="background: #0D4F8B; color: white;" | C5-C6
! style="background: #0D4F8B; color: white;" | C6-C1
|-
! style="background: #0D4F8B; color: white;"| Reactants
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|style="text-align: center;"| -
|-
! style="background: #0D4F8B; color: white;"| Transition State
|style="text-align: center;"| 1.38
|style="text-align: center;"| 1.41
|style="text-align: center;"| 1.38
|style="text-align: center;"| 2.11
|style="text-align: center;"| 1.38
|style="text-align: center;"| 2.11
|-
! style="background: #0D4F8B; color: white;"| Product
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}

As the reaction progresses, C1-C2, C3-C4 and C5-C6 elongate as the double bond breaks to form single carbon-carbon bonds, while C2-C3 shortens to form carbon-carbon double bond. Simultaneously, C4-C5 and C6-C1 decrease in distance and ultimately single carbon-carbon bonds are formed. A more detailed overview of how the internuclear distances change over the course of the reaction is shown on the graph on the right.

A typical carbon-carbon single bond length is 1.54 Å and a typical carbon-carbon double bond length is 1.34 Å. <ref name="OrganicChemistryJoseph" />

The Van der Waals radius of one carbon atom is 1.70 Å. <ref name="TheMoleculesofLife" /> The length of the partly formed carbon-carbon bonds in the transition state is about 2.11 Å. This distance is shorter than twice the Van der Waals radius of carbon atom (3.40 Å), indicating bonding interactions are occuring.
<br style="clear:right">

=== Vibration and Reaction Path ===

[[File:exercisa1imaginaryfrequency.jpg]]

The vibration that corresponds to the reaction path at the transition state is illustrated above. This vibration has an imaginary frequency that occurs at 948.97i cm<sup>-1</sup>.

The formation of the two bonds are synchronous as shown below. This means that the two sigma bonds are formed simultaneously. hence, the reaction between butadiene and ethylene goes by a concerted synchronous mechanism.

[[File:IRCgif.jpg]]

=== Calculation Files ===

[[File:TP1414 Exercise 1 Ethylene.log]]

[[File:TP1414 Exercise 1 Butadiene.log]]

[[File:TP1414 Exercise 1 Product.log]]

[[File:TP1414 Exercise 1 Transition State.log]]

[[File:TP1414 Exercise 1 IRC.log]]

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

[[File:exercise 2 reaction schemetp1414.jpg|center]]

=== Molecular Orbital Diagram ===

[[File:ex 2 MO diagram for exo TS TP1414.jpg|left|500px|thumb|Molecular orbital (MO) diagram for the reaction of cyclohexadiene and 1,3-dioxole (exo).]]

[[File:ex 2 MO diagram for endo TS TP1414.jpg|500px|thumb|Molecular orbital (MO) diagram for the reaction of cyclohexadiene and 1,3-dioxole (endo).]]

<br style="clear:left">

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Image
! style="background: #0D4F8B; color: white;" | Symmetry
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Image
! style="background: #0D4F8B; color: white;" | Symmetry
|-
! rowspan="4" style="background: #0D4F8B; color: white;"| Exo
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex2exoMO4tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO4 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
! rowspan="4" style="background: #0D4F8B; color: white;"| Endo
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex2endoMO4tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO4 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
|-
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex2exoMO3tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO3 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex2endoMO3tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO3 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex2exoMO2tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO2 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex2endoMO2tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO2 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex2exoMO1tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO1 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex2endoMO1tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO1 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
|-
|}

Inverse electron demand Diels-Alder

=== Thermochemistry ===
[[File:ex2energyprofiletp1414.jpeg|600px|thumb|Energy profile diagram for the reactions between cyclohexadiene and 1,3-dioxole]]
The energies of the reactants, transition state and product for both the exo and endo reactions are tabulated below. These are obtained from optimization at B3LYP/6-31G(d) level.

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;"| Exo
|style="text-align: center;"|-612591.48
|style="text-align: center;"|-701187.43
|style="text-align: center;"|-1313778.91
|style="text-align: center;"|-1313614.33
|style="text-align: center;"|-1313845.77
|style="text-align: center;"|164.58
|style="text-align: center;"|-66.86
|-
!style="background: #0D4F8B; color: white;"| Endo
|style="text-align: center;"|-612591.48
|style="text-align: center;"|-701187.43
|style="text-align: center;"|-1313778.91
|style="text-align: center;"|-1313622.15
|style="text-align: center;"|-1313849.37
|style="text-align: center;"|156.76
|style="text-align: center;"|-70.46
|-
|}

Both the exo and endo reactions are exothermic. However, it can be seen that the energy of the endo product is lower (or more negative) than the energy of the exo product, and the endo reaction also has a lower reaction barrier as compared to the exo reaction. This means that the endo product is both the thermodynamically and kinetically favourable product. This can be explained by considering both electronic and steric factors

[[File:seondaryorbitalinteractionstp1414.png|500px|thumb|left|Secondary orbital interactions in endo transition state]] Secondary orbital interactions stabilize the endo transition state, reducing the reaction barrier. On the left is the HOMO of the endo transition state in which there are obvious secondary orbital interactions between the oxygen p orbitals of the 1,3-dioxole and the p orbitals of the diene. An MO representation of this HOMO is shown below.
[[File:secondaryorbitalinteractionMOrepresentationtp1414.jpeg|350px]]
<br style="clear:left">

[[File:stericclashtp1414.png|500px|thumb|left|Steric clash in exo product]] Steric clash between the sp<sup>3</sup> CH<sub>2</sub> of the dioxole ring and the sp<sup>3</sup> CH<sub>2</sub>'s of the cyclohexadiene destabilize both the exo transition state and the exo product.
<br style="clear:left">

=== Vibration and Reaction Path ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
! style="background: #0D4F8B; color: white;"| Vibration
|style="text-align: center;"| [[File:exercise2 exo vibration tp1414.gif]]
|style="text-align: center;"| [[File:exercise2 endo vibration tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Vibrational Frequency
|style="text-align: center;"| 520.90i cm<sup>-1</sup>
|style="text-align: center;"| 528.85i cm<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| Reaction Pathway
|style="text-align: center;"| [[File:exercise2 exo reaction path tp1414.gif]]
|style="text-align: center;"| [[File:exercise2 endo reaction path tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Mechanism
|style="text-align: center;"| Synchronous concerted
|style="text-align: center;"| Synchronous concerted
|-
|}

=== Calculation Files ===

[[File:TP1414 Exercise 2 Cyclohexadiene 631Gd.log]]

[[File:TP1414 Exercise 2 1,2-Dioxole 631Gd.log]]

[[File:TP1414 Exercise 2 Exo Product 631Gd.log]]

[[File:TP1414 Exercise 2 Endo Product 631Gd.log]]

[[File:TP1414 Exercise 2 Exo Transition State 631Gd.log]]

[[File:TP1414 Exercise 2 Endo Transition State 631Gd.log]]

[[File:TP1414 Exercise 2 Exo IRC 631Gd.log]]

[[File:TP1414 Exercise 2 Endo IRC 631Gd.log]]

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

[[File:exercise3reactionschemetp1414.jpg|center]]

=== Thermochemistry ===
[[File:ex3energyprofiletp1414.jpg|600px|thumb|Energy profile diagram for the reactions between o-xylylene and SO<sub>2</sub>]]
The energies of the reactants, transition state and product for the exo, endo and cheletropic reactions are tabulated below. These are obtained from optimization at PM6 level.

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | o-Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;"| Exo
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|241.75
|style="text-align: center;"|56.31
|style="text-align: center;"|85.18
|style="text-align: center;"|-71.39
|-
!style="background: #0D4F8B; color: white;"| Endo
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|237.77
|style="text-align: center;"|56.98
|style="text-align: center;"|81.20
|style="text-align: center;"|-75.37
|-
!style="background: #0D4F8B; color: white;"| Cheletropic
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|260.09
|style="text-align: center;"|-0.01
|style="text-align: center;"|103.52
|style="text-align: center;"|-53.05
|-
|}

All three reactions are exothermic. The endo product is the kinetically favourable product as it has the lowest reaction barrier, while the cheletropic product is the thermodynamically favourable product as it has the lowest energy.
<br style="clear:right">

=== Vibration and Reaction Path ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
! style="background: #0D4F8B; color: white;" | Cheletropic
|-
! style="background: #0D4F8B; color: white;"| Vibration
|style="text-align: center;"| [[File:ex3 exo vibration tp1414.gif]]
|style="text-align: center;"| [[File:ex3 endo vibration tp1414.gif]]
|style="text-align: center;"| [[File:cheletropic vibration tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Vibrational Frequency
|style="text-align: center;"| 351.78i cm<sup>-1</sup>
|style="text-align: center;"| 334.38i cm<sup>-1</sup>
|style="text-align: center;"| 486.58i cm<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| Reaction Pathway
|style="text-align: center;"| [[File:exo IRC tp1414.gif]]
|style="text-align: center;"| [[File:endo IRC tp1414.gif]]
|style="text-align: center;"| [[File:cheletropic IRC tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Mechanism
|style="text-align: center;"| Asynchronous concerted
|style="text-align: center;"| Asynchronous concerted
|style="text-align: center;"| Synchronous concerted
|-
! style="background: #0D4F8B; color: white;"| IRC
|style="text-align: center;"| [[File:exoIRCtp1414.png]]
|style="text-align: center;"| [[File:endoIRCtp1414.png]]
|style="text-align: center;"| [[File:cheletropicIRCtp1414energy.png]]
|-
|}

It is interesting to note that the exo and endo reactions proceed via asynchronous mechanism in which the C-O bond is formed first before the C-S bond, while the cheletropic reaction proceeds via synchronous mechanism in which the two C-S bonds are formed simultaneously. However, even though the formation of the two bonds are asynchronous in the exo and endo reactions, the total energy along the IRC tells us that both reactions are concerted as the reactions do not have any intermediate steps.

In all three reaction pathways, the steepest part on the the total energy versus IRC graph corresponds to the re-aromatisation of the 6-membered ring on the o-xylylene, giving these reactions an aromatic driving force. This also shows the instability of the o-xylylene molecule. O-Xylylene is highly unstable as it is antiaromatic (planar and 4n electrons), and it will undergo an electrocyclic ring closure to form the stable aromatic isomer, benzocyclobutene as shown below.

[[File:xylyleneelectrocyclicreactionscheme.jpg]]

=== Alternate Diels-Alder Reaction ===

There is a second cis-butadiene fragment in o-xylylene that can undergo a Diels-Alder reaction. This second cis-butadiene is part of the cyclohexadiene ring. The exo and endo for this alternate Diels-Alder reaction proceed as follow:

[[File:alternatedielsalderexotp1414.gif]] [[File:alternatedielsalderendotp1414.gif]]

Both reactions proceed via an asynchronous mechanism.

[[File:energyprofilewithalternatedielsaldertp1414.jpg|600px|thumb|Energy profile diagram for the reactions between o-xylylene and SO<sub>2</sub>]]
The thermochemistry for this alternate Diels-Alder reaction is as follows:

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | o-Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;" | Exo
| style="text-align: center;" |467.99
| style="text-align: center;" |-311.42
| style="text-align: center;" |156.57
| style="text-align: center;" |275.82
| style="text-align: center;" |176.71
| style="text-align: center;" |119.25
| style="text-align: center;" |20.14
|-
! style="background: #0D4F8B; color: white;" | Endo
| style="text-align: center;" |467.99
| style="text-align: center;" |-311.42
| style="text-align: center;" |156.57
| style="text-align: center;" |267.98
| style="text-align: center;" |172.26
| style="text-align: center;" |111.41
| style="text-align: center;" |15.96
|-
|}

Comparing the energies for this alternate Diels-Alder reaction with the energies for the normal Diels-Alder and the cheletropic reactions, it can be seen that both the exo and endo alternate Diels-Alder reactoions are kinetically and thermodynamically unfavourable. The products are also higher in energies than the reactants, making the reactions endothermic.
<br style="clear:right">

=== Calculation Files ===

[[File:TP1414 Exercise 3 Xylylene.log]]

[[File:TP1414 Exercise 3 SO2.log]]

[[File:TP1414 Exercise 3 Exo Product.log]]

[[File:TP1414 Exercise 3 Endo Product.log]]

[[File:TP1414 Exercise 3 Cheletropic Product.log]]

[[File:TP1414 Exercise 3 Exo Transition State.log]]

[[File:TP1414 Exercise 3 Endo Transition State.log]]

[[File:TP1414 Exercise 3 Cheletropic Transition State.log]]

[[File:TP1414 Exercise 3 Exo IRC.log]]

[[File:TP1414 Exercise 3 Endo IRC.log]]

[[File:TP1414 Exercise 3 Cheletropic IRC.log]]

[[File:TP1414 Exercise 3 Alternate Exo Product.log]]

[[File:TP1414 Exercise 3 Alternate Endo Product.log]]

[[File:TP1414 Exercise 3 Alternate Exo Transition State.log]]

[[File:TP1414 Exercise 3 Alternate Endo Transition State.log]]

[[File:TP1414 Exercise 3 Alternate Exo IRC.log]]

[[File:TP1414 Exercise 3 Alternate Endo IRC.log]]

== Conclusion ==
Synchronous and asynchronous mechanism. Symmetrical molecules?

== References ==

<references>
<ref name="OrganicChemistryJoseph"> J. M. Hornback, ''Organic Chemistry'', Thomson Learning. Inc., Belmont, Second., 2006.</ref>
<ref name="TheMoleculesofLife"> J. Kuriyan, B. Konforti and D. Wemmer, ''The Molecules of Life: Physical and Chemical Principles'', Garland Science, New York, 2013.</ref>
<ref name="InverseElectronDemand"> A.-C. Knall and C. Slugovc, ''Chem Soc Rev'', 2013, '''42''', 5131–5142.</ref>
<ref name="TransitionsofElectronDemand"> E. Eibler, P. Hocht, B. Prantl, H. Rormaier, H. M. Schuhbauer and H. Wiest, ''Liebigs Ann.lRemei'', 1997, '''1997''', 2471–2484.</ref>
</references>

Rep:Mod:TP1414

2017-03-14T15:56:43Z

Tp1414: /* Vibration and Reaction Path */

== Introduction ==

=== Gaussian and Transition State Characterization ===

Gaussian is a molecular modelling software that allows researchers to carry out extensive investigation of molecules and their reactions. In these exercises, the transition states of several Diels-Alder reactions are located and characterized using Gaussian. A transition state is a first order saddle point on a potential energy surface (PES). It is the maximum along the minimum energy path (or reaction path) between two minima (the reactants and the products). ''Geometry optimization'' to find the minimum energy structure will usually lead to a stationary point that is closest to the initial geometry. The stationary point, where the first derivative of energy is zero, can be a global minimum, a local minimum or a saddle point. In a reaction path, the minima (global or local) correspond to the reactants and the products, while the saddle point corresponds to the transition state. To differentiate between a minimum and a saddle point, the second derivatives of energy will have to be analysed. For global or local minima, where energy rises in all directions, the second derivative of energy is positive. In contrast, for transition state, where the energy decreases in one direction (reaction path), the second derivative of energy along the reaction coordinate is negative. The analysis of the second derivatives of energy can be done by a ''frequency calculation'' of the optimized structure. If the structure corresponds to the reactants or products, all the vibrational frequencies are real. In contrast, if the structure corresponds to a transition state, there will be one imaginary frequency. This imaginary frequency indicates that the force constant (k), which is given by the second derivative, is negative.

[[File:frequencyequation.png|center]]

[[File:forceconstantequation.png|center]]

Following a successful frequency calculation (one imaginary frequency) of the transition state, an ''Intrinsic Reaction Coordinate (IRC) calculation'' may be set up to examine the transition state along the minimum energy path more closely. The reaction path, or minimum energy path, can be defined as the steepest descent path from the transition state to the reactions and products.

=== Diels-Alder Reactions ===

A Diels-Alder reaction is a [4+2] cycloadditon between a conjugated s-cis diene (4π-electron system) and a dienophile (2π-electron system). The reaction has a cyclic transition state with 6π-electrons, is concerted, and results in the formation of two new sigma bonds. According to the Woodward-Hoffmann Rules, the Diels-Alder reaction is thermally allowed and is an orbital-controlled reaction, in which the six electrons are interacting suprafacially. The reaction can mainly proceed in two ways:

# Normal electron demand: HOMO of diene overlaps with LUMO of dienophile
# Inverse electron demand: LUMO of diene overlaps with HOMO of dienophile

Several papers divide the Diels-Alder reactions into three categories instead of two <ref name="InverseElectronDemand"/> <ref name="TransitionsofElectronDemand"/>, the third being a neutral electron demand Diels-Alder, in which the energy separation between the HOMO and LUMO of both reactants is similar. <ref name="InverseElectronDemand"/> Neutral electron demand Diels-Alder reactions are seldom observed and believed to be a transition between normal electron demand and inverse electron demand Diels Alder reactions.<ref name="TransitionsofElectronDemand"/>

[[File:normalinverseneutral.jpeg|center|500px]]

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

The reaction between butadiene and ethylene presents the simplest type of Diels-Alder reaction, in which butadiene is the diene and ethylene is the dienophile. This reaction yields cyclohexene as the product, and the reaction scheme is as follow:

[[File:exercise 1 reaction scheme.jpg|center]]

=== Molecular Orbital Diagram ===

[[File:MO diagram for exercise 1 TP1414.jpg|500px|thumb|center|Molecular orbital (MO) diagram for the reaction of butadiene with ethylene]]
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Jmol
! style="background: #0D4F8B; color: white;" | Symmetry
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Jmol
! style="background: #0D4F8B; color: white;" | Symmetry
|-
! rowspan="2" style="background: #0D4F8B; color: white;"| Butadiene
! style="background: #0D4F8B; color: white;"| LUMO
|style="text-align: center;"| [[File:ex1butadieneLUMOtp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 BUTADIENE BREAK SYMMETRY JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 22; rotate x -90; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
! rowspan="4" style="background: #0D4F8B; color: white;"| Transition State
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex1mo4tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
|-
! style="background: #0D4F8B; color: white;"| HOMO
|style="text-align: center;"| [[File:ex1butadieneHOMOtp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 BUTADIENE BREAK SYMMETRY JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 22; rotate x -90; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex1mo3tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
|-
! rowspan="2" style="background: #0D4F8B; color: white;"| Ethylene
! style="background: #0D4F8B; color: white;"| LUMO
|style="text-align: center;"| [[File:ex1ethyleneLUMOtp1414.png|100px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 ETHYLENE JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 14; rotate z 90; rotate x 90; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex1mo2tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| HOMO
|style="text-align: center;"| [[File:ex1ethyleneHOMOtp1414.png|100px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 ETHYLENE JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 14; rotate z 90; rotate x 90; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex1mo1tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
|-
|}

<br style="clear:right">

Only orbitals of the same symmetry can interact to form molecular orbitals. This means that only symmetric-symmetric interactions and antisymmetric-antisymmetric interactions are allowed. Symmetric-antisymmetric interactions, on the other hand, are forbidden. This is because the orbital overlap integral is non-zero for interactions between orbitals of the same symmetry and zero for interactions between orbitals of different symmetry.

As shown on the MO diagram above, both interactions (between the HOMO of butadiene and the LUMO of ethylene, and between the LUMO of butadiene and the HOMO of ethylene) occur, generating four molecular orbitals for the transition state. As the energy separation for the two interactions is similar, the reaction between butadiene and ethylene progress with aspects of both normal electron demand and inverse electron demand. This is because both butadiene and ethylene are neutral molecules without any obvious nucleophilic or electrophilic reacting centrers. Both molecules are neither electron-rich nor electron-poor. As a result, orbital overlap is possible for both HOMO-LUMO sets. Several papers classify this reaction as a neutral electron demand Diels-Alder. <ref name="InverseElectronDemand"/> <ref name="TransitionsofElectronDemand"/> This particular Diels-Alder reaction between butadiene and ethylene is well-known for its poor yield.

<br style="clear:left">

=== Internuclear Distances ===

[[File:internuclear distance.pdf|600px|thumb|right|Internuclear distances for the reaction of butadiene with ethylene to form cyclohexene.]]

[[File:butadiene and ethylene.jpg]]

{| class="wikitable"
|+ Internuclear Distances (Å)
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | C1-C2
! style="background: #0D4F8B; color: white;" | C2-C3
! style="background: #0D4F8B; color: white;" | C3-C4
! style="background: #0D4F8B; color: white;" | C4-C5
! style="background: #0D4F8B; color: white;" | C5-C6
! style="background: #0D4F8B; color: white;" | C6-C1
|-
! style="background: #0D4F8B; color: white;"| Reactants
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|style="text-align: center;"| -
|-
! style="background: #0D4F8B; color: white;"| Transition State
|style="text-align: center;"| 1.38
|style="text-align: center;"| 1.41
|style="text-align: center;"| 1.38
|style="text-align: center;"| 2.11
|style="text-align: center;"| 1.38
|style="text-align: center;"| 2.11
|-
! style="background: #0D4F8B; color: white;"| Product
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}

As the reaction progresses, C1-C2, C3-C4 and C5-C6 elongate as the double bond breaks to form single carbon-carbon bonds, while C2-C3 shortens to form carbon-carbon double bond. Simultaneously, C4-C5 and C6-C1 decrease in distance and ultimately single carbon-carbon bonds are formed. A more detailed overview of how the internuclear distances change over the course of the reaction is shown on the graph on the right.

A typical carbon-carbon single bond length is 1.54 Å and a typical carbon-carbon double bond length is 1.34 Å. <ref name="OrganicChemistryJoseph" />

The Van der Waals radius of one carbon atom is 1.70 Å. <ref name="TheMoleculesofLife" /> The length of the partly formed carbon-carbon bonds in the transition state is about 2.11 Å. This distance is shorter than twice the Van der Waals radius of carbon atom (3.40 Å), indicating bonding interactions are occuring.
<br style="clear:right">

=== Vibration and Reaction Path ===

[[File:exercisa1imaginaryfrequency.jpg]]

The vibration that corresponds to the reaction path at the transition state is illustrated above. This vibration has an imaginary frequency that occurs at 948.97i cm<sup>-1</sup>.

The formation of the two bonds are synchronous as shown below. This means that the two sigma bonds are formed simultaneously. hence, the reaction between butadiene and ethylene goes by a concerted synchronous mechanism.

[[File:IRCgif.jpg]]

=== Calculation Files ===

[[File:TP1414 Exercise 1 Ethylene.log]]

[[File:TP1414 Exercise 1 Butadiene.log]]

[[File:TP1414 Exercise 1 Product.log]]

[[File:TP1414 Exercise 1 Transition State.log]]

[[File:TP1414 Exercise 1 IRC.log]]

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

[[File:exercise 2 reaction schemetp1414.jpg|center]]

=== Molecular Orbital Diagram ===

[[File:ex 2 MO diagram for exo TS TP1414.jpg|left|500px|thumb|Molecular orbital (MO) diagram for the reaction of cyclohexadiene and 1,3-dioxole (exo).]]

[[File:ex 2 MO diagram for endo TS TP1414.jpg|500px|thumb|Molecular orbital (MO) diagram for the reaction of cyclohexadiene and 1,3-dioxole (endo).]]

<br style="clear:left">

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Image
! style="background: #0D4F8B; color: white;" | Symmetry
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Image
! style="background: #0D4F8B; color: white;" | Symmetry
|-
! rowspan="4" style="background: #0D4F8B; color: white;"| Exo
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex2exoMO4tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO4 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
! rowspan="4" style="background: #0D4F8B; color: white;"| Endo
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex2endoMO4tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO4 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
|-
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex2exoMO3tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO3 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex2endoMO3tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO3 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex2exoMO2tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO2 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex2endoMO2tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO2 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex2exoMO1tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO1 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex2endoMO1tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO1 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
|-
|}

Inverse electron demand Diels-Alder

=== Thermochemistry ===
[[File:ex2energyprofiletp1414.jpeg|600px|thumb|Energy profile diagram for the reactions between cyclohexadiene and 1,3-dioxole]]
The energies of the reactants, transition state and product for both the exo and endo reactions are tabulated below. These are obtained from optimization at B3LYP/6-31G(d) level.

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;"| Exo
|style="text-align: center;"|-612591.48
|style="text-align: center;"|-701187.43
|style="text-align: center;"|-1313778.91
|style="text-align: center;"|-1313614.33
|style="text-align: center;"|-1313845.77
|style="text-align: center;"|164.58
|style="text-align: center;"|-66.86
|-
!style="background: #0D4F8B; color: white;"| Endo
|style="text-align: center;"|-612591.48
|style="text-align: center;"|-701187.43
|style="text-align: center;"|-1313778.91
|style="text-align: center;"|-1313622.15
|style="text-align: center;"|-1313849.37
|style="text-align: center;"|156.76
|style="text-align: center;"|-70.46
|-
|}

Both the exo and endo reactions are exothermic. However, it can be seen that the energy of the endo product is lower (or more negative) than the energy of the exo product, and the endo reaction also has a lower reaction barrier as compared to the exo reaction. This means that the endo product is both the thermodynamically and kinetically favourable product. This can be explained by considering both electronic and steric factors

[[File:seondaryorbitalinteractionstp1414.png|500px|thumb|left|Secondary orbital interactions in endo transition state]] Secondary orbital interactions stabilize the endo transition state, reducing the reaction barrier. On the left is the HOMO of the endo transition state in which there are obvious secondary orbital interactions between the oxygen p orbitals of the 1,3-dioxole and the p orbitals of the diene. An MO representation of this HOMO is shown below.
[[File:secondaryorbitalinteractionMOrepresentationtp1414.jpeg|350px]]
<br style="clear:left">

[[File:stericclashtp1414.png|500px|thumb|left|Steric clash in exo product]] Steric clash between the sp<sup>3</sup> CH<sub>2</sub> of the dioxole ring and the sp<sup>3</sup> CH<sub>2</sub>'s of the cyclohexadiene destabilize both the exo transition state and the exo product.
<br style="clear:left">

=== Vibration and Reaction Path ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
! style="background: #0D4F8B; color: white;"| Vibration
|style="text-align: center;"| [[File:exercise2 exo vibration tp1414.gif]]
|style="text-align: center;"| [[File:exercise2 endo vibration tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Vibrational Frequency
|style="text-align: center;"| 520.90i cm<sup>-1</sup>
|style="text-align: center;"| 528.85i cm<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| Reaction Pathway
|style="text-align: center;"| [[File:exercise2 exo reaction path tp1414.gif]]
|style="text-align: center;"| [[File:exercise2 endo reaction path tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Mechanism
|style="text-align: center;"| Synchronous concerted
|style="text-align: center;"| Synchronous concerted
|-
|}

=== Calculation Files ===

[[File:TP1414 Exercise 2 Cyclohexadiene 631Gd.log]]

[[File:TP1414 Exercise 2 1,2-Dioxole 631Gd.log]]

[[File:TP1414 Exercise 2 Exo Product 631Gd.log]]

[[File:TP1414 Exercise 2 Endo Product 631Gd.log]]

[[File:TP1414 Exercise 2 Exo Transition State 631Gd.log]]

[[File:TP1414 Exercise 2 Endo Transition State 631Gd.log]]

[[File:TP1414 Exercise 2 Exo IRC 631Gd.log]]

[[File:TP1414 Exercise 2 Endo IRC 631Gd.log]]

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

[[File:exercise3reactionschemetp1414.jpg|center]]

=== Thermochemistry ===
[[File:ex3energyprofiletp1414.jpg|600px|thumb|Energy profile diagram for the reactions between o-xylylene and SO<sub>2</sub>]]
The energies of the reactants, transition state and product for the exo, endo and cheletropic reactions are tabulated below. These are obtained from optimization at PM6 level.

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | o-Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;"| Exo
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|241.75
|style="text-align: center;"|56.31
|style="text-align: center;"|85.18
|style="text-align: center;"|-71.39
|-
!style="background: #0D4F8B; color: white;"| Endo
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|237.77
|style="text-align: center;"|56.98
|style="text-align: center;"|81.20
|style="text-align: center;"|-75.37
|-
!style="background: #0D4F8B; color: white;"| Cheletropic
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|260.09
|style="text-align: center;"|-0.01
|style="text-align: center;"|103.52
|style="text-align: center;"|-53.05
|-
|}

All three reactions are exothermic. The endo product is the kinetically favourable product as it has the lowest reaction barrier, while the cheletropic product is the thermodynamically favourable product as it has the lowest energy.
<br style="clear:right">

=== Vibration and Reaction Path ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
! style="background: #0D4F8B; color: white;" | Cheletropic
|-
! style="background: #0D4F8B; color: white;"| Vibration
|style="text-align: center;"| [[File:ex3 exo vibration tp1414.gif]]
|style="text-align: center;"| [[File:ex3 endo vibration tp1414.gif]]
|style="text-align: center;"| [[File:cheletropic vibration tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Vibrational Frequency
|style="text-align: center;"| 351.78i cm<sup>-1</sup>
|style="text-align: center;"| 334.38i cm<sup>-1</sup>
|style="text-align: center;"| 486.58i cm<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| Reaction Pathway
|style="text-align: center;"| [[File:exo IRC tp1414.gif]]
|style="text-align: center;"| [[File:endo IRC tp1414.gif]]
|style="text-align: center;"| [[File:cheletropic IRC tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Mechanism
|style="text-align: center;"| Asynchronous concerted
|style="text-align: center;"| Asynchronous concerted
|style="text-align: center;"| Synchronous concerted
|-
! style="background: #0D4F8B; color: white;"| IRC
|style="text-align: center;"| [[File:exoIRCtp1414.png]]
|style="text-align: center;"| [[File:endoIRCtp1414.png]]
|style="text-align: center;"| [[File:cheletropicIRCtp1414energy.png]]
|-
|}

It is interesting to note that the exo and endo reactions proceed via asynchronous mechanism in which the C-O bond is formed first before the C-S bond, while the cheletropic reaction proceeds via synchronous mechanism in which the two C-S bonds are formed simultaneously. However, even though the formation of the two bonds are asynchronous in the exo and endo reactions, the total energy along the IRC tells us that both reactions are concerted as the reactions do not have any intermediate steps.

In all three reaction pathways, the steepest part on the the total energy versus IRC graph corresponds to the re-aromatisation of the 6-membered ring on the o-xylylene, giving these reactions an aromatic driving force. This also shows the instability of the o-xylylene molecule. O-Xylylene is highly unstable as it is antiaromatic (planar and 4n electrons), and it will undergo an electrocyclic ring closure to form the stable aromatic isomer, benzocyclobutene as shown below.

=== Alternate Diels-Alder Reaction ===

There is a second cis-butadiene fragment in o-xylylene that can undergo a Diels-Alder reaction. This second cis-butadiene is part of the cyclohexadiene ring. The exo and endo for this alternate Diels-Alder reaction proceed as follow:

[[File:alternatedielsalderexotp1414.gif]] [[File:alternatedielsalderendotp1414.gif]]

Both reactions proceed via an asynchronous mechanism.

[[File:energyprofilewithalternatedielsaldertp1414.jpg|600px|thumb|Energy profile diagram for the reactions between o-xylylene and SO<sub>2</sub>]]
The thermochemistry for this alternate Diels-Alder reaction is as follows:

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | o-Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;" | Exo
| style="text-align: center;" |467.99
| style="text-align: center;" |-311.42
| style="text-align: center;" |156.57
| style="text-align: center;" |275.82
| style="text-align: center;" |176.71
| style="text-align: center;" |119.25
| style="text-align: center;" |20.14
|-
! style="background: #0D4F8B; color: white;" | Endo
| style="text-align: center;" |467.99
| style="text-align: center;" |-311.42
| style="text-align: center;" |156.57
| style="text-align: center;" |267.98
| style="text-align: center;" |172.26
| style="text-align: center;" |111.41
| style="text-align: center;" |15.96
|-
|}

Comparing the energies for this alternate Diels-Alder reaction with the energies for the normal Diels-Alder and the cheletropic reactions, it can be seen that both the exo and endo alternate Diels-Alder reactoions are kinetically and thermodynamically unfavourable. The products are also higher in energies than the reactants, making the reactions endothermic.
<br style="clear:right">

=== Calculation Files ===

[[File:TP1414 Exercise 3 Xylylene.log]]

[[File:TP1414 Exercise 3 SO2.log]]

[[File:TP1414 Exercise 3 Exo Product.log]]

[[File:TP1414 Exercise 3 Endo Product.log]]

[[File:TP1414 Exercise 3 Cheletropic Product.log]]

[[File:TP1414 Exercise 3 Exo Transition State.log]]

[[File:TP1414 Exercise 3 Endo Transition State.log]]

[[File:TP1414 Exercise 3 Cheletropic Transition State.log]]

[[File:TP1414 Exercise 3 Exo IRC.log]]

[[File:TP1414 Exercise 3 Endo IRC.log]]

[[File:TP1414 Exercise 3 Cheletropic IRC.log]]

[[File:TP1414 Exercise 3 Alternate Exo Product.log]]

[[File:TP1414 Exercise 3 Alternate Endo Product.log]]

[[File:TP1414 Exercise 3 Alternate Exo Transition State.log]]

[[File:TP1414 Exercise 3 Alternate Endo Transition State.log]]

[[File:TP1414 Exercise 3 Alternate Exo IRC.log]]

[[File:TP1414 Exercise 3 Alternate Endo IRC.log]]

== Conclusion ==
Synchronous and asynchronous mechanism. Symmetrical molecules?

== References ==

<references>
<ref name="OrganicChemistryJoseph"> J. M. Hornback, ''Organic Chemistry'', Thomson Learning. Inc., Belmont, Second., 2006.</ref>
<ref name="TheMoleculesofLife"> J. Kuriyan, B. Konforti and D. Wemmer, ''The Molecules of Life: Physical and Chemical Principles'', Garland Science, New York, 2013.</ref>
<ref name="InverseElectronDemand"> A.-C. Knall and C. Slugovc, ''Chem Soc Rev'', 2013, '''42''', 5131–5142.</ref>
<ref name="TransitionsofElectronDemand"> E. Eibler, P. Hocht, B. Prantl, H. Rormaier, H. M. Schuhbauer and H. Wiest, ''Liebigs Ann.lRemei'', 1997, '''1997''', 2471–2484.</ref>
</references>

Rep:Mod:TP1414

2017-03-14T15:38:15Z

Tp1414: /* Vibration and Reaction Path */

== Introduction ==

=== Gaussian and Transition State Characterization ===

Gaussian is a molecular modelling software that allows researchers to carry out extensive investigation of molecules and their reactions. In these exercises, the transition states of several Diels-Alder reactions are located and characterized using Gaussian. A transition state is a first order saddle point on a potential energy surface (PES). It is the maximum along the minimum energy path (or reaction path) between two minima (the reactants and the products). ''Geometry optimization'' to find the minimum energy structure will usually lead to a stationary point that is closest to the initial geometry. The stationary point, where the first derivative of energy is zero, can be a global minimum, a local minimum or a saddle point. In a reaction path, the minima (global or local) correspond to the reactants and the products, while the saddle point corresponds to the transition state. To differentiate between a minimum and a saddle point, the second derivatives of energy will have to be analysed. For global or local minima, where energy rises in all directions, the second derivative of energy is positive. In contrast, for transition state, where the energy decreases in one direction (reaction path), the second derivative of energy along the reaction coordinate is negative. The analysis of the second derivatives of energy can be done by a ''frequency calculation'' of the optimized structure. If the structure corresponds to the reactants or products, all the vibrational frequencies are real. In contrast, if the structure corresponds to a transition state, there will be one imaginary frequency. This imaginary frequency indicates that the force constant (k), which is given by the second derivative, is negative.

[[File:frequencyequation.png|center]]

[[File:forceconstantequation.png|center]]

Following a successful frequency calculation (one imaginary frequency) of the transition state, an ''Intrinsic Reaction Coordinate (IRC) calculation'' may be set up to examine the transition state along the minimum energy path more closely. The reaction path, or minimum energy path, can be defined as the steepest descent path from the transition state to the reactions and products.

=== Diels-Alder Reactions ===

A Diels-Alder reaction is a [4+2] cycloadditon between a conjugated s-cis diene (4π-electron system) and a dienophile (2π-electron system). The reaction has a cyclic transition state with 6π-electrons, is concerted, and results in the formation of two new sigma bonds. According to the Woodward-Hoffmann Rules, the Diels-Alder reaction is thermally allowed and is an orbital-controlled reaction, in which the six electrons are interacting suprafacially. The reaction can mainly proceed in two ways:

# Normal electron demand: HOMO of diene overlaps with LUMO of dienophile
# Inverse electron demand: LUMO of diene overlaps with HOMO of dienophile

Several papers divide the Diels-Alder reactions into three categories instead of two <ref name="InverseElectronDemand"/> <ref name="TransitionsofElectronDemand"/>, the third being a neutral electron demand Diels-Alder, in which the energy separation between the HOMO and LUMO of both reactants is similar. <ref name="InverseElectronDemand"/> Neutral electron demand Diels-Alder reactions are seldom observed and believed to be a transition between normal electron demand and inverse electron demand Diels Alder reactions.<ref name="TransitionsofElectronDemand"/>

[[File:normalinverseneutral.jpeg|center|500px]]

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

The reaction between butadiene and ethylene presents the simplest type of Diels-Alder reaction, in which butadiene is the diene and ethylene is the dienophile. This reaction yields cyclohexene as the product, and the reaction scheme is as follow:

[[File:exercise 1 reaction scheme.jpg|center]]

=== Molecular Orbital Diagram ===

[[File:MO diagram for exercise 1 TP1414.jpg|500px|thumb|center|Molecular orbital (MO) diagram for the reaction of butadiene with ethylene]]
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Jmol
! style="background: #0D4F8B; color: white;" | Symmetry
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Jmol
! style="background: #0D4F8B; color: white;" | Symmetry
|-
! rowspan="2" style="background: #0D4F8B; color: white;"| Butadiene
! style="background: #0D4F8B; color: white;"| LUMO
|style="text-align: center;"| [[File:ex1butadieneLUMOtp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 BUTADIENE BREAK SYMMETRY JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 22; rotate x -90; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
! rowspan="4" style="background: #0D4F8B; color: white;"| Transition State
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex1mo4tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
|-
! style="background: #0D4F8B; color: white;"| HOMO
|style="text-align: center;"| [[File:ex1butadieneHOMOtp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 BUTADIENE BREAK SYMMETRY JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 22; rotate x -90; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex1mo3tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
|-
! rowspan="2" style="background: #0D4F8B; color: white;"| Ethylene
! style="background: #0D4F8B; color: white;"| LUMO
|style="text-align: center;"| [[File:ex1ethyleneLUMOtp1414.png|100px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 ETHYLENE JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 14; rotate z 90; rotate x 90; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex1mo2tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| HOMO
|style="text-align: center;"| [[File:ex1ethyleneHOMOtp1414.png|100px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 ETHYLENE JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 14; rotate z 90; rotate x 90; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex1mo1tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
|-
|}

<br style="clear:right">

Only orbitals of the same symmetry can interact to form molecular orbitals. This means that only symmetric-symmetric interactions and antisymmetric-antisymmetric interactions are allowed. Symmetric-antisymmetric interactions, on the other hand, are forbidden. This is because the orbital overlap integral is non-zero for interactions between orbitals of the same symmetry and zero for interactions between orbitals of different symmetry.

As shown on the MO diagram above, both interactions (between the HOMO of butadiene and the LUMO of ethylene, and between the LUMO of butadiene and the HOMO of ethylene) occur, generating four molecular orbitals for the transition state. As the energy separation for the two interactions is similar, the reaction between butadiene and ethylene progress with aspects of both normal electron demand and inverse electron demand. This is because both butadiene and ethylene are neutral molecules without any obvious nucleophilic or electrophilic reacting centrers. Both molecules are neither electron-rich nor electron-poor. As a result, orbital overlap is possible for both HOMO-LUMO sets. Several papers classify this reaction as a neutral electron demand Diels-Alder. <ref name="InverseElectronDemand"/> <ref name="TransitionsofElectronDemand"/> This particular Diels-Alder reaction between butadiene and ethylene is well-known for its poor yield.

<br style="clear:left">

=== Internuclear Distances ===

[[File:internuclear distance.pdf|600px|thumb|right|Internuclear distances for the reaction of butadiene with ethylene to form cyclohexene.]]

[[File:butadiene and ethylene.jpg]]

{| class="wikitable"
|+ Internuclear Distances (Å)
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | C1-C2
! style="background: #0D4F8B; color: white;" | C2-C3
! style="background: #0D4F8B; color: white;" | C3-C4
! style="background: #0D4F8B; color: white;" | C4-C5
! style="background: #0D4F8B; color: white;" | C5-C6
! style="background: #0D4F8B; color: white;" | C6-C1
|-
! style="background: #0D4F8B; color: white;"| Reactants
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|style="text-align: center;"| -
|-
! style="background: #0D4F8B; color: white;"| Transition State
|style="text-align: center;"| 1.38
|style="text-align: center;"| 1.41
|style="text-align: center;"| 1.38
|style="text-align: center;"| 2.11
|style="text-align: center;"| 1.38
|style="text-align: center;"| 2.11
|-
! style="background: #0D4F8B; color: white;"| Product
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}

As the reaction progresses, C1-C2, C3-C4 and C5-C6 elongate as the double bond breaks to form single carbon-carbon bonds, while C2-C3 shortens to form carbon-carbon double bond. Simultaneously, C4-C5 and C6-C1 decrease in distance and ultimately single carbon-carbon bonds are formed. A more detailed overview of how the internuclear distances change over the course of the reaction is shown on the graph on the right.

A typical carbon-carbon single bond length is 1.54 Å and a typical carbon-carbon double bond length is 1.34 Å. <ref name="OrganicChemistryJoseph" />

The Van der Waals radius of one carbon atom is 1.70 Å. <ref name="TheMoleculesofLife" /> The length of the partly formed carbon-carbon bonds in the transition state is about 2.11 Å. This distance is shorter than twice the Van der Waals radius of carbon atom (3.40 Å), indicating bonding interactions are occuring.
<br style="clear:right">

=== Vibration and Reaction Path ===

[[File:exercisa1imaginaryfrequency.jpg]]

The vibration that corresponds to the reaction path at the transition state is illustrated above. This vibration has an imaginary frequency that occurs at 948.97i cm<sup>-1</sup>.

The formation of the two bonds are synchronous as shown below. This means that the two sigma bonds are formed simultaneously. hence, the reaction between butadiene and ethylene goes by a concerted synchronous mechanism.

[[File:IRCgif.jpg]]

=== Calculation Files ===

[[File:TP1414 Exercise 1 Ethylene.log]]

[[File:TP1414 Exercise 1 Butadiene.log]]

[[File:TP1414 Exercise 1 Product.log]]

[[File:TP1414 Exercise 1 Transition State.log]]

[[File:TP1414 Exercise 1 IRC.log]]

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

[[File:exercise 2 reaction schemetp1414.jpg|center]]

=== Molecular Orbital Diagram ===

[[File:ex 2 MO diagram for exo TS TP1414.jpg|left|500px|thumb|Molecular orbital (MO) diagram for the reaction of cyclohexadiene and 1,3-dioxole (exo).]]

[[File:ex 2 MO diagram for endo TS TP1414.jpg|500px|thumb|Molecular orbital (MO) diagram for the reaction of cyclohexadiene and 1,3-dioxole (endo).]]

<br style="clear:left">

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Image
! style="background: #0D4F8B; color: white;" | Symmetry
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Image
! style="background: #0D4F8B; color: white;" | Symmetry
|-
! rowspan="4" style="background: #0D4F8B; color: white;"| Exo
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex2exoMO4tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO4 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
! rowspan="4" style="background: #0D4F8B; color: white;"| Endo
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex2endoMO4tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO4 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
|-
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex2exoMO3tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO3 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex2endoMO3tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO3 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex2exoMO2tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO2 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex2endoMO2tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO2 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex2exoMO1tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO1 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex2endoMO1tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO1 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
|-
|}

Inverse electron demand Diels-Alder

=== Thermochemistry ===
[[File:ex2energyprofiletp1414.jpeg|600px|thumb|Energy profile diagram for the reactions between cyclohexadiene and 1,3-dioxole]]
The energies of the reactants, transition state and product for both the exo and endo reactions are tabulated below. These are obtained from optimization at B3LYP/6-31G(d) level.

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;"| Exo
|style="text-align: center;"|-612591.48
|style="text-align: center;"|-701187.43
|style="text-align: center;"|-1313778.91
|style="text-align: center;"|-1313614.33
|style="text-align: center;"|-1313845.77
|style="text-align: center;"|164.58
|style="text-align: center;"|-66.86
|-
!style="background: #0D4F8B; color: white;"| Endo
|style="text-align: center;"|-612591.48
|style="text-align: center;"|-701187.43
|style="text-align: center;"|-1313778.91
|style="text-align: center;"|-1313622.15
|style="text-align: center;"|-1313849.37
|style="text-align: center;"|156.76
|style="text-align: center;"|-70.46
|-
|}

Both the exo and endo reactions are exothermic. However, it can be seen that the energy of the endo product is lower (or more negative) than the energy of the exo product, and the endo reaction also has a lower reaction barrier as compared to the exo reaction. This means that the endo product is both the thermodynamically and kinetically favourable product. This can be explained by considering both electronic and steric factors

[[File:seondaryorbitalinteractionstp1414.png|500px|thumb|left|Secondary orbital interactions in endo transition state]] Secondary orbital interactions stabilize the endo transition state, reducing the reaction barrier. On the left is the HOMO of the endo transition state in which there are obvious secondary orbital interactions between the oxygen p orbitals of the 1,3-dioxole and the p orbitals of the diene. An MO representation of this HOMO is shown below.
[[File:secondaryorbitalinteractionMOrepresentationtp1414.jpeg|350px]]
<br style="clear:left">

[[File:stericclashtp1414.png|500px|thumb|left|Steric clash in exo product]] Steric clash between the sp<sup>3</sup> CH<sub>2</sub> of the dioxole ring and the sp<sup>3</sup> CH<sub>2</sub>'s of the cyclohexadiene destabilize both the exo transition state and the exo product.
<br style="clear:left">

=== Vibration and Reaction Path ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
! style="background: #0D4F8B; color: white;"| Vibration
|style="text-align: center;"| [[File:exercise2 exo vibration tp1414.gif]]
|style="text-align: center;"| [[File:exercise2 endo vibration tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Vibrational Frequency
|style="text-align: center;"| 520.90i cm<sup>-1</sup>
|style="text-align: center;"| 528.85i cm<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| Reaction Pathway
|style="text-align: center;"| [[File:exercise2 exo reaction path tp1414.gif]]
|style="text-align: center;"| [[File:exercise2 endo reaction path tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Mechanism
|style="text-align: center;"| Synchronous concerted
|style="text-align: center;"| Synchronous concerted
|-
|}

=== Calculation Files ===

[[File:TP1414 Exercise 2 Cyclohexadiene 631Gd.log]]

[[File:TP1414 Exercise 2 1,2-Dioxole 631Gd.log]]

[[File:TP1414 Exercise 2 Exo Product 631Gd.log]]

[[File:TP1414 Exercise 2 Endo Product 631Gd.log]]

[[File:TP1414 Exercise 2 Exo Transition State 631Gd.log]]

[[File:TP1414 Exercise 2 Endo Transition State 631Gd.log]]

[[File:TP1414 Exercise 2 Exo IRC 631Gd.log]]

[[File:TP1414 Exercise 2 Endo IRC 631Gd.log]]

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

[[File:exercise3reactionschemetp1414.jpg|center]]

=== Thermochemistry ===
[[File:ex3energyprofiletp1414.jpg|600px|thumb|Energy profile diagram for the reactions between o-xylylene and SO<sub>2</sub>]]
The energies of the reactants, transition state and product for the exo, endo and cheletropic reactions are tabulated below. These are obtained from optimization at PM6 level.

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | o-Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;"| Exo
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|241.75
|style="text-align: center;"|56.31
|style="text-align: center;"|85.18
|style="text-align: center;"|-71.39
|-
!style="background: #0D4F8B; color: white;"| Endo
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|237.77
|style="text-align: center;"|56.98
|style="text-align: center;"|81.20
|style="text-align: center;"|-75.37
|-
!style="background: #0D4F8B; color: white;"| Cheletropic
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|260.09
|style="text-align: center;"|-0.01
|style="text-align: center;"|103.52
|style="text-align: center;"|-53.05
|-
|}

All three reactions are exothermic. The endo product is the kinetically favourable product as it has the lowest reaction barrier, while the cheletropic product is the thermodynamically favourable product as it has the lowest energy.
<br style="clear:right">

=== Vibration and Reaction Path ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
! style="background: #0D4F8B; color: white;" | Cheletropic
|-
! style="background: #0D4F8B; color: white;"| Vibration
|style="text-align: center;"| [[File:ex3 exo vibration tp1414.gif]]
|style="text-align: center;"| [[File:ex3 endo vibration tp1414.gif]]
|style="text-align: center;"| [[File:cheletropic vibration tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Vibrational Frequency
|style="text-align: center;"| 351.78i cm<sup>-1</sup>
|style="text-align: center;"| 334.38i cm<sup>-1</sup>
|style="text-align: center;"| 486.58i cm<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| Reaction Pathway
|style="text-align: center;"| [[File:exo IRC tp1414.gif]]
|style="text-align: center;"| [[File:endo IRC tp1414.gif]]
|style="text-align: center;"| [[File:cheletropic IRC tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Mechanism
|style="text-align: center;"| Asynchronous concerted
|style="text-align: center;"| Asynchronous concerted
|style="text-align: center;"| Synchronous concerted
|-
! style="background: #0D4F8B; color: white;"| IRC
|style="text-align: center;"| [[File:exoIRCtp1414.png]]
|style="text-align: center;"| [[File:endoIRCtp1414.png]]
|style="text-align: center;"| [[File:cheletropicIRCtp1414energy.png]]
|-
|}

It is interesting to note that the exo and endo reactions proceed via asynchronous mechanism in which the C-O bond is formed first before the C-S bond, while the cheletropic reaction proceeds via synchronous mechanism in which the two C-S bonds are formed simultaneously. However, even though the formation of the two bonds are asynchronous in the exo and endo reactions, the total energy along the IRC tells us that both reactions are concerted as the reactions do not have any intermediate steps.

In all three reaction pathways, the steepest part on the the total energy versus IRC graph corresponds to the re-aromatisation of the 6-membered ring on the o-xylylene, giving these reactions an aromatic driving force. This also shows the instability of the o-xylylene molecule.

=== Alternate Diels-Alder Reaction ===

There is a second cis-butadiene fragment in o-xylylene that can undergo a Diels-Alder reaction. This second cis-butadiene is part of the cyclohexadiene ring. The exo and endo for this alternate Diels-Alder reaction proceed as follow:

[[File:alternatedielsalderexotp1414.gif]] [[File:alternatedielsalderendotp1414.gif]]

Both reactions proceed via an asynchronous mechanism.

[[File:energyprofilewithalternatedielsaldertp1414.jpg|600px|thumb|Energy profile diagram for the reactions between o-xylylene and SO<sub>2</sub>]]
The thermochemistry for this alternate Diels-Alder reaction is as follows:

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | o-Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;" | Exo
| style="text-align: center;" |467.99
| style="text-align: center;" |-311.42
| style="text-align: center;" |156.57
| style="text-align: center;" |275.82
| style="text-align: center;" |176.71
| style="text-align: center;" |119.25
| style="text-align: center;" |20.14
|-
! style="background: #0D4F8B; color: white;" | Endo
| style="text-align: center;" |467.99
| style="text-align: center;" |-311.42
| style="text-align: center;" |156.57
| style="text-align: center;" |267.98
| style="text-align: center;" |172.26
| style="text-align: center;" |111.41
| style="text-align: center;" |15.96
|-
|}

Comparing the energies for this alternate Diels-Alder reaction with the energies for the normal Diels-Alder and the cheletropic reactions, it can be seen that both the exo and endo alternate Diels-Alder reactoions are kinetically and thermodynamically unfavourable. The products are also higher in energies than the reactants, making the reactions endothermic.
<br style="clear:right">

=== Calculation Files ===

[[File:TP1414 Exercise 3 Xylylene.log]]

[[File:TP1414 Exercise 3 SO2.log]]

[[File:TP1414 Exercise 3 Exo Product.log]]

[[File:TP1414 Exercise 3 Endo Product.log]]

[[File:TP1414 Exercise 3 Cheletropic Product.log]]

[[File:TP1414 Exercise 3 Exo Transition State.log]]

[[File:TP1414 Exercise 3 Endo Transition State.log]]

[[File:TP1414 Exercise 3 Cheletropic Transition State.log]]

[[File:TP1414 Exercise 3 Exo IRC.log]]

[[File:TP1414 Exercise 3 Endo IRC.log]]

[[File:TP1414 Exercise 3 Cheletropic IRC.log]]

[[File:TP1414 Exercise 3 Alternate Exo Product.log]]

[[File:TP1414 Exercise 3 Alternate Endo Product.log]]

[[File:TP1414 Exercise 3 Alternate Exo Transition State.log]]

[[File:TP1414 Exercise 3 Alternate Endo Transition State.log]]

[[File:TP1414 Exercise 3 Alternate Exo IRC.log]]

[[File:TP1414 Exercise 3 Alternate Endo IRC.log]]

== Conclusion ==
Synchronous and asynchronous mechanism. Symmetrical molecules?

== References ==

<references>
<ref name="OrganicChemistryJoseph"> J. M. Hornback, ''Organic Chemistry'', Thomson Learning. Inc., Belmont, Second., 2006.</ref>
<ref name="TheMoleculesofLife"> J. Kuriyan, B. Konforti and D. Wemmer, ''The Molecules of Life: Physical and Chemical Principles'', Garland Science, New York, 2013.</ref>
<ref name="InverseElectronDemand"> A.-C. Knall and C. Slugovc, ''Chem Soc Rev'', 2013, '''42''', 5131–5142.</ref>
<ref name="TransitionsofElectronDemand"> E. Eibler, P. Hocht, B. Prantl, H. Rormaier, H. M. Schuhbauer and H. Wiest, ''Liebigs Ann.lRemei'', 1997, '''1997''', 2471–2484.</ref>
</references>

Rep:Mod:TP1414

2017-03-14T15:32:49Z

Tp1414: /* Vibration and Reaction Path */

== Introduction ==

=== Gaussian and Transition State Characterization ===

Gaussian is a molecular modelling software that allows researchers to carry out extensive investigation of molecules and their reactions. In these exercises, the transition states of several Diels-Alder reactions are located and characterized using Gaussian. A transition state is a first order saddle point on a potential energy surface (PES). It is the maximum along the minimum energy path (or reaction path) between two minima (the reactants and the products). ''Geometry optimization'' to find the minimum energy structure will usually lead to a stationary point that is closest to the initial geometry. The stationary point, where the first derivative of energy is zero, can be a global minimum, a local minimum or a saddle point. In a reaction path, the minima (global or local) correspond to the reactants and the products, while the saddle point corresponds to the transition state. To differentiate between a minimum and a saddle point, the second derivatives of energy will have to be analysed. For global or local minima, where energy rises in all directions, the second derivative of energy is positive. In contrast, for transition state, where the energy decreases in one direction (reaction path), the second derivative of energy along the reaction coordinate is negative. The analysis of the second derivatives of energy can be done by a ''frequency calculation'' of the optimized structure. If the structure corresponds to the reactants or products, all the vibrational frequencies are real. In contrast, if the structure corresponds to a transition state, there will be one imaginary frequency. This imaginary frequency indicates that the force constant (k), which is given by the second derivative, is negative.

[[File:frequencyequation.png|center]]

[[File:forceconstantequation.png|center]]

Following a successful frequency calculation (one imaginary frequency) of the transition state, an ''Intrinsic Reaction Coordinate (IRC) calculation'' may be set up to examine the transition state along the minimum energy path more closely. The reaction path, or minimum energy path, can be defined as the steepest descent path from the transition state to the reactions and products.

=== Diels-Alder Reactions ===

A Diels-Alder reaction is a [4+2] cycloadditon between a conjugated s-cis diene (4π-electron system) and a dienophile (2π-electron system). The reaction has a cyclic transition state with 6π-electrons, is concerted, and results in the formation of two new sigma bonds. According to the Woodward-Hoffmann Rules, the Diels-Alder reaction is thermally allowed and is an orbital-controlled reaction, in which the six electrons are interacting suprafacially. The reaction can mainly proceed in two ways:

# Normal electron demand: HOMO of diene overlaps with LUMO of dienophile
# Inverse electron demand: LUMO of diene overlaps with HOMO of dienophile

Several papers divide the Diels-Alder reactions into three categories instead of two <ref name="InverseElectronDemand"/> <ref name="TransitionsofElectronDemand"/>, the third being a neutral electron demand Diels-Alder, in which the energy separation between the HOMO and LUMO of both reactants is similar. <ref name="InverseElectronDemand"/> Neutral electron demand Diels-Alder reactions are seldom observed and believed to be a transition between normal electron demand and inverse electron demand Diels Alder reactions.<ref name="TransitionsofElectronDemand"/>

[[File:normalinverseneutral.jpeg|center|500px]]

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

The reaction between butadiene and ethylene presents the simplest type of Diels-Alder reaction, in which butadiene is the diene and ethylene is the dienophile. This reaction yields cyclohexene as the product, and the reaction scheme is as follow:

[[File:exercise 1 reaction scheme.jpg|center]]

=== Molecular Orbital Diagram ===

[[File:MO diagram for exercise 1 TP1414.jpg|500px|thumb|center|Molecular orbital (MO) diagram for the reaction of butadiene with ethylene]]
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Jmol
! style="background: #0D4F8B; color: white;" | Symmetry
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Jmol
! style="background: #0D4F8B; color: white;" | Symmetry
|-
! rowspan="2" style="background: #0D4F8B; color: white;"| Butadiene
! style="background: #0D4F8B; color: white;"| LUMO
|style="text-align: center;"| [[File:ex1butadieneLUMOtp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 BUTADIENE BREAK SYMMETRY JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 22; rotate x -90; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
! rowspan="4" style="background: #0D4F8B; color: white;"| Transition State
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex1mo4tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
|-
! style="background: #0D4F8B; color: white;"| HOMO
|style="text-align: center;"| [[File:ex1butadieneHOMOtp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 BUTADIENE BREAK SYMMETRY JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 22; rotate x -90; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex1mo3tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
|-
! rowspan="2" style="background: #0D4F8B; color: white;"| Ethylene
! style="background: #0D4F8B; color: white;"| LUMO
|style="text-align: center;"| [[File:ex1ethyleneLUMOtp1414.png|100px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 ETHYLENE JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 14; rotate z 90; rotate x 90; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex1mo2tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| HOMO
|style="text-align: center;"| [[File:ex1ethyleneHOMOtp1414.png|100px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 ETHYLENE JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 14; rotate z 90; rotate x 90; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex1mo1tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
|-
|}

<br style="clear:right">

Only orbitals of the same symmetry can interact to form molecular orbitals. This means that only symmetric-symmetric interactions and antisymmetric-antisymmetric interactions are allowed. Symmetric-antisymmetric interactions, on the other hand, are forbidden. This is because the orbital overlap integral is non-zero for interactions between orbitals of the same symmetry and zero for interactions between orbitals of different symmetry.

As shown on the MO diagram above, both interactions (between the HOMO of butadiene and the LUMO of ethylene, and between the LUMO of butadiene and the HOMO of ethylene) occur, generating four molecular orbitals for the transition state. As the energy separation for the two interactions is similar, the reaction between butadiene and ethylene progress with aspects of both normal electron demand and inverse electron demand. This is because both butadiene and ethylene are neutral molecules without any obvious nucleophilic or electrophilic reacting centrers. Both molecules are neither electron-rich nor electron-poor. As a result, orbital overlap is possible for both HOMO-LUMO sets. Several papers classify this reaction as a neutral electron demand Diels-Alder. <ref name="InverseElectronDemand"/> <ref name="TransitionsofElectronDemand"/> This particular Diels-Alder reaction between butadiene and ethylene is well-known for its poor yield.

<br style="clear:left">

=== Internuclear Distances ===

[[File:internuclear distance.pdf|600px|thumb|right|Internuclear distances for the reaction of butadiene with ethylene to form cyclohexene.]]

[[File:butadiene and ethylene.jpg]]

{| class="wikitable"
|+ Internuclear Distances (Å)
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | C1-C2
! style="background: #0D4F8B; color: white;" | C2-C3
! style="background: #0D4F8B; color: white;" | C3-C4
! style="background: #0D4F8B; color: white;" | C4-C5
! style="background: #0D4F8B; color: white;" | C5-C6
! style="background: #0D4F8B; color: white;" | C6-C1
|-
! style="background: #0D4F8B; color: white;"| Reactants
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|style="text-align: center;"| -
|-
! style="background: #0D4F8B; color: white;"| Transition State
|style="text-align: center;"| 1.38
|style="text-align: center;"| 1.41
|style="text-align: center;"| 1.38
|style="text-align: center;"| 2.11
|style="text-align: center;"| 1.38
|style="text-align: center;"| 2.11
|-
! style="background: #0D4F8B; color: white;"| Product
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}

As the reaction progresses, C1-C2, C3-C4 and C5-C6 elongate as the double bond breaks to form single carbon-carbon bonds, while C2-C3 shortens to form carbon-carbon double bond. Simultaneously, C4-C5 and C6-C1 decrease in distance and ultimately single carbon-carbon bonds are formed. A more detailed overview of how the internuclear distances change over the course of the reaction is shown on the graph on the right.

A typical carbon-carbon single bond length is 1.54 Å and a typical carbon-carbon double bond length is 1.34 Å. <ref name="OrganicChemistryJoseph" />

The Van der Waals radius of one carbon atom is 1.70 Å. <ref name="TheMoleculesofLife" /> The length of the partly formed carbon-carbon bonds in the transition state is about 2.11 Å. This distance is shorter than twice the Van der Waals radius of carbon atom (3.40 Å), indicating bonding interactions are occuring.
<br style="clear:right">

=== Vibration and Reaction Path ===

[[File:exercisa1imaginaryfrequency.jpg]]

The vibration that corresponds to the reaction path at the transition state is illustrated above. This vibration has an imaginary frequency that occurs at 948.97i cm<sup>-1</sup>.

The formation of the two bonds are synchronous as shown below. This means that the two sigma bonds are formed simultaneously. hence, the reaction between butadiene and ethylene goes by a concerted synchronous mechanism.

[[File:IRCgif.jpg]]

=== Calculation Files ===

[[File:TP1414 Exercise 1 Ethylene.log]]

[[File:TP1414 Exercise 1 Butadiene.log]]

[[File:TP1414 Exercise 1 Product.log]]

[[File:TP1414 Exercise 1 Transition State.log]]

[[File:TP1414 Exercise 1 IRC.log]]

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

[[File:exercise 2 reaction schemetp1414.jpg|center]]

=== Molecular Orbital Diagram ===

[[File:ex 2 MO diagram for exo TS TP1414.jpg|left|500px|thumb|Molecular orbital (MO) diagram for the reaction of cyclohexadiene and 1,3-dioxole (exo).]]

[[File:ex 2 MO diagram for endo TS TP1414.jpg|500px|thumb|Molecular orbital (MO) diagram for the reaction of cyclohexadiene and 1,3-dioxole (endo).]]

<br style="clear:left">

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Image
! style="background: #0D4F8B; color: white;" | Symmetry
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Image
! style="background: #0D4F8B; color: white;" | Symmetry
|-
! rowspan="4" style="background: #0D4F8B; color: white;"| Exo
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex2exoMO4tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO4 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
! rowspan="4" style="background: #0D4F8B; color: white;"| Endo
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex2endoMO4tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO4 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
|-
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex2exoMO3tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO3 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex2endoMO3tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO3 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex2exoMO2tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO2 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex2endoMO2tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO2 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex2exoMO1tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO1 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex2endoMO1tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO1 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
|-
|}

Inverse electron demand Diels-Alder

=== Thermochemistry ===
[[File:ex2energyprofiletp1414.jpeg|600px|thumb|Energy profile diagram for the reactions between cyclohexadiene and 1,3-dioxole]]
The energies of the reactants, transition state and product for both the exo and endo reactions are tabulated below. These are obtained from optimization at B3LYP/6-31G(d) level.

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;"| Exo
|style="text-align: center;"|-612591.48
|style="text-align: center;"|-701187.43
|style="text-align: center;"|-1313778.91
|style="text-align: center;"|-1313614.33
|style="text-align: center;"|-1313845.77
|style="text-align: center;"|164.58
|style="text-align: center;"|-66.86
|-
!style="background: #0D4F8B; color: white;"| Endo
|style="text-align: center;"|-612591.48
|style="text-align: center;"|-701187.43
|style="text-align: center;"|-1313778.91
|style="text-align: center;"|-1313622.15
|style="text-align: center;"|-1313849.37
|style="text-align: center;"|156.76
|style="text-align: center;"|-70.46
|-
|}

Both the exo and endo reactions are exothermic. However, it can be seen that the energy of the endo product is lower (or more negative) than the energy of the exo product, and the endo reaction also has a lower reaction barrier as compared to the exo reaction. This means that the endo product is both the thermodynamically and kinetically favourable product. This can be explained by considering both electronic and steric factors

[[File:seondaryorbitalinteractionstp1414.png|500px|thumb|left|Secondary orbital interactions in endo transition state]] Secondary orbital interactions stabilize the endo transition state, reducing the reaction barrier. On the left is the HOMO of the endo transition state in which there are obvious secondary orbital interactions between the oxygen p orbitals of the 1,3-dioxole and the p orbitals of the diene. An MO representation of this HOMO is shown below.
[[File:secondaryorbitalinteractionMOrepresentationtp1414.jpeg|350px]]
<br style="clear:left">

[[File:stericclashtp1414.png|500px|thumb|left|Steric clash in exo product]] Steric clash between the sp<sup>3</sup> CH<sub>2</sub> of the dioxole ring and the sp<sup>3</sup> CH<sub>2</sub>'s of the cyclohexadiene destabilize both the exo transition state and the exo product.
<br style="clear:left">

=== Vibration and Reaction Path ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
! style="background: #0D4F8B; color: white;"| Vibration
|style="text-align: center;"| [[File:exercise2 exo vibration tp1414.gif]]
|style="text-align: center;"| [[File:exercise2 endo vibration tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Vibrational Frequency
|style="text-align: center;"| 520.90i cm<sup>-1</sup>
|style="text-align: center;"| 528.85i cm<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| Reaction Pathway
|style="text-align: center;"| [[File:exercise2 exo reaction path tp1414.gif]]
|style="text-align: center;"| [[File:exercise2 endo reaction path tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Mechanism
|style="text-align: center;"| Synchronous concerted
|style="text-align: center;"| Synchronous concerted
|-
|}

=== Calculation Files ===

[[File:TP1414 Exercise 2 Cyclohexadiene 631Gd.log]]

[[File:TP1414 Exercise 2 1,2-Dioxole 631Gd.log]]

[[File:TP1414 Exercise 2 Exo Product 631Gd.log]]

[[File:TP1414 Exercise 2 Endo Product 631Gd.log]]

[[File:TP1414 Exercise 2 Exo Transition State 631Gd.log]]

[[File:TP1414 Exercise 2 Endo Transition State 631Gd.log]]

[[File:TP1414 Exercise 2 Exo IRC 631Gd.log]]

[[File:TP1414 Exercise 2 Endo IRC 631Gd.log]]

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

[[File:exercise3reactionschemetp1414.jpg|center]]

=== Thermochemistry ===
[[File:ex3energyprofiletp1414.jpg|600px|thumb|Energy profile diagram for the reactions between o-xylylene and SO<sub>2</sub>]]
The energies of the reactants, transition state and product for the exo, endo and cheletropic reactions are tabulated below. These are obtained from optimization at PM6 level.

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | o-Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;"| Exo
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|241.75
|style="text-align: center;"|56.31
|style="text-align: center;"|85.18
|style="text-align: center;"|-71.39
|-
!style="background: #0D4F8B; color: white;"| Endo
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|237.77
|style="text-align: center;"|56.98
|style="text-align: center;"|81.20
|style="text-align: center;"|-75.37
|-
!style="background: #0D4F8B; color: white;"| Cheletropic
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|260.09
|style="text-align: center;"|-0.01
|style="text-align: center;"|103.52
|style="text-align: center;"|-53.05
|-
|}

All three reactions are exothermic. The endo product is the kinetically favourable product as it has the lowest reaction barrier, while the cheletropic product is the thermodynamically favourable product as it has the lowest energy.
<br style="clear:right">

=== Vibration and Reaction Path ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
! style="background: #0D4F8B; color: white;" | Cheletropic
|-
! style="background: #0D4F8B; color: white;"| Vibration
|style="text-align: center;"| [[File:ex3 exo vibration tp1414.gif]]
|style="text-align: center;"| [[File:ex3 endo vibration tp1414.gif]]
|style="text-align: center;"| [[File:cheletropic vibration tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Vibrational Frequency
|style="text-align: center;"| 351.78i cm<sup>-1</sup>
|style="text-align: center;"| 334.38i cm<sup>-1</sup>
|style="text-align: center;"| 486.58i cm<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| Reaction Pathway
|style="text-align: center;"| [[File:exo IRC tp1414.gif]]
|style="text-align: center;"| [[File:endo IRC tp1414.gif]]
|style="text-align: center;"| [[File:cheletropic IRC tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Mechanism
|style="text-align: center;"| Asynchronous concerted
|style="text-align: center;"| Asynchronous concerted
|style="text-align: center;"| Synchronous concerted
|-
! style="background: #0D4F8B; color: white;"| IRC
|style="text-align: center;"| [[File:exoIRCtp1414.png]]
|style="text-align: center;"| [[File:endoIRCtp1414.png]]
|style="text-align: center;"| [[File:cheletropicIRCtp1414energy.png]]
|-
|}

It is interesting to note that the exo and endo reactions proceed via asynchronous mechanism in which the C-O bond is formed first before the C-S bond, while the cheletropic reaction proceeds via synchronous mechanism in which the two C-S bonds are formed simultaneously. However, even though the formation of the two bonds are asynchronous in the exo and endo reactions, the total energy along the IRC tells us that both reactions are concerted as the reactions do not have any intermediate steps.

In all three reaction pathways, the steepest part on the the total energy versus IRC graph corresponds to the re-aromatisation of the 6-membered ring on the o-xylylene.

=== Alternate Diels-Alder Reaction ===

There is a second cis-butadiene fragment in o-xylylene that can undergo a Diels-Alder reaction. This second cis-butadiene is part of the cyclohexadiene ring. The exo and endo for this alternate Diels-Alder reaction proceed as follow:

[[File:alternatedielsalderexotp1414.gif]] [[File:alternatedielsalderendotp1414.gif]]

Both reactions proceed via an asynchronous mechanism.

[[File:energyprofilewithalternatedielsaldertp1414.jpg|600px|thumb|Energy profile diagram for the reactions between o-xylylene and SO<sub>2</sub>]]
The thermochemistry for this alternate Diels-Alder reaction is as follows:

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | o-Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;" | Exo
| style="text-align: center;" |467.99
| style="text-align: center;" |-311.42
| style="text-align: center;" |156.57
| style="text-align: center;" |275.82
| style="text-align: center;" |176.71
| style="text-align: center;" |119.25
| style="text-align: center;" |20.14
|-
! style="background: #0D4F8B; color: white;" | Endo
| style="text-align: center;" |467.99
| style="text-align: center;" |-311.42
| style="text-align: center;" |156.57
| style="text-align: center;" |267.98
| style="text-align: center;" |172.26
| style="text-align: center;" |111.41
| style="text-align: center;" |15.96
|-
|}

Comparing the energies for this alternate Diels-Alder reaction with the energies for the normal Diels-Alder and the cheletropic reactions, it can be seen that both the exo and endo alternate Diels-Alder reactoions are kinetically and thermodynamically unfavourable. The products are also higher in energies than the reactants, making the reactions endothermic.
<br style="clear:right">

=== Calculation Files ===

[[File:TP1414 Exercise 3 Xylylene.log]]

[[File:TP1414 Exercise 3 SO2.log]]

[[File:TP1414 Exercise 3 Exo Product.log]]

[[File:TP1414 Exercise 3 Endo Product.log]]

[[File:TP1414 Exercise 3 Cheletropic Product.log]]

[[File:TP1414 Exercise 3 Exo Transition State.log]]

[[File:TP1414 Exercise 3 Endo Transition State.log]]

[[File:TP1414 Exercise 3 Cheletropic Transition State.log]]

[[File:TP1414 Exercise 3 Exo IRC.log]]

[[File:TP1414 Exercise 3 Endo IRC.log]]

[[File:TP1414 Exercise 3 Cheletropic IRC.log]]

[[File:TP1414 Exercise 3 Alternate Exo Product.log]]

[[File:TP1414 Exercise 3 Alternate Endo Product.log]]

[[File:TP1414 Exercise 3 Alternate Exo Transition State.log]]

[[File:TP1414 Exercise 3 Alternate Endo Transition State.log]]

[[File:TP1414 Exercise 3 Alternate Exo IRC.log]]

[[File:TP1414 Exercise 3 Alternate Endo IRC.log]]

== Conclusion ==
Synchronous and asynchronous mechanism. Symmetrical molecules?

== References ==

<references>
<ref name="OrganicChemistryJoseph"> J. M. Hornback, ''Organic Chemistry'', Thomson Learning. Inc., Belmont, Second., 2006.</ref>
<ref name="TheMoleculesofLife"> J. Kuriyan, B. Konforti and D. Wemmer, ''The Molecules of Life: Physical and Chemical Principles'', Garland Science, New York, 2013.</ref>
<ref name="InverseElectronDemand"> A.-C. Knall and C. Slugovc, ''Chem Soc Rev'', 2013, '''42''', 5131–5142.</ref>
<ref name="TransitionsofElectronDemand"> E. Eibler, P. Hocht, B. Prantl, H. Rormaier, H. M. Schuhbauer and H. Wiest, ''Liebigs Ann.lRemei'', 1997, '''1997''', 2471–2484.</ref>
</references>

Rep:Mod:TP1414

2017-03-14T15:22:52Z

Tp1414: /* Vibration and Reaction Path */

== Introduction ==

=== Gaussian and Transition State Characterization ===

Gaussian is a molecular modelling software that allows researchers to carry out extensive investigation of molecules and their reactions. In these exercises, the transition states of several Diels-Alder reactions are located and characterized using Gaussian. A transition state is a first order saddle point on a potential energy surface (PES). It is the maximum along the minimum energy path (or reaction path) between two minima (the reactants and the products). ''Geometry optimization'' to find the minimum energy structure will usually lead to a stationary point that is closest to the initial geometry. The stationary point, where the first derivative of energy is zero, can be a global minimum, a local minimum or a saddle point. In a reaction path, the minima (global or local) correspond to the reactants and the products, while the saddle point corresponds to the transition state. To differentiate between a minimum and a saddle point, the second derivatives of energy will have to be analysed. For global or local minima, where energy rises in all directions, the second derivative of energy is positive. In contrast, for transition state, where the energy decreases in one direction (reaction path), the second derivative of energy along the reaction coordinate is negative. The analysis of the second derivatives of energy can be done by a ''frequency calculation'' of the optimized structure. If the structure corresponds to the reactants or products, all the vibrational frequencies are real. In contrast, if the structure corresponds to a transition state, there will be one imaginary frequency. This imaginary frequency indicates that the force constant (k), which is given by the second derivative, is negative.

[[File:frequencyequation.png|center]]

[[File:forceconstantequation.png|center]]

Following a successful frequency calculation (one imaginary frequency) of the transition state, an ''Intrinsic Reaction Coordinate (IRC) calculation'' may be set up to examine the transition state along the minimum energy path more closely. The reaction path, or minimum energy path, can be defined as the steepest descent path from the transition state to the reactions and products.

=== Diels-Alder Reactions ===

A Diels-Alder reaction is a [4+2] cycloadditon between a conjugated s-cis diene (4π-electron system) and a dienophile (2π-electron system). The reaction has a cyclic transition state with 6π-electrons, is concerted, and results in the formation of two new sigma bonds. According to the Woodward-Hoffmann Rules, the Diels-Alder reaction is thermally allowed and is an orbital-controlled reaction, in which the six electrons are interacting suprafacially. The reaction can mainly proceed in two ways:

# Normal electron demand: HOMO of diene overlaps with LUMO of dienophile
# Inverse electron demand: LUMO of diene overlaps with HOMO of dienophile

Several papers divide the Diels-Alder reactions into three categories instead of two <ref name="InverseElectronDemand"/> <ref name="TransitionsofElectronDemand"/>, the third being a neutral electron demand Diels-Alder, in which the energy separation between the HOMO and LUMO of both reactants is similar. <ref name="InverseElectronDemand"/> Neutral electron demand Diels-Alder reactions are seldom observed and believed to be a transition between normal electron demand and inverse electron demand Diels Alder reactions.<ref name="TransitionsofElectronDemand"/>

[[File:normalinverseneutral.jpeg|center|500px]]

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

The reaction between butadiene and ethylene presents the simplest type of Diels-Alder reaction, in which butadiene is the diene and ethylene is the dienophile. This reaction yields cyclohexene as the product, and the reaction scheme is as follow:

[[File:exercise 1 reaction scheme.jpg|center]]

=== Molecular Orbital Diagram ===

[[File:MO diagram for exercise 1 TP1414.jpg|500px|thumb|center|Molecular orbital (MO) diagram for the reaction of butadiene with ethylene]]
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Jmol
! style="background: #0D4F8B; color: white;" | Symmetry
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Jmol
! style="background: #0D4F8B; color: white;" | Symmetry
|-
! rowspan="2" style="background: #0D4F8B; color: white;"| Butadiene
! style="background: #0D4F8B; color: white;"| LUMO
|style="text-align: center;"| [[File:ex1butadieneLUMOtp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 BUTADIENE BREAK SYMMETRY JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 22; rotate x -90; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
! rowspan="4" style="background: #0D4F8B; color: white;"| Transition State
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex1mo4tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
|-
! style="background: #0D4F8B; color: white;"| HOMO
|style="text-align: center;"| [[File:ex1butadieneHOMOtp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 BUTADIENE BREAK SYMMETRY JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 22; rotate x -90; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex1mo3tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
|-
! rowspan="2" style="background: #0D4F8B; color: white;"| Ethylene
! style="background: #0D4F8B; color: white;"| LUMO
|style="text-align: center;"| [[File:ex1ethyleneLUMOtp1414.png|100px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 ETHYLENE JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 14; rotate z 90; rotate x 90; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex1mo2tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| HOMO
|style="text-align: center;"| [[File:ex1ethyleneHOMOtp1414.png|100px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>TP1414 ETHYLENE JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 14; rotate z 90; rotate x 90; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex1mo1tp1414.png|150px]]
|style="text-align: center;"| <jmol><jmolApplet><uploadedFileContents>BUTADIENE ETHYLENE GUESSTS PM6 JMOL.LOG</uploadedFileContents><size>200</size><color>white</color><script>frame 38; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script></jmolApplet></jmol>
|style="text-align: center;"| Antisymmetric
|-
|}

<br style="clear:right">

Only orbitals of the same symmetry can interact to form molecular orbitals. This means that only symmetric-symmetric interactions and antisymmetric-antisymmetric interactions are allowed. Symmetric-antisymmetric interactions, on the other hand, are forbidden. This is because the orbital overlap integral is non-zero for interactions between orbitals of the same symmetry and zero for interactions between orbitals of different symmetry.

As shown on the MO diagram above, both interactions (between the HOMO of butadiene and the LUMO of ethylene, and between the LUMO of butadiene and the HOMO of ethylene) occur, generating four molecular orbitals for the transition state. As the energy separation for the two interactions is similar, the reaction between butadiene and ethylene progress with aspects of both normal electron demand and inverse electron demand. This is because both butadiene and ethylene are neutral molecules without any obvious nucleophilic or electrophilic reacting centrers. Both molecules are neither electron-rich nor electron-poor. As a result, orbital overlap is possible for both HOMO-LUMO sets. Several papers classify this reaction as a neutral electron demand Diels-Alder. <ref name="InverseElectronDemand"/> <ref name="TransitionsofElectronDemand"/> This particular Diels-Alder reaction between butadiene and ethylene is well-known for its poor yield.

<br style="clear:left">

=== Internuclear Distances ===

[[File:internuclear distance.pdf|600px|thumb|right|Internuclear distances for the reaction of butadiene with ethylene to form cyclohexene.]]

[[File:butadiene and ethylene.jpg]]

{| class="wikitable"
|+ Internuclear Distances (Å)
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | C1-C2
! style="background: #0D4F8B; color: white;" | C2-C3
! style="background: #0D4F8B; color: white;" | C3-C4
! style="background: #0D4F8B; color: white;" | C4-C5
! style="background: #0D4F8B; color: white;" | C5-C6
! style="background: #0D4F8B; color: white;" | C6-C1
|-
! style="background: #0D4F8B; color: white;"| Reactants
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.47
|style="text-align: center;"| 1.34
|style="text-align: center;"| -
|style="text-align: center;"| 1.33
|style="text-align: center;"| -
|-
! style="background: #0D4F8B; color: white;"| Transition State
|style="text-align: center;"| 1.38
|style="text-align: center;"| 1.41
|style="text-align: center;"| 1.38
|style="text-align: center;"| 2.11
|style="text-align: center;"| 1.38
|style="text-align: center;"| 2.11
|-
! style="background: #0D4F8B; color: white;"| Product
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.34
|style="text-align: center;"| 1.50
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|style="text-align: center;"| 1.54
|}

As the reaction progresses, C1-C2, C3-C4 and C5-C6 elongate as the double bond breaks to form single carbon-carbon bonds, while C2-C3 shortens to form carbon-carbon double bond. Simultaneously, C4-C5 and C6-C1 decrease in distance and ultimately single carbon-carbon bonds are formed. A more detailed overview of how the internuclear distances change over the course of the reaction is shown on the graph on the right.

A typical carbon-carbon single bond length is 1.54 Å and a typical carbon-carbon double bond length is 1.34 Å. <ref name="OrganicChemistryJoseph" />

The Van der Waals radius of one carbon atom is 1.70 Å. <ref name="TheMoleculesofLife" /> The length of the partly formed carbon-carbon bonds in the transition state is about 2.11 Å. This distance is shorter than twice the Van der Waals radius of carbon atom (3.40 Å), indicating bonding interactions are occuring.
<br style="clear:right">

=== Vibration and Reaction Path ===

[[File:exercisa1imaginaryfrequency.jpg]]

The vibration that corresponds to the reaction path at the transition state is illustrated above. This vibration has an imaginary frequency that occurs at 948.97i cm<sup>-1</sup>.

The formation of the two bonds are synchronous as shown below. This means that the two sigma bonds are formed simultaneously. hence, the reaction between butadiene and ethylene goes by a concerted synchronous mechanism.

[[File:IRCgif.jpg]]

=== Calculation Files ===

[[File:TP1414 Exercise 1 Ethylene.log]]

[[File:TP1414 Exercise 1 Butadiene.log]]

[[File:TP1414 Exercise 1 Product.log]]

[[File:TP1414 Exercise 1 Transition State.log]]

[[File:TP1414 Exercise 1 IRC.log]]

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

[[File:exercise 2 reaction schemetp1414.jpg|center]]

=== Molecular Orbital Diagram ===

[[File:ex 2 MO diagram for exo TS TP1414.jpg|left|500px|thumb|Molecular orbital (MO) diagram for the reaction of cyclohexadiene and 1,3-dioxole (exo).]]

[[File:ex 2 MO diagram for endo TS TP1414.jpg|500px|thumb|Molecular orbital (MO) diagram for the reaction of cyclohexadiene and 1,3-dioxole (endo).]]

<br style="clear:left">

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Image
! style="background: #0D4F8B; color: white;" | Symmetry
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | MO Representation
! style="background: #0D4F8B; color: white;" | Image
! style="background: #0D4F8B; color: white;" | Symmetry
|-
! rowspan="4" style="background: #0D4F8B; color: white;"| Exo
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex2exoMO4tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO4 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
! rowspan="4" style="background: #0D4F8B; color: white;"| Endo
! style="background: #0D4F8B; color: white;"| MO 4
LUMO+1
|style="text-align: center;"| [[File:ex2endoMO4tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO4 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
|-
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex2exoMO3tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO3 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 3
LUMO
|style="text-align: center;"| [[File:ex2endoMO3tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO3 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex2exoMO2tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO2 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
! style="background: #0D4F8B; color: white;"| MO 2
HOMO
|style="text-align: center;"| [[File:ex2endoMO2tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO2 tp1414.jpg|400px]]
|style="text-align: center;"| Symmetric
|-
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex2exoMO1tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 exo TS MO1 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
! style="background: #0D4F8B; color: white;"| MO 1
HOMO-1
|style="text-align: center;"| [[File:ex2endoMO1tp1414.png|100px]]
|style="text-align: center;"| [[File:ex2 endo MO1 tp1414.jpg|400px]]
|style="text-align: center;"| Antisymmetric
|-
|}

Inverse electron demand Diels-Alder

=== Thermochemistry ===
[[File:ex2energyprofiletp1414.jpeg|600px|thumb|Energy profile diagram for the reactions between cyclohexadiene and 1,3-dioxole]]
The energies of the reactants, transition state and product for both the exo and endo reactions are tabulated below. These are obtained from optimization at B3LYP/6-31G(d) level.

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | Cyclohexadiene
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;"| Exo
|style="text-align: center;"|-612591.48
|style="text-align: center;"|-701187.43
|style="text-align: center;"|-1313778.91
|style="text-align: center;"|-1313614.33
|style="text-align: center;"|-1313845.77
|style="text-align: center;"|164.58
|style="text-align: center;"|-66.86
|-
!style="background: #0D4F8B; color: white;"| Endo
|style="text-align: center;"|-612591.48
|style="text-align: center;"|-701187.43
|style="text-align: center;"|-1313778.91
|style="text-align: center;"|-1313622.15
|style="text-align: center;"|-1313849.37
|style="text-align: center;"|156.76
|style="text-align: center;"|-70.46
|-
|}

Both the exo and endo reactions are exothermic. However, it can be seen that the energy of the endo product is lower (or more negative) than the energy of the exo product, and the endo reaction also has a lower reaction barrier as compared to the exo reaction. This means that the endo product is both the thermodynamically and kinetically favourable product. This can be explained by considering both electronic and steric factors

[[File:seondaryorbitalinteractionstp1414.png|500px|thumb|left|Secondary orbital interactions in endo transition state]] Secondary orbital interactions stabilize the endo transition state, reducing the reaction barrier. On the left is the HOMO of the endo transition state in which there are obvious secondary orbital interactions between the oxygen p orbitals of the 1,3-dioxole and the p orbitals of the diene. An MO representation of this HOMO is shown below.
[[File:secondaryorbitalinteractionMOrepresentationtp1414.jpeg|350px]]
<br style="clear:left">

[[File:stericclashtp1414.png|500px|thumb|left|Steric clash in exo product]] Steric clash between the sp<sup>3</sup> CH<sub>2</sub> of the dioxole ring and the sp<sup>3</sup> CH<sub>2</sub>'s of the cyclohexadiene destabilize both the exo transition state and the exo product.
<br style="clear:left">

=== Vibration and Reaction Path ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
! style="background: #0D4F8B; color: white;"| Vibration
|style="text-align: center;"| [[File:exercise2 exo vibration tp1414.gif]]
|style="text-align: center;"| [[File:exercise2 endo vibration tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Vibrational Frequency
|style="text-align: center;"| 520.90i cm<sup>-1</sup>
|style="text-align: center;"| 528.85i cm<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| Reaction Pathway
|style="text-align: center;"| [[File:exercise2 exo reaction path tp1414.gif]]
|style="text-align: center;"| [[File:exercise2 endo reaction path tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Mechanism
|style="text-align: center;"| Synchronous concerted
|style="text-align: center;"| Synchronous concerted
|-
|}

=== Calculation Files ===

[[File:TP1414 Exercise 2 Cyclohexadiene 631Gd.log]]

[[File:TP1414 Exercise 2 1,2-Dioxole 631Gd.log]]

[[File:TP1414 Exercise 2 Exo Product 631Gd.log]]

[[File:TP1414 Exercise 2 Endo Product 631Gd.log]]

[[File:TP1414 Exercise 2 Exo Transition State 631Gd.log]]

[[File:TP1414 Exercise 2 Endo Transition State 631Gd.log]]

[[File:TP1414 Exercise 2 Exo IRC 631Gd.log]]

[[File:TP1414 Exercise 2 Endo IRC 631Gd.log]]

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

[[File:exercise3reactionschemetp1414.jpg|center]]

=== Thermochemistry ===
[[File:ex3energyprofiletp1414.jpg|600px|thumb|Energy profile diagram for the reactions between o-xylylene and SO<sub>2</sub>]]
The energies of the reactants, transition state and product for the exo, endo and cheletropic reactions are tabulated below. These are obtained from optimization at PM6 level.

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | o-Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;"| Exo
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|241.75
|style="text-align: center;"|56.31
|style="text-align: center;"|85.18
|style="text-align: center;"|-71.39
|-
!style="background: #0D4F8B; color: white;"| Endo
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|237.77
|style="text-align: center;"|56.98
|style="text-align: center;"|81.20
|style="text-align: center;"|-75.37
|-
!style="background: #0D4F8B; color: white;"| Cheletropic
|style="text-align: center;"|467.99
|style="text-align: center;"|-311.42
|style="text-align: center;"|156.57
|style="text-align: center;"|260.09
|style="text-align: center;"|-0.01
|style="text-align: center;"|103.52
|style="text-align: center;"|-53.05
|-
|}

All three reactions are exothermic. The endo product is the kinetically favourable product as it has the lowest reaction barrier, while the cheletropic product is the thermodynamically favourable product as it has the lowest energy.
<br style="clear:right">

=== Vibration and Reaction Path ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
! style="background: #0D4F8B; color: white;" | Cheletropic
|-
! style="background: #0D4F8B; color: white;"| Vibration
|style="text-align: center;"| [[File:ex3 exo vibration tp1414.gif]]
|style="text-align: center;"| [[File:ex3 endo vibration tp1414.gif]]
|style="text-align: center;"| [[File:cheletropic vibration tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Vibrational Frequency
|style="text-align: center;"| 351.78i cm<sup>-1</sup>
|style="text-align: center;"| 334.38i cm<sup>-1</sup>
|style="text-align: center;"| 486.58i cm<sup>-1</sup>
|-
! style="background: #0D4F8B; color: white;"| Reaction Pathway
|style="text-align: center;"| [[File:exo IRC tp1414.gif]]
|style="text-align: center;"| [[File:endo IRC tp1414.gif]]
|style="text-align: center;"| [[File:cheletropic IRC tp1414.gif]]
|-
! style="background: #0D4F8B; color: white;"| Mechanism
|style="text-align: center;"| Asynchronous concerted
|style="text-align: center;"| Asynchronous concerted
|style="text-align: center;"| Synchronous concerted
|-
! style="background: #0D4F8B; color: white;"| IRC
|style="text-align: center;"| [[File:exoIRCtp1414.png]]
|style="text-align: center;"| [[File:endoIRCtp1414.png]]
|style="text-align: center;"| [[File:cheletropicIRCtp1414energy.png]]
|-
|}

It is interesting to note that the exo and endo reactions proceed via asynchronous mechanism in which the C-O bond is formed first before the C-S bond, while the cheletropic reaction proceeds via synchronous mechanism in which the two C-S bonds are formed simultaneously. However, even though the formation of the two bonds are asynchronous in the exo and endo reactions, the total energy along the IRC tells us that both reactions are a concerted process as the reactions do not have any intermediate steps.

=== Alternate Diels-Alder Reaction ===

There is a second cis-butadiene fragment in o-xylylene that can undergo a Diels-Alder reaction. This second cis-butadiene is part of the cyclohexadiene ring. The exo and endo for this alternate Diels-Alder reaction proceed as follow:

[[File:alternatedielsalderexotp1414.gif]] [[File:alternatedielsalderendotp1414.gif]]

Both reactions proceed via an asynchronous mechanism.

[[File:energyprofilewithalternatedielsaldertp1414.jpg|600px|thumb|Energy profile diagram for the reactions between o-xylylene and SO<sub>2</sub>]]
The thermochemistry for this alternate Diels-Alder reaction is as follows:

{| class="wikitable"
|-
! rowspan="2" style="background: #0D4F8B; color: white;" |
! colspan="3" style="background: #0D4F8B; color: white;" | Energy of Reactants (kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Transition State
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Energy of Product
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Barrier
(kJ/mol)
! rowspan="2" style="background: #0D4F8B; color: white;" | Reaction Energy
(kJ/mol)
|-
! style="background: #0D4F8B; color: white;" | o-Xylylene
! style="background: #0D4F8B; color: white;" | SO<sub>2</sub>
! style="background: #0D4F8B; color: white;" | Total
|-
! style="background: #0D4F8B; color: white;" | Exo
| style="text-align: center;" |467.99
| style="text-align: center;" |-311.42
| style="text-align: center;" |156.57
| style="text-align: center;" |275.82
| style="text-align: center;" |176.71
| style="text-align: center;" |119.25
| style="text-align: center;" |20.14
|-
! style="background: #0D4F8B; color: white;" | Endo
| style="text-align: center;" |467.99
| style="text-align: center;" |-311.42
| style="text-align: center;" |156.57
| style="text-align: center;" |267.98
| style="text-align: center;" |172.26
| style="text-align: center;" |111.41
| style="text-align: center;" |15.96
|-
|}

Comparing the energies for this alternate Diels-Alder reaction with the energies for the normal Diels-Alder and the cheletropic reactions, it can be seen that both the exo and endo alternate Diels-Alder reactoions are kinetically and thermodynamically unfavourable. The products are also higher in energies than the reactants, making the reactions endothermic.
<br style="clear:right">

=== Calculation Files ===

[[File:TP1414 Exercise 3 Xylylene.log]]

[[File:TP1414 Exercise 3 SO2.log]]

[[File:TP1414 Exercise 3 Exo Product.log]]

[[File:TP1414 Exercise 3 Endo Product.log]]

[[File:TP1414 Exercise 3 Cheletropic Product.log]]

[[File:TP1414 Exercise 3 Exo Transition State.log]]

[[File:TP1414 Exercise 3 Endo Transition State.log]]

[[File:TP1414 Exercise 3 Cheletropic Transition State.log]]

[[File:TP1414 Exercise 3 Exo IRC.log]]

[[File:TP1414 Exercise 3 Endo IRC.log]]

[[File:TP1414 Exercise 3 Cheletropic IRC.log]]

[[File:TP1414 Exercise 3 Alternate Exo Product.log]]

[[File:TP1414 Exercise 3 Alternate Endo Product.log]]

[[File:TP1414 Exercise 3 Alternate Exo Transition State.log]]

[[File:TP1414 Exercise 3 Alternate Endo Transition State.log]]

[[File:TP1414 Exercise 3 Alternate Exo IRC.log]]

[[File:TP1414 Exercise 3 Alternate Endo IRC.log]]

== Conclusion ==
Synchronous and asynchronous mechanism. Symmetrical molecules?

== References ==

<references>
<ref name="OrganicChemistryJoseph"> J. M. Hornback, ''Organic Chemistry'', Thomson Learning. Inc., Belmont, Second., 2006.</ref>
<ref name="TheMoleculesofLife"> J. Kuriyan, B. Konforti and D. Wemmer, ''The Molecules of Life: Physical and Chemical Principles'', Garland Science, New York, 2013.</ref>
<ref name="InverseElectronDemand"> A.-C. Knall and C. Slugovc, ''Chem Soc Rev'', 2013, '''42''', 5131–5142.</ref>
<ref name="TransitionsofElectronDemand"> E. Eibler, P. Hocht, B. Prantl, H. Rormaier, H. M. Schuhbauer and H. Wiest, ''Liebigs Ann.lRemei'', 1997, '''1997''', 2471–2484.</ref>
</references>