Rep:Mod:tsch3114

2017-03-09T18:35:47Z

Ch3114: /* Thermochemistry */

2017-03-09T16:40:41Z

Ch3114:

Rep:Mod:tsch3114

2017-03-09T16:35:53Z

Ch3114: /* IRC */

== Introduction ==
During this lab, computational techniques were used to locate and characterise transition state structures during pericyclic reactions. A transition state is the configuration that corresponds to the highest energy point along the a reaction coordinate. It is a maximum point that links the reactants and the products. Knowing the location of a transition state gives important information regarding how a reaction progresses. Information on the mechanism (stepwise or concerted?), thermodynamics and kinetics can be obtained.

A reaction coordinate is an abstract one-dimensional representation of how far a reaction has progressed. In reality, all reactions have multiple degrees of freedom that will determine the energy of the system as for example, all atoms involved are able to move in three directions. The reaction coordinate is an abstraction of all degrees of freedom used to follow it. A potential energy surface (PES) is a 3D plot that includes two dimensions or coordinates. In a PES, the transition state is a saddle point between the reactants and products.

Gaussian and Gaussview were used to explore transitions state structures. Two computational techniques were used throughout the lab. The semi-empirical PM6 method, which is much faster as it relies on experimental data but less accurate, and the ab initio density functional theory (DFT) method which was used later on in each exercise as it gives a more accurate result but requires much more computation and time.

Throughout the lab, carbon atoms involved in bond formation were held at 2.2 Å. This value is found in-between an sp3 C-C bond and 2x carbon Van der Waals radii. Hence it is a good approximation for the transition state carbon-carbon distance.

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

=== Method ===
This reaction is the simplest possible example of a [4+2] cycloaddition, or Diels-Alder reaction, between a diene and a dienophile that are studied in this lab. It is a concerted pericyclic reaction that involves the formation of 2 σ-bonds and 1 π-bond and breaking 3 π-bonds, or the reverse. For this reaction, no regioselectivity needs to be considered because there are no addition groups bonded to either reactant.

Method 2 was used to calculate the TS structure for this reaction. It was decided that not enough information was known of the transition state structure to make an accurate guess. Initially reactants were constructed separately in Gaussian and optimised to a minimum to a PM6 level. They were confirmed to have no imaginary (i.e. negative) frequencies.

The reactants were then combined. Reacting carbons were held approximately 2.2 Å apart and the system was optimised to a minimum at a PM6 level. The transitions state (TS(berny)) was then optimised and the frequency was found at a PM6 level. It was confirmed that a transition state had been obtained by the presence of a single imaginary frequency. The transition state was then determined more accurately using DFT B3LYP/6-31G(d) technique. From this, transition state MOs were determined. An intrinsic reaction coordinate (IRC) calculation was carried out with 200 steps which further confirmed that the correct TS had been obtained.

=== IRC ===
{| class="wikitable" border=""1!"
|Intrinsic Reaction Coordinate || RMS Gradient Norm
|-
| style="text-align: center;" | [[File:IRC.jpg|600px]] || style="text-align: center;" | [[File:RMS.jpg|600px]] ||
|}

It can be seen that the transition state is found at a maximum and that the products and the reactants are found at minima. This can be used to confirm the success of the computation.

=== MOs ===

The MO diagrams shows that there has been a net destabalisation of reactants in order to form the transition state. This is expected as the transition state is found at an energy maximum.
Only fragment orbitals with the same symmetry label (gerade or ungerade) are able to combine to form MOs. Combinations of orbitals with opposite symmetry labels results in an overlap integral equal to zero. The given arrangement allows for constructive overlap (i.e. non-zero overlap integral) of orbitals found at the end of both pi system.

=== Normal vs. Inverse electron-demand Diels-Alder Reactions ===

This is an example of a normal electron-demand Diels-Alder reaction. Electrons are donated from the diene HOMO to the dienophile LUMO. This is the case for the majority of Diels-Alder reactions. Inverse electron-demand Diels-Alder reactions occur when the diene fragment orbitals are found lower in energy with respect to the dienophile. This is the result of an electron withdrawing group found on the diene and an electron donating group bonded to the dienophile.

=== C-C Bond Lengths ===
{| class="wikitable" border="1!
|+
|colspan = 4; style=text-align: center|C-C Bond Lengths/Å
|-
|C-C bond|| Reactants || Transition State || Products
|-
|1-2||1.33344||1.38307||1.50901
|-
|2-3||1.47083||1.40721||1.33697
|-
|3-4||1.33344||1.38307||1.50901
|-
|4-5||infinite||2.27215||1.54961
|-
|5-6||1.32731||1.38607||1.55524
|-
|6-1||infinite||2.27215||1.54961
|}

Bond Lengths changes as expected throughout the reaction. In the reactants, the three π-bonds (1-2, 3-4, 5-6) are shorter than the SIGMA bond (2-3). At the transition structure, the π-bonds are elongated as the π-bond interaction is broken to give a σ-bond. The SIGMA bond is shorter as it begins to form a π-bond. 3-4 and 6-1 are no longer an infinite distance apart. They are close enough to have a begin to form a bonding interaction in the transition structure. For the product, it can be seen that 1-2 and 3-4 are the same length, as are 4-5 and 6-1. σ-bond. This reflects the symmetric nature of the cyclohexene product. 2-3 is the only π-bond that remains. It is a similar length to π-bonds in reactants, reflecting the similar bonding environment.

=== Imaginary Vibration ===

A single imaginary vibration is found at the transition state of a reaction that corresponds to the reaction pathway. In this reaction, it is highly symmetrical, with both sets of carbons approaching each other at once. This is indicative of a single synchronous or concerted bond forming step.

[[File:CH3114_TS_imaginary_vibration.gif|thumb|400px|none| Imaginary vibration corresponding to the TS reaction path]]

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

This is another example of a Diels-Alder Reaction. Regioselectivity had to be taken into account as both endo and exo products are possible depending on the angle of approach of the reactants. Both isomers were computed using the same method as in excercise 1. Imaginary frequencies (endo: i520.87 cm-1; exo: i528.84 cm-1) were used to confirm that transition state structures had been obtained. The product structure was obtained by minimising the final structure of the forwards reaction of a PM6 IRC calculation using DFT to a B3lyp-631(g) level.

The MOs involved in bonding of the reactants and TSs are shown below.

This is an example of an inverse electron-demand Diels-Alder reaction. Two oxygen atoms bonded to the π-bond are electron-withdrawing groups. This raises the HOMO energy enough to change how bonding occurs.

===Thermochemistry ===

Thermochemistry data was taken from the B3lyp-631(g) minima. It was found that PM6 data was very different but showed the same trends.

{| class="wikitable"
!
!Reactants kJ/mol
!Transition State kJ/mol
!Product kJ/mol
!Activation Energy kJ/mol
!Gibbs Free Energy of reaction kJ/mol
|-

|Exo reaction
!-1313780.527
!-1313614.231
!-1313845.679
!166.2965445
!-65.1517825
|-

|Endo reaction
!-1313780.527
!-1313622.057
!-1313849.273
!158.469929
!-68.746092
|}

The thermochemistry data shows that the endo Diels-Alder reaction is kinetically more favoured than the exo reaction as the transition state has a lower energy. This can be explained by considering the through-space interaction of the O atom p-orbital lone pairs and the forming π-bond. This positive interaction lowers the energy of the transition state structure. Hence the endo product is formed faster. In the exo transition state, the oxygen atoms face away from the π-bond so no stabalising interaction can take place

The endo product is also thermodynamically more favoured as the Gibbs Free Energy of reaction is more negative. Both reactions have a negative Gibbs so the forwards reaction is more favoured. It is evident that they should have similar Gibbs values as they are structurally very similar.

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

A Cheletropic reaction is another example of a pericylci reaction. It differs from a Diels-Alder reaction as both new bonds are bonded to the same atom.
===IRC===
{| class="wikitable" border="1!
| Exo DA || Endo DA || Cheletropic
|-
| [[File:CH3114 GIF 3 EXO IRC.gif|400px]] || [[File:CH3114_2_3_ENDO_IRC.gif|400px]] https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:CH3114_2_3_ENDO_IRC.gif || [[File:CH3114_3_CHEL_IRC.gif|400px]]
|-
| [[File:CH3114_3_EXO_IRC.jpg|350px]] || [[File:CH3114_2_3_ENDO_IRC.jpg|350px]] || [[File:CH3114_CHELO_IRC.jpg|350px]]
|}

===Thermochemistry===
{| class="wikitable"
!
!Reactants kJ/mol
!Transition State kJ/mol
!Product kJ/mol
!Activation Energy kJ/mol
!Gibbs Free Energy of reaction kJ/mol
|-

|Exo reaction
!153.470977
!241.7481635
!56.3301025
!88.2771865
!-97.1408745
|-

|Endo reaction
!153.470977
!237.76528
!56.962848
!84.294303
!-96.508129
|-

|Cheletropic reaction
!153.470977
!260.0846555
!0.0078765
!106.6136785
!-153.4631005
|}

It can be seen that the cheletropic reaction is has the highest activation energy so is the kinetically least favoured. It is however the most thermodynamically favoured.

The Exo Diels-Alder reaction is less kinetically favoured and more thermodynamically favoured. This is for the same reasons as in exercise 2.

Rep:Mod:tsch3114

2017-03-09T16:35:26Z

Ch3114: /* IRC */

== Introduction ==
During this lab, computational techniques were used to locate and characterise transition state structures during pericyclic reactions. A transition state is the configuration that corresponds to the highest energy point along the a reaction coordinate. It is a maximum point that links the reactants and the products. Knowing the location of a transition state gives important information regarding how a reaction progresses. Information on the mechanism (stepwise or concerted?), thermodynamics and kinetics can be obtained.

A reaction coordinate is an abstract one-dimensional representation of how far a reaction has progressed. In reality, all reactions have multiple degrees of freedom that will determine the energy of the system as for example, all atoms involved are able to move in three directions. The reaction coordinate is an abstraction of all degrees of freedom used to follow it. A potential energy surface (PES) is a 3D plot that includes two dimensions or coordinates. In a PES, the transition state is a saddle point between the reactants and products.

Gaussian and Gaussview were used to explore transitions state structures. Two computational techniques were used throughout the lab. The semi-empirical PM6 method, which is much faster as it relies on experimental data but less accurate, and the ab initio density functional theory (DFT) method which was used later on in each exercise as it gives a more accurate result but requires much more computation and time.

Throughout the lab, carbon atoms involved in bond formation were held at 2.2 Å. This value is found in-between an sp3 C-C bond and 2x carbon Van der Waals radii. Hence it is a good approximation for the transition state carbon-carbon distance.

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

=== Method ===
This reaction is the simplest possible example of a [4+2] cycloaddition, or Diels-Alder reaction, between a diene and a dienophile that are studied in this lab. It is a concerted pericyclic reaction that involves the formation of 2 σ-bonds and 1 π-bond and breaking 3 π-bonds, or the reverse. For this reaction, no regioselectivity needs to be considered because there are no addition groups bonded to either reactant.

Method 2 was used to calculate the TS structure for this reaction. It was decided that not enough information was known of the transition state structure to make an accurate guess. Initially reactants were constructed separately in Gaussian and optimised to a minimum to a PM6 level. They were confirmed to have no imaginary (i.e. negative) frequencies.

The reactants were then combined. Reacting carbons were held approximately 2.2 Å apart and the system was optimised to a minimum at a PM6 level. The transitions state (TS(berny)) was then optimised and the frequency was found at a PM6 level. It was confirmed that a transition state had been obtained by the presence of a single imaginary frequency. The transition state was then determined more accurately using DFT B3LYP/6-31G(d) technique. From this, transition state MOs were determined. An intrinsic reaction coordinate (IRC) calculation was carried out with 200 steps which further confirmed that the correct TS had been obtained.

=== IRC ===
{| class="wikitable" border=""1!"
|Intrinsic Reaction Coordinate || RMS Gradient Norm
|-
| style="text-align: center;" | [[File:IRC.jpg|600px]] || style="text-align: center;" | [[File:RMS.jpg|600px]] ||
|}

It can be seen that the transition state is found at a maximum and that the products and the reactants are found at minima. This can be used to confirm the success of the computation.

=== MOs ===

The MO diagrams shows that there has been a net destabalisation of reactants in order to form the transition state. This is expected as the transition state is found at an energy maximum.
Only fragment orbitals with the same symmetry label (gerade or ungerade) are able to combine to form MOs. Combinations of orbitals with opposite symmetry labels results in an overlap integral equal to zero. The given arrangement allows for constructive overlap (i.e. non-zero overlap integral) of orbitals found at the end of both pi system.

=== Normal vs. Inverse electron-demand Diels-Alder Reactions ===

This is an example of a normal electron-demand Diels-Alder reaction. Electrons are donated from the diene HOMO to the dienophile LUMO. This is the case for the majority of Diels-Alder reactions. Inverse electron-demand Diels-Alder reactions occur when the diene fragment orbitals are found lower in energy with respect to the dienophile. This is the result of an electron withdrawing group found on the diene and an electron donating group bonded to the dienophile.

=== C-C Bond Lengths ===
{| class="wikitable" border="1!
|+
|colspan = 4; style=text-align: center|C-C Bond Lengths/Å
|-
|C-C bond|| Reactants || Transition State || Products
|-
|1-2||1.33344||1.38307||1.50901
|-
|2-3||1.47083||1.40721||1.33697
|-
|3-4||1.33344||1.38307||1.50901
|-
|4-5||infinite||2.27215||1.54961
|-
|5-6||1.32731||1.38607||1.55524
|-
|6-1||infinite||2.27215||1.54961
|}

Bond Lengths changes as expected throughout the reaction. In the reactants, the three π-bonds (1-2, 3-4, 5-6) are shorter than the SIGMA bond (2-3). At the transition structure, the π-bonds are elongated as the π-bond interaction is broken to give a σ-bond. The SIGMA bond is shorter as it begins to form a π-bond. 3-4 and 6-1 are no longer an infinite distance apart. They are close enough to have a begin to form a bonding interaction in the transition structure. For the product, it can be seen that 1-2 and 3-4 are the same length, as are 4-5 and 6-1. σ-bond. This reflects the symmetric nature of the cyclohexene product. 2-3 is the only π-bond that remains. It is a similar length to π-bonds in reactants, reflecting the similar bonding environment.

=== Imaginary Vibration ===

A single imaginary vibration is found at the transition state of a reaction that corresponds to the reaction pathway. In this reaction, it is highly symmetrical, with both sets of carbons approaching each other at once. This is indicative of a single synchronous or concerted bond forming step.

[[File:CH3114_TS_imaginary_vibration.gif|thumb|400px|none| Imaginary vibration corresponding to the TS reaction path]]

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

This is another example of a Diels-Alder Reaction. Regioselectivity had to be taken into account as both endo and exo products are possible depending on the angle of approach of the reactants. Both isomers were computed using the same method as in excercise 1. Imaginary frequencies (endo: i520.87 cm-1; exo: i528.84 cm-1) were used to confirm that transition state structures had been obtained. The product structure was obtained by minimising the final structure of the forwards reaction of a PM6 IRC calculation using DFT to a B3lyp-631(g) level.

The MOs involved in bonding of the reactants and TSs are shown below.

This is an example of an inverse electron-demand Diels-Alder reaction. Two oxygen atoms bonded to the π-bond are electron-withdrawing groups. This raises the HOMO energy enough to change how bonding occurs.

===Thermochemistry ===

Thermochemistry data was taken from the B3lyp-631(g) minima. It was found that PM6 data was very different but showed the same trends.

{| class="wikitable"
!
!Reactants kJ/mol
!Transition State kJ/mol
!Product kJ/mol
!Activation Energy kJ/mol
!Gibbs Free Energy of reaction kJ/mol
|-

|Exo reaction
!-1313780.527
!-1313614.231
!-1313845.679
!166.2965445
!-65.1517825
|-

|Endo reaction
!-1313780.527
!-1313622.057
!-1313849.273
!158.469929
!-68.746092
|}

The thermochemistry data shows that the endo Diels-Alder reaction is kinetically more favoured than the exo reaction as the transition state has a lower energy. This can be explained by considering the through-space interaction of the O atom p-orbital lone pairs and the forming π-bond. This positive interaction lowers the energy of the transition state structure. Hence the endo product is formed faster. In the exo transition state, the oxygen atoms face away from the π-bond so no stabalising interaction can take place

The endo product is also thermodynamically more favoured as the Gibbs Free Energy of reaction is more negative. Both reactions have a negative Gibbs so the forwards reaction is more favoured. It is evident that they should have similar Gibbs values as they are structurally very similar.

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

A Cheletropic reaction is another example of a pericylci reaction. It differs from a Diels-Alder reaction as both new bonds are bonded to the same atom.
===IRC===
{| class="wikitable" border="1!
| Exo DA || Endo DA || Cheletropic
|-
| [[File:CH3114 GIF 3 EXO IRC.gif|400px]] || [[File:CH3114_2_3_ENDO_IRC.gif|400px]] || [[File:CH3114_3_CHEL_IRC.gif|400px]]
|-
| [[File:CH3114_3_EXO_IRC.jpg|350px]] || [[File:CH3114_2_3_ENDO_IRC.jpg|350px]] || [[File:CH3114_CHELO_IRC.jpg|350px]]
|}

===Thermochemistry===
{| class="wikitable"
!
!Reactants kJ/mol
!Transition State kJ/mol
!Product kJ/mol
!Activation Energy kJ/mol
!Gibbs Free Energy of reaction kJ/mol
|-

|Exo reaction
!153.470977
!241.7481635
!56.3301025
!88.2771865
!-97.1408745
|-

|Endo reaction
!153.470977
!237.76528
!56.962848
!84.294303
!-96.508129
|-

|Cheletropic reaction
!153.470977
!260.0846555
!0.0078765
!106.6136785
!-153.4631005
|}

It can be seen that the cheletropic reaction is has the highest activation energy so is the kinetically least favoured. It is however the most thermodynamically favoured.

The Exo Diels-Alder reaction is less kinetically favoured and more thermodynamically favoured. This is for the same reasons as in exercise 2.

File:CH3114 2 3 ENDO IRC.gif

2017-03-09T16:35:04Z

Ch3114:

File:CH3114 GIF 3 ENDO IRC.gif

2017-03-09T16:34:08Z

Ch3114: Ch3114 uploaded a new version of File:CH3114 GIF 3 ENDO IRC.gif

Rep:Mod:tsch3114

2017-03-09T16:33:21Z

Ch3114: /* Exercise 3: Diels-Alder vs Cheletropic */

== Introduction ==
During this lab, computational techniques were used to locate and characterise transition state structures during pericyclic reactions. A transition state is the configuration that corresponds to the highest energy point along the a reaction coordinate. It is a maximum point that links the reactants and the products. Knowing the location of a transition state gives important information regarding how a reaction progresses. Information on the mechanism (stepwise or concerted?), thermodynamics and kinetics can be obtained.

A reaction coordinate is an abstract one-dimensional representation of how far a reaction has progressed. In reality, all reactions have multiple degrees of freedom that will determine the energy of the system as for example, all atoms involved are able to move in three directions. The reaction coordinate is an abstraction of all degrees of freedom used to follow it. A potential energy surface (PES) is a 3D plot that includes two dimensions or coordinates. In a PES, the transition state is a saddle point between the reactants and products.

Gaussian and Gaussview were used to explore transitions state structures. Two computational techniques were used throughout the lab. The semi-empirical PM6 method, which is much faster as it relies on experimental data but less accurate, and the ab initio density functional theory (DFT) method which was used later on in each exercise as it gives a more accurate result but requires much more computation and time.

Throughout the lab, carbon atoms involved in bond formation were held at 2.2 Å. This value is found in-between an sp3 C-C bond and 2x carbon Van der Waals radii. Hence it is a good approximation for the transition state carbon-carbon distance.

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

=== Method ===
This reaction is the simplest possible example of a [4+2] cycloaddition, or Diels-Alder reaction, between a diene and a dienophile that are studied in this lab. It is a concerted pericyclic reaction that involves the formation of 2 σ-bonds and 1 π-bond and breaking 3 π-bonds, or the reverse. For this reaction, no regioselectivity needs to be considered because there are no addition groups bonded to either reactant.

Method 2 was used to calculate the TS structure for this reaction. It was decided that not enough information was known of the transition state structure to make an accurate guess. Initially reactants were constructed separately in Gaussian and optimised to a minimum to a PM6 level. They were confirmed to have no imaginary (i.e. negative) frequencies.

The reactants were then combined. Reacting carbons were held approximately 2.2 Å apart and the system was optimised to a minimum at a PM6 level. The transitions state (TS(berny)) was then optimised and the frequency was found at a PM6 level. It was confirmed that a transition state had been obtained by the presence of a single imaginary frequency. The transition state was then determined more accurately using DFT B3LYP/6-31G(d) technique. From this, transition state MOs were determined. An intrinsic reaction coordinate (IRC) calculation was carried out with 200 steps which further confirmed that the correct TS had been obtained.

=== IRC ===
{| class="wikitable" border=""1!"
|Intrinsic Reaction Coordinate || RMS Gradient Norm
|-
| style="text-align: center;" | [[File:IRC.jpg|600px]] || style="text-align: center;" | [[File:RMS.jpg|600px]] ||
|}

It can be seen that the transition state is found at a maximum and that the products and the reactants are found at minima. This can be used to confirm the success of the computation.

=== MOs ===

The MO diagrams shows that there has been a net destabalisation of reactants in order to form the transition state. This is expected as the transition state is found at an energy maximum.
Only fragment orbitals with the same symmetry label (gerade or ungerade) are able to combine to form MOs. Combinations of orbitals with opposite symmetry labels results in an overlap integral equal to zero. The given arrangement allows for constructive overlap (i.e. non-zero overlap integral) of orbitals found at the end of both pi system.

=== Normal vs. Inverse electron-demand Diels-Alder Reactions ===

This is an example of a normal electron-demand Diels-Alder reaction. Electrons are donated from the diene HOMO to the dienophile LUMO. This is the case for the majority of Diels-Alder reactions. Inverse electron-demand Diels-Alder reactions occur when the diene fragment orbitals are found lower in energy with respect to the dienophile. This is the result of an electron withdrawing group found on the diene and an electron donating group bonded to the dienophile.

=== C-C Bond Lengths ===
{| class="wikitable" border="1!
|+
|colspan = 4; style=text-align: center|C-C Bond Lengths/Å
|-
|C-C bond|| Reactants || Transition State || Products
|-
|1-2||1.33344||1.38307||1.50901
|-
|2-3||1.47083||1.40721||1.33697
|-
|3-4||1.33344||1.38307||1.50901
|-
|4-5||infinite||2.27215||1.54961
|-
|5-6||1.32731||1.38607||1.55524
|-
|6-1||infinite||2.27215||1.54961
|}

Bond Lengths changes as expected throughout the reaction. In the reactants, the three π-bonds (1-2, 3-4, 5-6) are shorter than the SIGMA bond (2-3). At the transition structure, the π-bonds are elongated as the π-bond interaction is broken to give a σ-bond. The SIGMA bond is shorter as it begins to form a π-bond. 3-4 and 6-1 are no longer an infinite distance apart. They are close enough to have a begin to form a bonding interaction in the transition structure. For the product, it can be seen that 1-2 and 3-4 are the same length, as are 4-5 and 6-1. σ-bond. This reflects the symmetric nature of the cyclohexene product. 2-3 is the only π-bond that remains. It is a similar length to π-bonds in reactants, reflecting the similar bonding environment.

=== Imaginary Vibration ===

A single imaginary vibration is found at the transition state of a reaction that corresponds to the reaction pathway. In this reaction, it is highly symmetrical, with both sets of carbons approaching each other at once. This is indicative of a single synchronous or concerted bond forming step.

[[File:CH3114_TS_imaginary_vibration.gif|thumb|400px|none| Imaginary vibration corresponding to the TS reaction path]]

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

This is another example of a Diels-Alder Reaction. Regioselectivity had to be taken into account as both endo and exo products are possible depending on the angle of approach of the reactants. Both isomers were computed using the same method as in excercise 1. Imaginary frequencies (endo: i520.87 cm-1; exo: i528.84 cm-1) were used to confirm that transition state structures had been obtained. The product structure was obtained by minimising the final structure of the forwards reaction of a PM6 IRC calculation using DFT to a B3lyp-631(g) level.

The MOs involved in bonding of the reactants and TSs are shown below.

This is an example of an inverse electron-demand Diels-Alder reaction. Two oxygen atoms bonded to the π-bond are electron-withdrawing groups. This raises the HOMO energy enough to change how bonding occurs.

===Thermochemistry ===

Thermochemistry data was taken from the B3lyp-631(g) minima. It was found that PM6 data was very different but showed the same trends.

{| class="wikitable"
!
!Reactants kJ/mol
!Transition State kJ/mol
!Product kJ/mol
!Activation Energy kJ/mol
!Gibbs Free Energy of reaction kJ/mol
|-

|Exo reaction
!-1313780.527
!-1313614.231
!-1313845.679
!166.2965445
!-65.1517825
|-

|Endo reaction
!-1313780.527
!-1313622.057
!-1313849.273
!158.469929
!-68.746092
|}

The thermochemistry data shows that the endo Diels-Alder reaction is kinetically more favoured than the exo reaction as the transition state has a lower energy. This can be explained by considering the through-space interaction of the O atom p-orbital lone pairs and the forming π-bond. This positive interaction lowers the energy of the transition state structure. Hence the endo product is formed faster. In the exo transition state, the oxygen atoms face away from the π-bond so no stabalising interaction can take place

The endo product is also thermodynamically more favoured as the Gibbs Free Energy of reaction is more negative. Both reactions have a negative Gibbs so the forwards reaction is more favoured. It is evident that they should have similar Gibbs values as they are structurally very similar.

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

A Cheletropic reaction is another example of a pericylci reaction. It differs from a Diels-Alder reaction as both new bonds are bonded to the same atom.
===IRC===
{| class="wikitable" border="1!
| Exo DA || Endo DA || Cheletropic
|-
| [[File:CH3114 GIF 3 EXO IRC.gif|400px]] || [[File:CH3114 GIF 3 ENDO IRC.gif|400px]] || [[File:CH3114_3_CHEL_IRC.gif|400px]]
|-
| [[File:CH3114_3_EXO_IRC.jpg|350px]] || [[File:CH3114_2_3_ENDO_IRC.jpg|350px]] || [[File:CH3114_CHELO_IRC.jpg|350px]]
|}

===Thermochemistry===
{| class="wikitable"
!
!Reactants kJ/mol
!Transition State kJ/mol
!Product kJ/mol
!Activation Energy kJ/mol
!Gibbs Free Energy of reaction kJ/mol
|-

|Exo reaction
!153.470977
!241.7481635
!56.3301025
!88.2771865
!-97.1408745
|-

|Endo reaction
!153.470977
!237.76528
!56.962848
!84.294303
!-96.508129
|-

|Cheletropic reaction
!153.470977
!260.0846555
!0.0078765
!106.6136785
!-153.4631005
|}

It can be seen that the cheletropic reaction is has the highest activation energy so is the kinetically least favoured. It is however the most thermodynamically favoured.

The Exo Diels-Alder reaction is less kinetically favoured and more thermodynamically favoured. This is for the same reasons as in exercise 2.

File:CH3114 2 3 ENDO IRC.jpg

2017-03-09T16:32:34Z

Ch3114:

Rep:Mod:tsch3114

2017-03-09T16:32:16Z

Ch3114: /* Exercise 3: Diels-Alder vs Cheletropic */

== Introduction ==
During this lab, computational techniques were used to locate and characterise transition state structures during pericyclic reactions. A transition state is the configuration that corresponds to the highest energy point along the a reaction coordinate. It is a maximum point that links the reactants and the products. Knowing the location of a transition state gives important information regarding how a reaction progresses. Information on the mechanism (stepwise or concerted?), thermodynamics and kinetics can be obtained.

A reaction coordinate is an abstract one-dimensional representation of how far a reaction has progressed. In reality, all reactions have multiple degrees of freedom that will determine the energy of the system as for example, all atoms involved are able to move in three directions. The reaction coordinate is an abstraction of all degrees of freedom used to follow it. A potential energy surface (PES) is a 3D plot that includes two dimensions or coordinates. In a PES, the transition state is a saddle point between the reactants and products.

Gaussian and Gaussview were used to explore transitions state structures. Two computational techniques were used throughout the lab. The semi-empirical PM6 method, which is much faster as it relies on experimental data but less accurate, and the ab initio density functional theory (DFT) method which was used later on in each exercise as it gives a more accurate result but requires much more computation and time.

Throughout the lab, carbon atoms involved in bond formation were held at 2.2 Å. This value is found in-between an sp3 C-C bond and 2x carbon Van der Waals radii. Hence it is a good approximation for the transition state carbon-carbon distance.

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

=== Method ===
This reaction is the simplest possible example of a [4+2] cycloaddition, or Diels-Alder reaction, between a diene and a dienophile that are studied in this lab. It is a concerted pericyclic reaction that involves the formation of 2 σ-bonds and 1 π-bond and breaking 3 π-bonds, or the reverse. For this reaction, no regioselectivity needs to be considered because there are no addition groups bonded to either reactant.

Method 2 was used to calculate the TS structure for this reaction. It was decided that not enough information was known of the transition state structure to make an accurate guess. Initially reactants were constructed separately in Gaussian and optimised to a minimum to a PM6 level. They were confirmed to have no imaginary (i.e. negative) frequencies.

The reactants were then combined. Reacting carbons were held approximately 2.2 Å apart and the system was optimised to a minimum at a PM6 level. The transitions state (TS(berny)) was then optimised and the frequency was found at a PM6 level. It was confirmed that a transition state had been obtained by the presence of a single imaginary frequency. The transition state was then determined more accurately using DFT B3LYP/6-31G(d) technique. From this, transition state MOs were determined. An intrinsic reaction coordinate (IRC) calculation was carried out with 200 steps which further confirmed that the correct TS had been obtained.

=== IRC ===
{| class="wikitable" border=""1!"
|Intrinsic Reaction Coordinate || RMS Gradient Norm
|-
| style="text-align: center;" | [[File:IRC.jpg|600px]] || style="text-align: center;" | [[File:RMS.jpg|600px]] ||
|}

It can be seen that the transition state is found at a maximum and that the products and the reactants are found at minima. This can be used to confirm the success of the computation.

=== MOs ===

The MO diagrams shows that there has been a net destabalisation of reactants in order to form the transition state. This is expected as the transition state is found at an energy maximum.
Only fragment orbitals with the same symmetry label (gerade or ungerade) are able to combine to form MOs. Combinations of orbitals with opposite symmetry labels results in an overlap integral equal to zero. The given arrangement allows for constructive overlap (i.e. non-zero overlap integral) of orbitals found at the end of both pi system.

=== Normal vs. Inverse electron-demand Diels-Alder Reactions ===

This is an example of a normal electron-demand Diels-Alder reaction. Electrons are donated from the diene HOMO to the dienophile LUMO. This is the case for the majority of Diels-Alder reactions. Inverse electron-demand Diels-Alder reactions occur when the diene fragment orbitals are found lower in energy with respect to the dienophile. This is the result of an electron withdrawing group found on the diene and an electron donating group bonded to the dienophile.

=== C-C Bond Lengths ===
{| class="wikitable" border="1!
|+
|colspan = 4; style=text-align: center|C-C Bond Lengths/Å
|-
|C-C bond|| Reactants || Transition State || Products
|-
|1-2||1.33344||1.38307||1.50901
|-
|2-3||1.47083||1.40721||1.33697
|-
|3-4||1.33344||1.38307||1.50901
|-
|4-5||infinite||2.27215||1.54961
|-
|5-6||1.32731||1.38607||1.55524
|-
|6-1||infinite||2.27215||1.54961
|}

Bond Lengths changes as expected throughout the reaction. In the reactants, the three π-bonds (1-2, 3-4, 5-6) are shorter than the SIGMA bond (2-3). At the transition structure, the π-bonds are elongated as the π-bond interaction is broken to give a σ-bond. The SIGMA bond is shorter as it begins to form a π-bond. 3-4 and 6-1 are no longer an infinite distance apart. They are close enough to have a begin to form a bonding interaction in the transition structure. For the product, it can be seen that 1-2 and 3-4 are the same length, as are 4-5 and 6-1. σ-bond. This reflects the symmetric nature of the cyclohexene product. 2-3 is the only π-bond that remains. It is a similar length to π-bonds in reactants, reflecting the similar bonding environment.

=== Imaginary Vibration ===

A single imaginary vibration is found at the transition state of a reaction that corresponds to the reaction pathway. In this reaction, it is highly symmetrical, with both sets of carbons approaching each other at once. This is indicative of a single synchronous or concerted bond forming step.

[[File:CH3114_TS_imaginary_vibration.gif|thumb|400px|none| Imaginary vibration corresponding to the TS reaction path]]

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

This is another example of a Diels-Alder Reaction. Regioselectivity had to be taken into account as both endo and exo products are possible depending on the angle of approach of the reactants. Both isomers were computed using the same method as in excercise 1. Imaginary frequencies (endo: i520.87 cm-1; exo: i528.84 cm-1) were used to confirm that transition state structures had been obtained. The product structure was obtained by minimising the final structure of the forwards reaction of a PM6 IRC calculation using DFT to a B3lyp-631(g) level.

The MOs involved in bonding of the reactants and TSs are shown below.

This is an example of an inverse electron-demand Diels-Alder reaction. Two oxygen atoms bonded to the π-bond are electron-withdrawing groups. This raises the HOMO energy enough to change how bonding occurs.

===Thermochemistry ===

Thermochemistry data was taken from the B3lyp-631(g) minima. It was found that PM6 data was very different but showed the same trends.

{| class="wikitable"
!
!Reactants kJ/mol
!Transition State kJ/mol
!Product kJ/mol
!Activation Energy kJ/mol
!Gibbs Free Energy of reaction kJ/mol
|-

|Exo reaction
!-1313780.527
!-1313614.231
!-1313845.679
!166.2965445
!-65.1517825
|-

|Endo reaction
!-1313780.527
!-1313622.057
!-1313849.273
!158.469929
!-68.746092
|}

The thermochemistry data shows that the endo Diels-Alder reaction is kinetically more favoured than the exo reaction as the transition state has a lower energy. This can be explained by considering the through-space interaction of the O atom p-orbital lone pairs and the forming π-bond. This positive interaction lowers the energy of the transition state structure. Hence the endo product is formed faster. In the exo transition state, the oxygen atoms face away from the π-bond so no stabalising interaction can take place

The endo product is also thermodynamically more favoured as the Gibbs Free Energy of reaction is more negative. Both reactions have a negative Gibbs so the forwards reaction is more favoured. It is evident that they should have similar Gibbs values as they are structurally very similar.

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

A Cheletropic reaction is another example of a pericylci reaction. It differs from a Diels-Alder reaction as both new bonds are bonded to the same atom.
===IRC===
{| class="wikitable" border="1!
| Exo DA || Endo DA || Cheletropic
|-
| [[File:CH3114 GIF 3 EXO IRC.gif|400px]] || [[File:CH3114_GIF_3_ENDO_IRC.gif|400px]] || [[File:CH3114_3_CHEL_IRC.gif|400px]]
|-
| [[File:CH3114_3_EXO_IRC.jpg|350px]] || [[File:CH3114_2_3_ENDO_IRC.jpg|350px]] || [[File:CH3114_CHELO_IRC.jpg|350px]]
|}

===Thermochemistry===
{| class="wikitable"
!
!Reactants kJ/mol
!Transition State kJ/mol
!Product kJ/mol
!Activation Energy kJ/mol
!Gibbs Free Energy of reaction kJ/mol
|-

|Exo reaction
!153.470977
!241.7481635
!56.3301025
!88.2771865
!-97.1408745
|-

|Endo reaction
!153.470977
!237.76528
!56.962848
!84.294303
!-96.508129
|-

|Cheletropic reaction
!153.470977
!260.0846555
!0.0078765
!106.6136785
!-153.4631005
|}

It can be seen that the cheletropic reaction is has the highest activation energy so is the kinetically least favoured. It is however the most thermodynamically favoured.

The Exo Diels-Alder reaction is less kinetically favoured and more thermodynamically favoured. This is for the same reasons as in exercise 2.

File:CH3114 3 ENDO IRC.jpg

2017-03-09T16:29:57Z

Ch3114: Ch3114 uploaded a new version of File:CH3114 3 ENDO IRC.jpg

Rep:Mod:tsch3114

2017-03-09T16:28:57Z

Ch3114: /* IRC */

== Introduction ==
During this lab, computational techniques were used to locate and characterise transition state structures during pericyclic reactions. A transition state is the configuration that corresponds to the highest energy point along the a reaction coordinate. It is a maximum point that links the reactants and the products. Knowing the location of a transition state gives important information regarding how a reaction progresses. Information on the mechanism (stepwise or concerted?), thermodynamics and kinetics can be obtained.

A reaction coordinate is an abstract one-dimensional representation of how far a reaction has progressed. In reality, all reactions have multiple degrees of freedom that will determine the energy of the system as for example, all atoms involved are able to move in three directions. The reaction coordinate is an abstraction of all degrees of freedom used to follow it. A potential energy surface (PES) is a 3D plot that includes two dimensions or coordinates. In a PES, the transition state is a saddle point between the reactants and products.

Gaussian and Gaussview were used to explore transitions state structures. Two computational techniques were used throughout the lab. The semi-empirical PM6 method, which is much faster as it relies on experimental data but less accurate, and the ab initio density functional theory (DFT) method which was used later on in each exercise as it gives a more accurate result but requires much more computation and time.

Throughout the lab, carbon atoms involved in bond formation were held at 2.2 Å. This value is found in-between an sp3 C-C bond and 2x carbon Van der Waals radii. Hence it is a good approximation for the transition state carbon-carbon distance.

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

=== Method ===
This reaction is the simplest possible example of a [4+2] cycloaddition, or Diels-Alder reaction, between a diene and a dienophile that are studied in this lab. It is a concerted pericyclic reaction that involves the formation of 2 σ-bonds and 1 π-bond and breaking 3 π-bonds, or the reverse. For this reaction, no regioselectivity needs to be considered because there are no addition groups bonded to either reactant.

Method 2 was used to calculate the TS structure for this reaction. It was decided that not enough information was known of the transition state structure to make an accurate guess. Initially reactants were constructed separately in Gaussian and optimised to a minimum to a PM6 level. They were confirmed to have no imaginary (i.e. negative) frequencies.

The reactants were then combined. Reacting carbons were held approximately 2.2 Å apart and the system was optimised to a minimum at a PM6 level. The transitions state (TS(berny)) was then optimised and the frequency was found at a PM6 level. It was confirmed that a transition state had been obtained by the presence of a single imaginary frequency. The transition state was then determined more accurately using DFT B3LYP/6-31G(d) technique. From this, transition state MOs were determined. An intrinsic reaction coordinate (IRC) calculation was carried out with 200 steps which further confirmed that the correct TS had been obtained.

=== IRC ===
{| class="wikitable" border=""1!"
|Intrinsic Reaction Coordinate || RMS Gradient Norm
|-
| style="text-align: center;" | [[File:IRC.jpg|600px]] || style="text-align: center;" | [[File:RMS.jpg|600px]] ||
|}

It can be seen that the transition state is found at a maximum and that the products and the reactants are found at minima. This can be used to confirm the success of the computation.

=== MOs ===

The MO diagrams shows that there has been a net destabalisation of reactants in order to form the transition state. This is expected as the transition state is found at an energy maximum.
Only fragment orbitals with the same symmetry label (gerade or ungerade) are able to combine to form MOs. Combinations of orbitals with opposite symmetry labels results in an overlap integral equal to zero. The given arrangement allows for constructive overlap (i.e. non-zero overlap integral) of orbitals found at the end of both pi system.

=== Normal vs. Inverse electron-demand Diels-Alder Reactions ===

This is an example of a normal electron-demand Diels-Alder reaction. Electrons are donated from the diene HOMO to the dienophile LUMO. This is the case for the majority of Diels-Alder reactions. Inverse electron-demand Diels-Alder reactions occur when the diene fragment orbitals are found lower in energy with respect to the dienophile. This is the result of an electron withdrawing group found on the diene and an electron donating group bonded to the dienophile.

=== C-C Bond Lengths ===
{| class="wikitable" border="1!
|+
|colspan = 4; style=text-align: center|C-C Bond Lengths/Å
|-
|C-C bond|| Reactants || Transition State || Products
|-
|1-2||1.33344||1.38307||1.50901
|-
|2-3||1.47083||1.40721||1.33697
|-
|3-4||1.33344||1.38307||1.50901
|-
|4-5||infinite||2.27215||1.54961
|-
|5-6||1.32731||1.38607||1.55524
|-
|6-1||infinite||2.27215||1.54961
|}

Bond Lengths changes as expected throughout the reaction. In the reactants, the three π-bonds (1-2, 3-4, 5-6) are shorter than the SIGMA bond (2-3). At the transition structure, the π-bonds are elongated as the π-bond interaction is broken to give a σ-bond. The SIGMA bond is shorter as it begins to form a π-bond. 3-4 and 6-1 are no longer an infinite distance apart. They are close enough to have a begin to form a bonding interaction in the transition structure. For the product, it can be seen that 1-2 and 3-4 are the same length, as are 4-5 and 6-1. σ-bond. This reflects the symmetric nature of the cyclohexene product. 2-3 is the only π-bond that remains. It is a similar length to π-bonds in reactants, reflecting the similar bonding environment.

=== Imaginary Vibration ===

A single imaginary vibration is found at the transition state of a reaction that corresponds to the reaction pathway. In this reaction, it is highly symmetrical, with both sets of carbons approaching each other at once. This is indicative of a single synchronous or concerted bond forming step.

[[File:CH3114_TS_imaginary_vibration.gif|thumb|400px|none| Imaginary vibration corresponding to the TS reaction path]]

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

This is another example of a Diels-Alder Reaction. Regioselectivity had to be taken into account as both endo and exo products are possible depending on the angle of approach of the reactants. Both isomers were computed using the same method as in excercise 1. Imaginary frequencies (endo: i520.87 cm-1; exo: i528.84 cm-1) were used to confirm that transition state structures had been obtained. The product structure was obtained by minimising the final structure of the forwards reaction of a PM6 IRC calculation using DFT to a B3lyp-631(g) level.

The MOs involved in bonding of the reactants and TSs are shown below.

This is an example of an inverse electron-demand Diels-Alder reaction. Two oxygen atoms bonded to the π-bond are electron-withdrawing groups. This raises the HOMO energy enough to change how bonding occurs.

===Thermochemistry ===

Thermochemistry data was taken from the B3lyp-631(g) minima. It was found that PM6 data was very different but showed the same trends.

{| class="wikitable"
!
!Reactants kJ/mol
!Transition State kJ/mol
!Product kJ/mol
!Activation Energy kJ/mol
!Gibbs Free Energy of reaction kJ/mol
|-

|Exo reaction
!-1313780.527
!-1313614.231
!-1313845.679
!166.2965445
!-65.1517825
|-

|Endo reaction
!-1313780.527
!-1313622.057
!-1313849.273
!158.469929
!-68.746092
|}

The thermochemistry data shows that the endo Diels-Alder reaction is kinetically more favoured than the exo reaction as the transition state has a lower energy. This can be explained by considering the through-space interaction of the O atom p-orbital lone pairs and the forming π-bond. This positive interaction lowers the energy of the transition state structure. Hence the endo product is formed faster. In the exo transition state, the oxygen atoms face away from the π-bond so no stabalising interaction can take place

The endo product is also thermodynamically more favoured as the Gibbs Free Energy of reaction is more negative. Both reactions have a negative Gibbs so the forwards reaction is more favoured. It is evident that they should have similar Gibbs values as they are structurally very similar.

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

A Cheletropic reaction is another example of a pericylci reaction. It differs from a Diels-Alder reaction as both new bonds are bonded to the same atom.
===IRC===
{| class="wikitable" border="1!
| Exo DA || Endo DA || Cheletropic
|-
| [[File:CH3114 GIF 3 EXO IRC.gif|400px]] || [[File:CH3114 GIF 3 ENDO IRC.gif|400px]] || [[File:CH3114_3_CHEL_IRC.gif|400px]]
|-
| [[File:CH3114_3_EXO_IRC.jpg|300px]] || [[File:CH3114_3_ENDO_IRC.jpg|300px]] || [[File:CH3114_CHELO_IRC.jpg|350px]]
|}

===Thermochemistry===
{| class="wikitable"
!
!Reactants kJ/mol
!Transition State kJ/mol
!Product kJ/mol
!Activation Energy kJ/mol
!Gibbs Free Energy of reaction kJ/mol
|-

|Exo reaction
!153.470977
!241.7481635
!56.3301025
!88.2771865
!-97.1408745
|-

|Endo reaction
!153.470977
!237.76528
!56.962848
!84.294303
!-96.508129
|-

|Cheletropic reaction
!153.470977
!260.0846555
!0.0078765
!106.6136785
!-153.4631005
|}

It can be seen that the cheletropic reaction is has the highest activation energy so is the kinetically least favoured. It is however the most thermodynamically favoured.

The Exo Diels-Alder reaction is less kinetically favoured and more thermodynamically favoured. This is for the same reasons as in exercise 2.

File:CH3114 3 ENDO IRC.jpg

2017-03-09T16:28:28Z

Ch3114: Ch3114 uploaded a new version of File:CH3114 3 ENDO IRC.jpg

File:CH3114 GIF 3 ENDO IRC.gif

2017-03-09T16:25:44Z

Ch3114: Ch3114 uploaded a new version of File:CH3114 GIF 3 ENDO IRC.gif

2017-03-09T14:28:14Z

Ch3114:

File:CH3114 3 ENDO IRC.jpg

2017-03-09T14:27:48Z

Ch3114: