ChemWiki - User contributions [en]

Rep:Mod:physicalccrossland

2014-11-07T11:56:44Z

Cc3210: /* Finding the Transition State */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this. All energies are presented in hartrees (au) unless otherwise stated.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 60 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification involved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
|+ Summary of Transition State Energies
! Chair !! Boat
|-
| E = -234.55698291 || E = -234.54309307
|-
|}

IRC analysis suggests the chair transition state has a gauche conformer precursor, and the boat an APP one. This gives the following activation energies (TS energy - reactant energy).

{| class="wikitable"
! Gauche-Chair
! APP-Boat
|-
| 33.70 Kcal/mol
| 43.05 Kcal/mol
|}

These activation values for the chair and boat reaction pathways agree well with experimental values (33.5 & 44.7 Kcal/mol respectively), errors of -0.59 % and 3.69 %.

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

=== Example 1: Ethylene + Butadiene ===

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| || Antisymmetric || Symmetric
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|-
| || Symmetric || Antisymmetric
|-
|}

=== Finding the Transition State ===

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised.. First, both cis-butadiene and ethylene were independently optimised (by AM1 semi-empirical method), then positioned in the same plane as each other and optimised using again the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

The transition state has the following Molecular orbitals.

{| class="wikitable"
! HOMO
! LUMO

|-
| [[File:HOMO cisbutadiene+ethylene TS.png|300px]]
| [[File:LUMO cisbutadiene+ethylene.png|300px]]

|-
| Antisymmetric
| Symmetric
|}

=== Example 2: Cyclohexadiene + Maleic Anhydride ===

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| || Antisymmetric||Symmetric
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|-
| ||Symmetric||Antisymmetric
|}

=== Locating the Endo Transition State ===

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO FINAL REAL.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:ENDO MOVIE FINAL.gif|center|frame|300px|Endo Transition State Animation]]

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

=== Locating the Exo Transition State ===

In order to find the exo transition state, the procedure was repeated but with the direction of the maleic anhydride reversed. The result is shown below.

<jmol>
<jmolApplet>
<title>Exo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXO DERIV.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:exo ts.gif|center|frame|300px|Exo Transition State Animation]]

This transition state has the following molecular orbitals.

{| class="wikitable"
! HOMO
! LUMO

|-
| [[File:HOMO Exo TS.png|300px]]
| [[File:LUMO Exo TS.png|300px]]
|}

=== Explanation ===

The exo and endo transition structures have energies of -0.05041984 and -0.06407816 hartrees, respectively. This clearly shows the endo to be the lower energy transition state, and since this is the major yet thermodynamically unfavoured product, the reaction must be under kinetic control, as hypothesised.

The reason for the favouring of the endo transition state lies in secondary orbital interactions. The pi-system of the carbonyl bonds can interact efficiently with the pi system of the diene in the endo orientation, an effect which is no present in the exo transition state. This serves to stabilise the endo transition state, despite this structure being more sterically demanding.

== Conclusion ==

In this study Gaussian was used to probe the reaction pathways of two different reactions, the Cope rearrangement and the Diels-Alder cycloaddition. The expected major product of the Diels-Alder reaction was rationalised through characterisation of the transition state.

== References ==

Imperial College Labscript (on Wiki) consulted throughout. Clayden's Organic Chemistry used for Diels-Alder section.

Rep:Mod:physicalccrossland

2014-11-07T11:55:58Z

Cc3210: /* Finding the Transition State */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this. All energies are presented in hartrees (au) unless otherwise stated.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 60 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification involved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
|+ Summary of Transition State Energies
! Chair !! Boat
|-
| E = -234.55698291 || E = -234.54309307
|-
|}

IRC analysis suggests the chair transition state has a gauche conformer precursor, and the boat an APP one. This gives the following activation energies (TS energy - reactant energy).

{| class="wikitable"
! Gauche-Chair
! APP-Boat
|-
| 33.70 Kcal/mol
| 43.05 Kcal/mol
|}

These activation values for the chair and boat reaction pathways agree well with experimental values (33.5 & 44.7 Kcal/mol respectively), errors of -0.59 % and 3.69 %.

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

=== Example 1: Ethylene + Butadiene ===

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| || Antisymmetric || Symmetric
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|-
| || Symmetric || Antisymmetric
|-
|}

=== Finding the Transition State ===

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised by the semi-empirical Am1 method. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

The transition state has the following Molecular orbitals.

{| class="wikitable"
! HOMO
! LUMO

|-
| [[File:HOMO cisbutadiene+ethylene TS.png|300px]]
| [[File:LUMO cisbutadiene+ethylene.png|300px]]

|-
| Antisymmetric
| Symmetric
|}

=== Example 2: Cyclohexadiene + Maleic Anhydride ===

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| || Antisymmetric||Symmetric
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|-
| ||Symmetric||Antisymmetric
|}

=== Locating the Endo Transition State ===

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO FINAL REAL.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:ENDO MOVIE FINAL.gif|center|frame|300px|Endo Transition State Animation]]

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

=== Locating the Exo Transition State ===

In order to find the exo transition state, the procedure was repeated but with the direction of the maleic anhydride reversed. The result is shown below.

<jmol>
<jmolApplet>
<title>Exo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXO DERIV.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:exo ts.gif|center|frame|300px|Exo Transition State Animation]]

This transition state has the following molecular orbitals.

{| class="wikitable"
! HOMO
! LUMO

|-
| [[File:HOMO Exo TS.png|300px]]
| [[File:LUMO Exo TS.png|300px]]
|}

=== Explanation ===

The exo and endo transition structures have energies of -0.05041984 and -0.06407816 hartrees, respectively. This clearly shows the endo to be the lower energy transition state, and since this is the major yet thermodynamically unfavoured product, the reaction must be under kinetic control, as hypothesised.

The reason for the favouring of the endo transition state lies in secondary orbital interactions. The pi-system of the carbonyl bonds can interact efficiently with the pi system of the diene in the endo orientation, an effect which is no present in the exo transition state. This serves to stabilise the endo transition state, despite this structure being more sterically demanding.

== Conclusion ==

In this study Gaussian was used to probe the reaction pathways of two different reactions, the Cope rearrangement and the Diels-Alder cycloaddition. The expected major product of the Diels-Alder reaction was rationalised through characterisation of the transition state.

== References ==

Imperial College Labscript (on Wiki) consulted throughout. Clayden's Organic Chemistry used for Diels-Alder section.

Rep:Mod:physicalccrossland

2014-11-07T11:54:59Z

Cc3210: /* Optimising the Transition Structure */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this. All energies are presented in hartrees (au) unless otherwise stated.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 60 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification involved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
|+ Summary of Transition State Energies
! Chair !! Boat
|-
| E = -234.55698291 || E = -234.54309307
|-
|}

IRC analysis suggests the chair transition state has a gauche conformer precursor, and the boat an APP one. This gives the following activation energies (TS energy - reactant energy).

{| class="wikitable"
! Gauche-Chair
! APP-Boat
|-
| 33.70 Kcal/mol
| 43.05 Kcal/mol
|}

These activation values for the chair and boat reaction pathways agree well with experimental values (33.5 & 44.7 Kcal/mol respectively), errors of -0.59 % and 3.69 %.

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

=== Example 1: Ethylene + Butadiene ===

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| || Antisymmetric || Symmetric
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|-
| || Symmetric || Antisymmetric
|-
|}

=== Finding the Transition State ===

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

The transition state has the following Molecular orbitals.

{| class="wikitable"
! HOMO
! LUMO

|-
| [[File:HOMO cisbutadiene+ethylene TS.png|300px]]
| [[File:LUMO cisbutadiene+ethylene.png|300px]]

|-
| Antisymmetric
| Symmetric
|}

=== Example 2: Cyclohexadiene + Maleic Anhydride ===

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| || Antisymmetric||Symmetric
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|-
| ||Symmetric||Antisymmetric
|}

=== Locating the Endo Transition State ===

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO FINAL REAL.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:ENDO MOVIE FINAL.gif|center|frame|300px|Endo Transition State Animation]]

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

=== Locating the Exo Transition State ===

In order to find the exo transition state, the procedure was repeated but with the direction of the maleic anhydride reversed. The result is shown below.

<jmol>
<jmolApplet>
<title>Exo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXO DERIV.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:exo ts.gif|center|frame|300px|Exo Transition State Animation]]

This transition state has the following molecular orbitals.

{| class="wikitable"
! HOMO
! LUMO

|-
| [[File:HOMO Exo TS.png|300px]]
| [[File:LUMO Exo TS.png|300px]]
|}

=== Explanation ===

The exo and endo transition structures have energies of -0.05041984 and -0.06407816 hartrees, respectively. This clearly shows the endo to be the lower energy transition state, and since this is the major yet thermodynamically unfavoured product, the reaction must be under kinetic control, as hypothesised.

The reason for the favouring of the endo transition state lies in secondary orbital interactions. The pi-system of the carbonyl bonds can interact efficiently with the pi system of the diene in the endo orientation, an effect which is no present in the exo transition state. This serves to stabilise the endo transition state, despite this structure being more sterically demanding.

== Conclusion ==

In this study Gaussian was used to probe the reaction pathways of two different reactions, the Cope rearrangement and the Diels-Alder cycloaddition. The expected major product of the Diels-Alder reaction was rationalised through characterisation of the transition state.

== References ==

Imperial College Labscript (on Wiki) consulted throughout. Clayden's Organic Chemistry used for Diels-Alder section.

Rep:Mod:physicalccrossland

2014-11-07T11:51:32Z

Cc3210: /* Conclusion */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this. All energies are presented in hartrees (au) unless otherwise stated.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 60 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification involved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
|+ Summary of Transition State Energies
! Chair !! Boat
|-
| E = -234.55698291 || E = -234.54309307
|-
|}

IRC analysis suggests the chair transition state has a gauche conformer precursor, and the boat an APP one. This gives the following activation energies (TS energy - reactant energy).

{| class="wikitable"
! Gauche-Chair
! APP-Boat
|-
| 33.70 Kcal/mol
| 43.05 Kcal/mol
|}

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

=== Example 1: Ethylene + Butadiene ===

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| || Antisymmetric || Symmetric
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|-
| || Symmetric || Antisymmetric
|-
|}

=== Finding the Transition State ===

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

The transition state has the following Molecular orbitals.

{| class="wikitable"
! HOMO
! LUMO

|-
| [[File:HOMO cisbutadiene+ethylene TS.png|300px]]
| [[File:LUMO cisbutadiene+ethylene.png|300px]]

|-
| Antisymmetric
| Symmetric
|}

=== Example 2: Cyclohexadiene + Maleic Anhydride ===

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| || Antisymmetric||Symmetric
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|-
| ||Symmetric||Antisymmetric
|}

=== Locating the Endo Transition State ===

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO FINAL REAL.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:ENDO MOVIE FINAL.gif|center|frame|300px|Endo Transition State Animation]]

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

=== Locating the Exo Transition State ===

In order to find the exo transition state, the procedure was repeated but with the direction of the maleic anhydride reversed. The result is shown below.

<jmol>
<jmolApplet>
<title>Exo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXO DERIV.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:exo ts.gif|center|frame|300px|Exo Transition State Animation]]

This transition state has the following molecular orbitals.

{| class="wikitable"
! HOMO
! LUMO

|-
| [[File:HOMO Exo TS.png|300px]]
| [[File:LUMO Exo TS.png|300px]]
|}

=== Explanation ===

The exo and endo transition structures have energies of -0.05041984 and -0.06407816 hartrees, respectively. This clearly shows the endo to be the lower energy transition state, and since this is the major yet thermodynamically unfavoured product, the reaction must be under kinetic control, as hypothesised.

The reason for the favouring of the endo transition state lies in secondary orbital interactions. The pi-system of the carbonyl bonds can interact efficiently with the pi system of the diene in the endo orientation, an effect which is no present in the exo transition state. This serves to stabilise the endo transition state, despite this structure being more sterically demanding.

== Conclusion ==

In this study Gaussian was used to probe the reaction pathways of two different reactions, the Cope rearrangement and the Diels-Alder cycloaddition. The expected major product of the Diels-Alder reaction was rationalised through characterisation of the transition state.

== References ==

Imperial College Labscript (on Wiki) consulted throughout. Clayden's Organic Chemistry used for Diels-Alder section.

Rep:Mod:physicalccrossland

2014-11-07T11:50:24Z

Cc3210: /* Introduction */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this. All energies are presented in hartrees (au) unless otherwise stated.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 60 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification involved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
|+ Summary of Transition State Energies
! Chair !! Boat
|-
| E = -234.55698291 || E = -234.54309307
|-
|}

IRC analysis suggests the chair transition state has a gauche conformer precursor, and the boat an APP one. This gives the following activation energies (TS energy - reactant energy).

{| class="wikitable"
! Gauche-Chair
! APP-Boat
|-
| 33.70 Kcal/mol
| 43.05 Kcal/mol
|}

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

=== Example 1: Ethylene + Butadiene ===

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| || Antisymmetric || Symmetric
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|-
| || Symmetric || Antisymmetric
|-
|}

=== Finding the Transition State ===

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

The transition state has the following Molecular orbitals.

{| class="wikitable"
! HOMO
! LUMO

|-
| [[File:HOMO cisbutadiene+ethylene TS.png|300px]]
| [[File:LUMO cisbutadiene+ethylene.png|300px]]

|-
| Antisymmetric
| Symmetric
|}

=== Example 2: Cyclohexadiene + Maleic Anhydride ===

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| || Antisymmetric||Symmetric
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|-
| ||Symmetric||Antisymmetric
|}

=== Locating the Endo Transition State ===

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO FINAL REAL.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:ENDO MOVIE FINAL.gif|center|frame|300px|Endo Transition State Animation]]

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

=== Locating the Exo Transition State ===

In order to find the exo transition state, the procedure was repeated but with the direction of the maleic anhydride reversed. The result is shown below.

<jmol>
<jmolApplet>
<title>Exo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXO DERIV.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:exo ts.gif|center|frame|300px|Exo Transition State Animation]]

This transition state has the following molecular orbitals.

{| class="wikitable"
! HOMO
! LUMO

|-
| [[File:HOMO Exo TS.png|300px]]
| [[File:LUMO Exo TS.png|300px]]
|}

=== Explanation ===

The exo and endo transition structures have energies of -0.05041984 and -0.06407816 hartrees, respectively. This clearly shows the endo to be the lower energy transition state, and since this is the major yet thermodynamically unfavoured product, the reaction must be under kinetic control, as hypothesised.

The reason for the favouring of the endo transition state lies in secondary orbital interactions. The pi-system of the carbonyl bonds can interact efficiently with the pi system of the diene in the endo orientation, an effect which is no present in the exo transition state. This serves to stabilise the endo transition state, despite this structure being more sterically demanding.

== Conclusion ==

In this study Gaussian was used to probe the reaction pathways of two different reactions, the Cope rearrangement and the Diels-Alder cycloaddition. The expected major product of the Diels-Alder reaction was rationalised through characterisation of the transition state.

Rep:Mod:physicalccrossland

2014-11-07T11:49:28Z

Cc3210: /* Optimizing Reactants & Products */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 60 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification involved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
|+ Summary of Transition State Energies
! Chair !! Boat
|-
| E = -234.55698291 || E = -234.54309307
|-
|}

IRC analysis suggests the chair transition state has a gauche conformer precursor, and the boat an APP one. This gives the following activation energies (TS energy - reactant energy).

{| class="wikitable"
! Gauche-Chair
! APP-Boat
|-
| 33.70 Kcal/mol
| 43.05 Kcal/mol
|}

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

=== Example 1: Ethylene + Butadiene ===

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| || Antisymmetric || Symmetric
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|-
| || Symmetric || Antisymmetric
|-
|}

=== Finding the Transition State ===

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

The transition state has the following Molecular orbitals.

{| class="wikitable"
! HOMO
! LUMO

|-
| [[File:HOMO cisbutadiene+ethylene TS.png|300px]]
| [[File:LUMO cisbutadiene+ethylene.png|300px]]

|-
| Antisymmetric
| Symmetric
|}

=== Example 2: Cyclohexadiene + Maleic Anhydride ===

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| || Antisymmetric||Symmetric
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|-
| ||Symmetric||Antisymmetric
|}

=== Locating the Endo Transition State ===

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO FINAL REAL.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:ENDO MOVIE FINAL.gif|center|frame|300px|Endo Transition State Animation]]

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

=== Locating the Exo Transition State ===

In order to find the exo transition state, the procedure was repeated but with the direction of the maleic anhydride reversed. The result is shown below.

<jmol>
<jmolApplet>
<title>Exo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXO DERIV.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:exo ts.gif|center|frame|300px|Exo Transition State Animation]]

This transition state has the following molecular orbitals.

{| class="wikitable"
! HOMO
! LUMO

|-
| [[File:HOMO Exo TS.png|300px]]
| [[File:LUMO Exo TS.png|300px]]
|}

=== Explanation ===

The exo and endo transition structures have energies of -0.05041984 and -0.06407816 hartrees, respectively. This clearly shows the endo to be the lower energy transition state, and since this is the major yet thermodynamically unfavoured product, the reaction must be under kinetic control, as hypothesised.

The reason for the favouring of the endo transition state lies in secondary orbital interactions. The pi-system of the carbonyl bonds can interact efficiently with the pi system of the diene in the endo orientation, an effect which is no present in the exo transition state. This serves to stabilise the endo transition state, despite this structure being more sterically demanding.

== Conclusion ==

In this study Gaussian was used to probe the reaction pathways of two different reactions, the Cope rearrangement and the Diels-Alder cycloaddition. The expected major product of the Diels-Alder reaction was rationalised through characterisation of the transition state.

Rep:Mod:physicalccrossland

2014-11-07T11:46:48Z

Cc3210: /* Conclusion */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 120 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification involved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
|+ Summary of Transition State Energies
! Chair !! Boat
|-
| E = -234.55698291 || E = -234.54309307
|-
|}

IRC analysis suggests the chair transition state has a gauche conformer precursor, and the boat an APP one. This gives the following activation energies (TS energy - reactant energy).

{| class="wikitable"
! Gauche-Chair
! APP-Boat
|-
| 33.70 Kcal/mol
| 43.05 Kcal/mol
|}

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

=== Example 1: Ethylene + Butadiene ===

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| || Antisymmetric || Symmetric
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|-
| || Symmetric || Antisymmetric
|-
|}

=== Finding the Transition State ===

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

The transition state has the following Molecular orbitals.

{| class="wikitable"
! HOMO
! LUMO

|-
| [[File:HOMO cisbutadiene+ethylene TS.png|300px]]
| [[File:LUMO cisbutadiene+ethylene.png|300px]]

|-
| Antisymmetric
| Symmetric
|}

=== Example 2: Cyclohexadiene + Maleic Anhydride ===

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| || Antisymmetric||Symmetric
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|-
| ||Symmetric||Antisymmetric
|}

=== Locating the Endo Transition State ===

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO FINAL REAL.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:ENDO MOVIE FINAL.gif|center|frame|300px|Endo Transition State Animation]]

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

=== Locating the Exo Transition State ===

In order to find the exo transition state, the procedure was repeated but with the direction of the maleic anhydride reversed. The result is shown below.

<jmol>
<jmolApplet>
<title>Exo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXO DERIV.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:exo ts.gif|center|frame|300px|Exo Transition State Animation]]

This transition state has the following molecular orbitals.

{| class="wikitable"
! HOMO
! LUMO

|-
| [[File:HOMO Exo TS.png|300px]]
| [[File:LUMO Exo TS.png|300px]]
|}

=== Explanation ===

The exo and endo transition structures have energies of -0.05041984 and -0.06407816 hartrees, respectively. This clearly shows the endo to be the lower energy transition state, and since this is the major yet thermodynamically unfavoured product, the reaction must be under kinetic control, as hypothesised.

The reason for the favouring of the endo transition state lies in secondary orbital interactions. The pi-system of the carbonyl bonds can interact efficiently with the pi system of the diene in the endo orientation, an effect which is no present in the exo transition state. This serves to stabilise the endo transition state, despite this structure being more sterically demanding.

== Conclusion ==

In this study Gaussian was used to probe the reaction pathways of two different reactions, the Cope rearrangement and the Diels-Alder cycloaddition. The expected major product of the Diels-Alder reaction was rationalised through characterisation of the transition state.

Rep:Mod:physicalccrossland

2014-11-07T11:43:23Z

Cc3210: /* Locating the Endo Transition State */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 120 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification involved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
|+ Summary of Transition State Energies
! Chair !! Boat
|-
| E = -234.55698291 || E = -234.54309307
|-
|}

IRC analysis suggests the chair transition state has a gauche conformer precursor, and the boat an APP one. This gives the following activation energies (TS energy - reactant energy).

{| class="wikitable"
! Gauche-Chair
! APP-Boat
|-
| 33.70 Kcal/mol
| 43.05 Kcal/mol
|}

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

=== Example 1: Ethylene + Butadiene ===

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| || Antisymmetric || Symmetric
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|-
| || Symmetric || Antisymmetric
|-
|}

=== Finding the Transition State ===

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

The transition state has the following Molecular orbitals.

{| class="wikitable"
! HOMO
! LUMO

|-
| [[File:HOMO cisbutadiene+ethylene TS.png|300px]]
| [[File:LUMO cisbutadiene+ethylene.png|300px]]

|-
| Antisymmetric
| Symmetric
|}

=== Example 2: Cyclohexadiene + Maleic Anhydride ===

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| || Antisymmetric||Symmetric
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|-
| ||Symmetric||Antisymmetric
|}

=== Locating the Endo Transition State ===

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO FINAL REAL.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:ENDO MOVIE FINAL.gif|center|frame|300px|Endo Transition State Animation]]

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

=== Locating the Exo Transition State ===

In order to find the exo transition state, the procedure was repeated but with the direction of the maleic anhydride reversed. The result is shown below.

<jmol>
<jmolApplet>
<title>Exo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXO DERIV.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:exo ts.gif|center|frame|300px|Exo Transition State Animation]]

This transition state has the following molecular orbitals.

{| class="wikitable"
! HOMO
! LUMO

|-
| [[File:HOMO Exo TS.png|300px]]
| [[File:LUMO Exo TS.png|300px]]
|}

=== Explanation ===

The exo and endo transition structures have energies of -0.05041984 and -0.06407816 hartrees, respectively. This clearly shows the endo to be the lower energy transition state, and since this is the major yet thermodynamically unfavoured product, the reaction must be under kinetic control, as hypothesised.

The reason for the favouring of the endo transition state lies in secondary orbital interactions. The pi-system of the carbonyl bonds can interact efficiently with the pi system of the diene in the endo orientation, an effect which is no present in the exo transition state. This serves to stabilise the endo transition state, despite this structure being more sterically demanding.

== Conclusion ==

Rep:Mod:physicalccrossland

2014-11-07T11:42:02Z

Cc3210: /* Locating the Endo Transition State */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 120 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification involved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
|+ Summary of Transition State Energies
! Chair !! Boat
|-
| E = -234.55698291 || E = -234.54309307
|-
|}

IRC analysis suggests the chair transition state has a gauche conformer precursor, and the boat an APP one. This gives the following activation energies (TS energy - reactant energy).

{| class="wikitable"
! Gauche-Chair
! APP-Boat
|-
| 33.70 Kcal/mol
| 43.05 Kcal/mol
|}

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

=== Example 1: Ethylene + Butadiene ===

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| || Antisymmetric || Symmetric
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|-
| || Symmetric || Antisymmetric
|-
|}

=== Finding the Transition State ===

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

The transition state has the following Molecular orbitals.

{| class="wikitable"
! HOMO
! LUMO

|-
| [[File:HOMO cisbutadiene+ethylene TS.png|300px]]
| [[File:LUMO cisbutadiene+ethylene.png|300px]]

|-
| Antisymmetric
| Symmetric
|}

=== Example 2: Cyclohexadiene + Maleic Anhydride ===

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| || Antisymmetric||Symmetric
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|-
| ||Symmetric||Antisymmetric
|}

=== Locating the Endo Transition State ===

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO FINAL REAL.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:ENDO MOVIE FINAL.gif|center|frame|300px|Endo Transition State Animation]]

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
| Symmetric||Antisymmetric
|}

=== Locating the Exo Transition State ===

In order to find the exo transition state, the procedure was repeated but with the direction of the maleic anhydride reversed. The result is shown below.

<jmol>
<jmolApplet>
<title>Exo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXO DERIV.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:exo ts.gif|center|frame|300px|Exo Transition State Animation]]

This transition state has the following molecular orbitals.

{| class="wikitable"
! HOMO
! LUMO

|-
| [[File:HOMO Exo TS.png|300px]]
| [[File:LUMO Exo TS.png|300px]]
|}

=== Explanation ===

The exo and endo transition structures have energies of -0.05041984 and -0.06407816 hartrees, respectively. This clearly shows the endo to be the lower energy transition state, and since this is the major yet thermodynamically unfavoured product, the reaction must be under kinetic control, as hypothesised.

The reason for the favouring of the endo transition state lies in secondary orbital interactions. The pi-system of the carbonyl bonds can interact efficiently with the pi system of the diene in the endo orientation, an effect which is no present in the exo transition state. This serves to stabilise the endo transition state, despite this structure being more sterically demanding.

== Conclusion ==

Rep:Mod:physicalccrossland

2014-11-07T11:41:03Z

Cc3210: /* Example 2: Cyclohexadiene + Maleic Anhydride */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 120 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification involved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
|+ Summary of Transition State Energies
! Chair !! Boat
|-
| E = -234.55698291 || E = -234.54309307
|-
|}

IRC analysis suggests the chair transition state has a gauche conformer precursor, and the boat an APP one. This gives the following activation energies (TS energy - reactant energy).

{| class="wikitable"
! Gauche-Chair
! APP-Boat
|-
| 33.70 Kcal/mol
| 43.05 Kcal/mol
|}

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

=== Example 1: Ethylene + Butadiene ===

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| || Antisymmetric || Symmetric
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|-
| || Symmetric || Antisymmetric
|-
|}

=== Finding the Transition State ===

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

The transition state has the following Molecular orbitals.

{| class="wikitable"
! HOMO
! LUMO

|-
| [[File:HOMO cisbutadiene+ethylene TS.png|300px]]
| [[File:LUMO cisbutadiene+ethylene.png|300px]]

|-
| Antisymmetric
| Symmetric
|}

=== Example 2: Cyclohexadiene + Maleic Anhydride ===

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| || Antisymmetric||Symmetric
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|-
| ||Symmetric||Antisymmetric
|}

=== Locating the Endo Transition State ===

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO FINAL REAL.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:ENDO MOVIE FINAL.gif|center|frame|300px|Endo Transition State Animation]]

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

=== Locating the Exo Transition State ===

In order to find the exo transition state, the procedure was repeated but with the direction of the maleic anhydride reversed. The result is shown below.

<jmol>
<jmolApplet>
<title>Exo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXO DERIV.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:exo ts.gif|center|frame|300px|Exo Transition State Animation]]

This transition state has the following molecular orbitals.

{| class="wikitable"
! HOMO
! LUMO

|-
| [[File:HOMO Exo TS.png|300px]]
| [[File:LUMO Exo TS.png|300px]]
|}

=== Explanation ===

The exo and endo transition structures have energies of -0.05041984 and -0.06407816 hartrees, respectively. This clearly shows the endo to be the lower energy transition state, and since this is the major yet thermodynamically unfavoured product, the reaction must be under kinetic control, as hypothesised.

The reason for the favouring of the endo transition state lies in secondary orbital interactions. The pi-system of the carbonyl bonds can interact efficiently with the pi system of the diene in the endo orientation, an effect which is no present in the exo transition state. This serves to stabilise the endo transition state, despite this structure being more sterically demanding.

== Conclusion ==

Rep:Mod:physicalccrossland

2014-11-07T11:38:58Z

Cc3210: /* Finding the Transition State */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 120 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification involved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
|+ Summary of Transition State Energies
! Chair !! Boat
|-
| E = -234.55698291 || E = -234.54309307
|-
|}

IRC analysis suggests the chair transition state has a gauche conformer precursor, and the boat an APP one. This gives the following activation energies (TS energy - reactant energy).

{| class="wikitable"
! Gauche-Chair
! APP-Boat
|-
| 33.70 Kcal/mol
| 43.05 Kcal/mol
|}

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

=== Example 1: Ethylene + Butadiene ===

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| || Antisymmetric || Symmetric
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|-
| || Symmetric || Antisymmetric
|-
|}

=== Finding the Transition State ===

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

The transition state has the following Molecular orbitals.

{| class="wikitable"
! HOMO
! LUMO

|-
| [[File:HOMO cisbutadiene+ethylene TS.png|300px]]
| [[File:LUMO cisbutadiene+ethylene.png|300px]]

|-
| Antisymmetric
| Symmetric
|}

=== Example 2: Cyclohexadiene + Maleic Anhydride ===

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|}

=== Locating the Endo Transition State ===

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO FINAL REAL.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:ENDO MOVIE FINAL.gif|center|frame|300px|Endo Transition State Animation]]

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

=== Locating the Exo Transition State ===

In order to find the exo transition state, the procedure was repeated but with the direction of the maleic anhydride reversed. The result is shown below.

<jmol>
<jmolApplet>
<title>Exo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXO DERIV.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:exo ts.gif|center|frame|300px|Exo Transition State Animation]]

This transition state has the following molecular orbitals.

{| class="wikitable"
! HOMO
! LUMO

|-
| [[File:HOMO Exo TS.png|300px]]
| [[File:LUMO Exo TS.png|300px]]
|}

=== Explanation ===

The exo and endo transition structures have energies of -0.05041984 and -0.06407816 hartrees, respectively. This clearly shows the endo to be the lower energy transition state, and since this is the major yet thermodynamically unfavoured product, the reaction must be under kinetic control, as hypothesised.

The reason for the favouring of the endo transition state lies in secondary orbital interactions. The pi-system of the carbonyl bonds can interact efficiently with the pi system of the diene in the endo orientation, an effect which is no present in the exo transition state. This serves to stabilise the endo transition state, despite this structure being more sterically demanding.

== Conclusion ==

Rep:Mod:physicalccrossland

2014-11-07T11:37:44Z

Cc3210: /* Example 1: Ethylene + Butadiene */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 120 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification involved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
|+ Summary of Transition State Energies
! Chair !! Boat
|-
| E = -234.55698291 || E = -234.54309307
|-
|}

IRC analysis suggests the chair transition state has a gauche conformer precursor, and the boat an APP one. This gives the following activation energies (TS energy - reactant energy).

{| class="wikitable"
! Gauche-Chair
! APP-Boat
|-
| 33.70 Kcal/mol
| 43.05 Kcal/mol
|}

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

=== Example 1: Ethylene + Butadiene ===

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| || Antisymmetric || Symmetric
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|-
| || Symmetric || Antisymmetric
|-
|}

=== Finding the Transition State ===

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

The transition state has the following Molecular orbitals.

{| class="wikitable"
! HOMO
! LUMO
! Column 3, Row 1
|-
| [[File:HOMO cisbutadiene+ethylene TS.png|300px]]
| [[File:LUMO cisbutadiene+ethylene.png|300px]]
| Column 3, Row 2
|-
| Column 1, Row 3
| Column 2, Row 3
| Column 3, Row 3
|}

=== Example 2: Cyclohexadiene + Maleic Anhydride ===

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|}

=== Locating the Endo Transition State ===

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO FINAL REAL.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:ENDO MOVIE FINAL.gif|center|frame|300px|Endo Transition State Animation]]

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

=== Locating the Exo Transition State ===

In order to find the exo transition state, the procedure was repeated but with the direction of the maleic anhydride reversed. The result is shown below.

<jmol>
<jmolApplet>
<title>Exo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXO DERIV.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:exo ts.gif|center|frame|300px|Exo Transition State Animation]]

This transition state has the following molecular orbitals.

{| class="wikitable"
! HOMO
! LUMO

|-
| [[File:HOMO Exo TS.png|300px]]
| [[File:LUMO Exo TS.png|300px]]
|}

=== Explanation ===

The exo and endo transition structures have energies of -0.05041984 and -0.06407816 hartrees, respectively. This clearly shows the endo to be the lower energy transition state, and since this is the major yet thermodynamically unfavoured product, the reaction must be under kinetic control, as hypothesised.

The reason for the favouring of the endo transition state lies in secondary orbital interactions. The pi-system of the carbonyl bonds can interact efficiently with the pi system of the diene in the endo orientation, an effect which is no present in the exo transition state. This serves to stabilise the endo transition state, despite this structure being more sterically demanding.

== Conclusion ==

Rep:Mod:physicalccrossland

2014-11-07T11:25:53Z

Cc3210: /* Finding the Transition State */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 120 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification involved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
|+ Summary of Transition State Energies
! Chair !! Boat
|-
| E = -234.55698291 || E = -234.54309307
|-
|}

IRC analysis suggests the chair transition state has a gauche conformer precursor, and the boat an APP one. This gives the following activation energies (TS energy - reactant energy).

{| class="wikitable"
! Gauche-Chair
! APP-Boat
|-
| 33.70 Kcal/mol
| 43.05 Kcal/mol
|}

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

=== Example 1: Ethylene + Butadiene ===

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|}

=== Finding the Transition State ===

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

The transition state has the following Molecular orbitals.

{| class="wikitable"
! HOMO
! LUMO
! Column 3, Row 1
|-
| [[File:HOMO cisbutadiene+ethylene TS.png|300px]]
| [[File:LUMO cisbutadiene+ethylene.png|300px]]
| Column 3, Row 2
|-
| Column 1, Row 3
| Column 2, Row 3
| Column 3, Row 3
|}

=== Example 2: Cyclohexadiene + Maleic Anhydride ===

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|}

=== Locating the Endo Transition State ===

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO FINAL REAL.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:ENDO MOVIE FINAL.gif|center|frame|300px|Endo Transition State Animation]]

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

=== Locating the Exo Transition State ===

In order to find the exo transition state, the procedure was repeated but with the direction of the maleic anhydride reversed. The result is shown below.

<jmol>
<jmolApplet>
<title>Exo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXO DERIV.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:exo ts.gif|center|frame|300px|Exo Transition State Animation]]

This transition state has the following molecular orbitals.

{| class="wikitable"
! HOMO
! LUMO

|-
| [[File:HOMO Exo TS.png|300px]]
| [[File:LUMO Exo TS.png|300px]]
|}

=== Explanation ===

The exo and endo transition structures have energies of -0.05041984 and -0.06407816 hartrees, respectively. This clearly shows the endo to be the lower energy transition state, and since this is the major yet thermodynamically unfavoured product, the reaction must be under kinetic control, as hypothesised.

The reason for the favouring of the endo transition state lies in secondary orbital interactions. The pi-system of the carbonyl bonds can interact efficiently with the pi system of the diene in the endo orientation, an effect which is no present in the exo transition state. This serves to stabilise the endo transition state, despite this structure being more sterically demanding.

== Conclusion ==

File:LUMO cisbutadiene+ethylene.png

2014-11-07T11:24:42Z

Cc3210:

File:HOMO cisbutadiene+ethylene TS.png

2014-11-07T11:22:59Z

Cc3210:

Rep:Mod:physicalccrossland

2014-11-07T11:16:21Z

Cc3210: /* Explanation */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 120 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification involved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
|+ Summary of Transition State Energies
! Chair !! Boat
|-
| E = -234.55698291 || E = -234.54309307
|-
|}

IRC analysis suggests the chair transition state has a gauche conformer precursor, and the boat an APP one. This gives the following activation energies (TS energy - reactant energy).

{| class="wikitable"
! Gauche-Chair
! APP-Boat
|-
| 33.70 Kcal/mol
| 43.05 Kcal/mol
|}

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

=== Example 1: Ethylene + Butadiene ===

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|}

=== Finding the Transition State ===

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

=== Example 2: Cyclohexadiene + Maleic Anhydride ===

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|}

=== Locating the Endo Transition State ===

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO FINAL REAL.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:ENDO MOVIE FINAL.gif|center|frame|300px|Endo Transition State Animation]]

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

=== Locating the Exo Transition State ===

In order to find the exo transition state, the procedure was repeated but with the direction of the maleic anhydride reversed. The result is shown below.

<jmol>
<jmolApplet>
<title>Exo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXO DERIV.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:exo ts.gif|center|frame|300px|Exo Transition State Animation]]

This transition state has the following molecular orbitals.

{| class="wikitable"
! HOMO
! LUMO

|-
| [[File:HOMO Exo TS.png|300px]]
| [[File:LUMO Exo TS.png|300px]]
|}

=== Explanation ===

The exo and endo transition structures have energies of -0.05041984 and -0.06407816 hartrees, respectively. This clearly shows the endo to be the lower energy transition state, and since this is the major yet thermodynamically unfavoured product, the reaction must be under kinetic control, as hypothesised.

The reason for the favouring of the endo transition state lies in secondary orbital interactions. The pi-system of the carbonyl bonds can interact efficiently with the pi system of the diene in the endo orientation, an effect which is no present in the exo transition state. This serves to stabilise the endo transition state, despite this structure being more sterically demanding.

== Conclusion ==

Rep:Mod:physicalccrossland

2014-11-07T11:13:21Z

Cc3210: /* Optimising the Transition Structure */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 120 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification involved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
|+ Summary of Transition State Energies
! Chair !! Boat
|-
| E = -234.55698291 || E = -234.54309307
|-
|}

IRC analysis suggests the chair transition state has a gauche conformer precursor, and the boat an APP one. This gives the following activation energies (TS energy - reactant energy).

{| class="wikitable"
! Gauche-Chair
! APP-Boat
|-
| 33.70 Kcal/mol
| 43.05 Kcal/mol
|}

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

=== Example 1: Ethylene + Butadiene ===

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|}

=== Finding the Transition State ===

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

=== Example 2: Cyclohexadiene + Maleic Anhydride ===

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|}

=== Locating the Endo Transition State ===

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO FINAL REAL.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:ENDO MOVIE FINAL.gif|center|frame|300px|Endo Transition State Animation]]

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

=== Locating the Exo Transition State ===

In order to find the exo transition state, the procedure was repeated but with the direction of the maleic anhydride reversed. The result is shown below.

<jmol>
<jmolApplet>
<title>Exo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXO DERIV.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:exo ts.gif|center|frame|300px|Exo Transition State Animation]]

This transition state has the following molecular orbitals.

{| class="wikitable"
! HOMO
! LUMO

|-
| [[File:HOMO Exo TS.png|300px]]
| [[File:LUMO Exo TS.png|300px]]
|}

=== Explanation ===

The exo and endo transition structures have energies of -0.05041984 and -0.06407816 hartrees, respectively. This clearly shows the endo to be the lower energy transition state, and since this is the major yet thermodynamically unfavoured product, the reaction must be under kinetic control, as hypothesised.

== Conclusion ==

Rep:Mod:physicalccrossland

2014-11-07T11:09:35Z

Cc3210: /* Locating the Exo Transition State */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 120 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification invlved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
|+ Summary of Transition State Energies
! Chair !! Boat
|-
| E = -234.55698291 || E = -234.54309307
|-
|}

IRC analysis suggests the chair transition state has a gauche conformer precursor, and the boat an APP one. This gives the following activation energies (TS energy - reactant energy).

{| class="wikitable"
! Gauche-Chair
! APP-Boat
|-
| 33.70 Kcal/mol
| 43.05 Kcal/mol
|}

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

=== Example 1: Ethylene + Butadiene ===

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|}

=== Finding the Transition State ===

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

=== Example 2: Cyclohexadiene + Maleic Anhydride ===

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|}

=== Locating the Endo Transition State ===

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO FINAL REAL.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:ENDO MOVIE FINAL.gif|center|frame|300px|Endo Transition State Animation]]

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

=== Locating the Exo Transition State ===

In order to find the exo transition state, the procedure was repeated but with the direction of the maleic anhydride reversed. The result is shown below.

<jmol>
<jmolApplet>
<title>Exo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXO DERIV.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:exo ts.gif|center|frame|300px|Exo Transition State Animation]]

This transition state has the following molecular orbitals.

{| class="wikitable"
! HOMO
! LUMO

|-
| [[File:HOMO Exo TS.png|300px]]
| [[File:LUMO Exo TS.png|300px]]
|}

=== Explanation ===

The exo and endo transition structures have energies of -0.05041984 and -0.06407816 hartrees, respectively. This clearly shows the endo to be the lower energy transition state, and since this is the major yet thermodynamically unfavoured product, the reaction must be under kinetic control, as hypothesised.

== Conclusion ==

Rep:Mod:physicalccrossland

2014-11-07T11:03:57Z

Cc3210: /* Locating the Exo Transition State */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 120 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification invlved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
|+ Summary of Transition State Energies
! Chair !! Boat
|-
| E = -234.55698291 || E = -234.54309307
|-
|}

IRC analysis suggests the chair transition state has a gauche conformer precursor, and the boat an APP one. This gives the following activation energies (TS energy - reactant energy).

{| class="wikitable"
! Gauche-Chair
! APP-Boat
|-
| 33.70 Kcal/mol
| 43.05 Kcal/mol
|}

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

=== Example 1: Ethylene + Butadiene ===

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|}

=== Finding the Transition State ===

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

=== Example 2: Cyclohexadiene + Maleic Anhydride ===

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|}

=== Locating the Endo Transition State ===

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO FINAL REAL.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:ENDO MOVIE FINAL.gif|center|frame|300px|Endo Transition State Animation]]

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

=== Locating the Exo Transition State ===

In order to find the exo transition state, the procedure was repeated but with the direction of the maleic anhydride reversed. The result is shown below.

<jmol>
<jmolApplet>
<title>Exo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXO DERIV.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:exo ts.gif|center|frame|300px|Exo Transition State Animation]]

This transition state has the following molecular orbitals.

{| class="wikitable"
! HOMO
! LUMO

|-
| [[File:HOMO Exo TS.png|300px]]
| [[File:LUMO Exo TS.png|300px]]
|}

== Conclusion ==

Rep:Mod:physicalccrossland

2014-11-07T11:03:33Z

Cc3210: /* Locating the Exo Transition State */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 120 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification invlved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
|+ Summary of Transition State Energies
! Chair !! Boat
|-
| E = -234.55698291 || E = -234.54309307
|-
|}

IRC analysis suggests the chair transition state has a gauche conformer precursor, and the boat an APP one. This gives the following activation energies (TS energy - reactant energy).

{| class="wikitable"
! Gauche-Chair
! APP-Boat
|-
| 33.70 Kcal/mol
| 43.05 Kcal/mol
|}

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

=== Example 1: Ethylene + Butadiene ===

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|}

=== Finding the Transition State ===

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

=== Example 2: Cyclohexadiene + Maleic Anhydride ===

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|}

=== Locating the Endo Transition State ===

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO FINAL REAL.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:ENDO MOVIE FINAL.gif|center|frame|300px|Endo Transition State Animation]]

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

=== Locating the Exo Transition State ===

In order to find the exo transition state, the procedure was repeated but with the direction of the maleic anhydride reversed. The result is shown below.

<jmol>
<jmolApplet>
<title>Exo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXO DERIV.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:exo ts.gif|center|frame|300px|Exo Transition State Animation]]

This transition state has the following molecular orbitals.

{| class="wikitable"
! HOMO
! LUMO

|-
| [[File:HOMO Exo TS.png|200px]]
| [[File:LUMO Exo TS.png|200px]]
|}

== Conclusion ==

Rep:Mod:physicalccrossland

2014-11-07T11:02:45Z

Cc3210: /* Locating the Exo Transition State */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 120 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification invlved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
|+ Summary of Transition State Energies
! Chair !! Boat
|-
| E = -234.55698291 || E = -234.54309307
|-
|}

IRC analysis suggests the chair transition state has a gauche conformer precursor, and the boat an APP one. This gives the following activation energies (TS energy - reactant energy).

{| class="wikitable"
! Gauche-Chair
! APP-Boat
|-
| 33.70 Kcal/mol
| 43.05 Kcal/mol
|}

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

=== Example 1: Ethylene + Butadiene ===

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|}

=== Finding the Transition State ===

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

=== Example 2: Cyclohexadiene + Maleic Anhydride ===

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|}

=== Locating the Endo Transition State ===

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO FINAL REAL.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:ENDO MOVIE FINAL.gif|center|frame|300px|Endo Transition State Animation]]

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

=== Locating the Exo Transition State ===

In order to find the exo transition state, the procedure was repeated but with the direction of the maleic anhydride reversed. The result is shown below.

<jmol>
<jmolApplet>
<title>Exo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXO DERIV.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:exo ts.gif|center|frame|300px|Exo Transition State Animation]]

This transition state has the following molecular orbitals.

{| class="wikitable"
! HOMO
! LUMO

|-
| [[File:HOMO Exo TS.png]]
| [[File:LUMO Exo TS.png]]
|}

== Conclusion ==

File:LUMO Exo TS.png

2014-11-07T11:00:21Z

Cc3210:

File:HOMO Exo TS.png

2014-11-07T10:59:33Z

Cc3210:

Rep:Mod:physicalccrossland

2014-11-07T10:48:23Z

Cc3210: /* Locating the Exo Transition State */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 120 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification invlved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
|+ Summary of Transition State Energies
! Chair !! Boat
|-
| E = -234.55698291 || E = -234.54309307
|-
|}

IRC analysis suggests the chair transition state has a gauche conformer precursor, and the boat an APP one. This gives the following activation energies (TS energy - reactant energy).

{| class="wikitable"
! Gauche-Chair
! APP-Boat
|-
| 33.70 Kcal/mol
| 43.05 Kcal/mol
|}

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

=== Example 1: Ethylene + Butadiene ===

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|}

=== Finding the Transition State ===

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

=== Example 2: Cyclohexadiene + Maleic Anhydride ===

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|}

=== Locating the Endo Transition State ===

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO FINAL REAL.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:ENDO MOVIE FINAL.gif|center|frame|300px|Endo Transition State Animation]]

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

=== Locating the Exo Transition State ===

In order to find the exo transition state, the procedure was repeated but with the direction of the maleic anhydride reversed. The result is shown below.

<jmol>
<jmolApplet>
<title>Exo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXO DERIV.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:exo ts.gif|center|frame|300px|Exo Transition State Animation]]

== Conclusion ==

Rep:Mod:physicalccrossland

2014-11-07T10:47:57Z

Cc3210:

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 120 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification invlved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
|+ Summary of Transition State Energies
! Chair !! Boat
|-
| E = -234.55698291 || E = -234.54309307
|-
|}

IRC analysis suggests the chair transition state has a gauche conformer precursor, and the boat an APP one. This gives the following activation energies (TS energy - reactant energy).

{| class="wikitable"
! Gauche-Chair
! APP-Boat
|-
| 33.70 Kcal/mol
| 43.05 Kcal/mol
|}

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

=== Example 1: Ethylene + Butadiene ===

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|}

=== Finding the Transition State ===

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

=== Example 2: Cyclohexadiene + Maleic Anhydride ===

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|}

=== Locating the Endo Transition State ===

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO FINAL REAL.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:ENDO MOVIE FINAL.gif|center|frame|300px|Endo Transition State Animation]]

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

=== Locating the Exo Transition State ===

In order to find the exo transition state, the procedure was repeated but with the direction of the maleic anhydride reversed. The result is shown below.

<jmol>
<jmolApplet>
<title>Exo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXO DERIV.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:exo ts.gif|center|frame|300px|Exo Transition State ANimation]]

== Conclusion ==

Rep:Mod:physicalccrossland

2014-11-07T10:46:55Z

Cc3210: /* Reaction 2: The Diels-Alder Cycloaddition */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 120 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification invlved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
|+ Summary of Transition State Energies
! Chair !! Boat
|-
| E = -234.55698291 || E = -234.54309307
|-
|}

IRC analysis suggests the chair transition state has a gauche conformer precursor, and the boat an APP one. This gives the following activation energies (TS energy - reactant energy).

{| class="wikitable"
! Gauche-Chair
! APP-Boat
|-
| 33.70 Kcal/mol
| 43.05 Kcal/mol
|}

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

=== Example 1: Ethylene + Butadiene ===

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|}

=== Finding the Transition State ===

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

=== Example 2: Cyclohexadiene + Maleic Anhydride ===

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|}

=== Locating the Endo Transition State ===

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO FINAL REAL.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:ENDO MOVIE FINAL.gif|center|frame|300px|Endo Transition State Animation]]

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

=== Locating the Exo Transition State ===

In order to find the exo transition state, the procedure was repeated but with the direction of the maleic anhydride reversed. The result is shown below.

<jmol>
<jmolApplet>
<title>Exo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EXO DERIV.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:exo ts.gif|center|frame|300px|Exo Transition State ANimation]]

File:EXO DERIV.mol

2014-11-07T10:45:54Z

Cc3210:

Rep:Mod:physicalccrossland

2014-11-07T10:42:58Z

Cc3210: /* Example 2: Cyclohexadiene + Maleic Anhydride */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 120 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification invlved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
|+ Summary of Transition State Energies
! Chair !! Boat
|-
| E = -234.55698291 || E = -234.54309307
|-
|}

IRC analysis suggests the chair transition state has a gauche conformer precursor, and the boat an APP one. This gives the following activation energies (TS energy - reactant energy).

{| class="wikitable"
! Gauche-Chair
! APP-Boat
|-
| 33.70 Kcal/mol
| 43.05 Kcal/mol
|}

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

=== Example 1: Ethylene + Butadiene ===

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|}

=== Finding the Transition State ===

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

=== Example 2: Cyclohexadiene + Maleic Anhydride ===

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|}

=== Locating the Endo Transition State ===

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO FINAL REAL.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:ENDO MOVIE FINAL.gif|center|frame|300px|Endo Transition State Animation]]

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

=== Locating the Exo Transition State ===

In order to find the exo transition state, the procedure was repeated but with the direction of the maleic anhydride reversed. The result is shown below.

[[File:exo ts.gif|center|frame|300px|Exo Transition State ANimation]]

Rep:Mod:physicalccrossland

2014-11-07T10:42:02Z

Cc3210: /* Example 2: Cyclohexadiene + Maleic Anhydride */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 120 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification invlved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
|+ Summary of Transition State Energies
! Chair !! Boat
|-
| E = -234.55698291 || E = -234.54309307
|-
|}

IRC analysis suggests the chair transition state has a gauche conformer precursor, and the boat an APP one. This gives the following activation energies (TS energy - reactant energy).

{| class="wikitable"
! Gauche-Chair
! APP-Boat
|-
| 33.70 Kcal/mol
| 43.05 Kcal/mol
|}

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

=== Example 1: Ethylene + Butadiene ===

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|}

=== Finding the Transition State ===

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

=== Example 2: Cyclohexadiene + Maleic Anhydride ===

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|}

'''Locating the Endo Transition State'''

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO FINAL REAL.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:ENDO MOVIE FINAL.gif|center|frame|300px|Endo Transition State Animation]]

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

'''Locating the Exo Transition State'''

In order to find the exo transition state, the procedure was repeated but with the direction of the maleic anhydride reversed. The result is shown below.

[[File:exo ts.gif|center|frame|300px|Exo Transition State ANimation]]

Rep:Mod:physicalccrossland

2014-11-07T10:38:43Z

Cc3210: /* Example 2: Cyclohexadiene + Maleic Anhydride */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 120 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification invlved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
|+ Summary of Transition State Energies
! Chair !! Boat
|-
| E = -234.55698291 || E = -234.54309307
|-
|}

IRC analysis suggests the chair transition state has a gauche conformer precursor, and the boat an APP one. This gives the following activation energies (TS energy - reactant energy).

{| class="wikitable"
! Gauche-Chair
! APP-Boat
|-
| 33.70 Kcal/mol
| 43.05 Kcal/mol
|}

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

=== Example 1: Ethylene + Butadiene ===

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|}

=== Finding the Transition State ===

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

=== Example 2: Cyclohexadiene + Maleic Anhydride ===

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|}

'''Locating the Endo Transition State'''

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO FINAL REAL.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:ENDO MOVIE FINAL.gif|frame|center|300px|Endo Transition State Animation]]

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

'''Locating the Exo Transition State'''

In order to find the exo transition state, the procedure was repeated but with the direction of the maleic anhydride reversed. The result is shown below.

[[File:exo ts.gif|center|frame|300px|Exo Transition State]]

Rep:Mod:physicalccrossland

2014-11-07T10:38:08Z

Cc3210: /* Example 2: Cyclohexadiene + Maleic Anhydride */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 120 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification invlved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
|+ Summary of Transition State Energies
! Chair !! Boat
|-
| E = -234.55698291 || E = -234.54309307
|-
|}

IRC analysis suggests the chair transition state has a gauche conformer precursor, and the boat an APP one. This gives the following activation energies (TS energy - reactant energy).

{| class="wikitable"
! Gauche-Chair
! APP-Boat
|-
| 33.70 Kcal/mol
| 43.05 Kcal/mol
|}

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

=== Example 1: Ethylene + Butadiene ===

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|}

=== Finding the Transition State ===

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

=== Example 2: Cyclohexadiene + Maleic Anhydride ===

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|}

'''Locating the Endo Transition State'''

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO FINAL REAL.mol</uploadedFileContents>
</jmolApplet>
</jmol>

[[File:ENDO MOVIE FINAL.gif|frame|center|Endo Transition State Animation]]

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

'''Locating the Exo Transition State'''

In order to find the exo transition state, the procedure was repeated but with the direction of the maleic anhydride reversed. The result is shown below.

[[File:exo ts.gif|center|frame|300px|Exo Transition State]]

File:ENDO MOVIE FINAL.gif

2014-11-07T10:37:18Z

Cc3210:

Rep:Mod:physicalccrossland

2014-11-07T10:34:07Z

Cc3210: /* Example 2: Cyclohexadiene + Maleic Anhydride */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 120 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification invlved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
|+ Summary of Transition State Energies
! Chair !! Boat
|-
| E = -234.55698291 || E = -234.54309307
|-
|}

IRC analysis suggests the chair transition state has a gauche conformer precursor, and the boat an APP one. This gives the following activation energies (TS energy - reactant energy).

{| class="wikitable"
! Gauche-Chair
! APP-Boat
|-
| 33.70 Kcal/mol
| 43.05 Kcal/mol
|}

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

=== Example 1: Ethylene + Butadiene ===

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|}

=== Finding the Transition State ===

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

=== Example 2: Cyclohexadiene + Maleic Anhydride ===

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|}

'''Locating the Endo Transition State'''

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ENDO FINAL REAL.mol</uploadedFileContents>
</jmolApplet>
</jmol>

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

'''Locating the Exo Transition State'''

In order to find the exo transition state, the procedure was repeated but with the direction of the maleic anhydride reversed. The result is shown below.

[[File:exo ts.gif|center|frame|300px|Exo Transition State]]

File:ENDO FINAL REAL.mol

2014-11-07T10:33:08Z

Cc3210:

File:ENDO FINAL.png

2014-11-07T10:31:58Z

Cc3210:

Rep:Mod:physicalccrossland

2014-11-07T10:29:47Z

Cc3210: /* Example 2: Cyclohexadiene + Maleic Anhydride */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 120 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification invlved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
|+ Summary of Transition State Energies
! Chair !! Boat
|-
| E = -234.55698291 || E = -234.54309307
|-
|}

IRC analysis suggests the chair transition state has a gauche conformer precursor, and the boat an APP one. This gives the following activation energies (TS energy - reactant energy).

{| class="wikitable"
! Gauche-Chair
! APP-Boat
|-
| 33.70 Kcal/mol
| 43.05 Kcal/mol
|}

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

=== Example 1: Ethylene + Butadiene ===

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|}

=== Finding the Transition State ===

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

=== Example 2: Cyclohexadiene + Maleic Anhydride ===

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|}

'''Locating the Endo Transition State'''

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>FROZEN COORDINATE ENDO2 NEW.mol</uploadedFileContents>
</jmolApplet>
</jmol>

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

'''Locating the Exo Transition State'''

In order to find the exo transition state, the procedure was repeated but with the direction of the maleic anhydride reversed. The result is shown below.

[[File:exo ts.gif|center|frame|300px|Exo Transition State]]

Rep:Mod:physicalccrossland

2014-11-07T10:27:52Z

Cc3210: /* Example 2: Cyclohexadiene + Maleic Anhydride */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 120 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification invlved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
|+ Summary of Transition State Energies
! Chair !! Boat
|-
| E = -234.55698291 || E = -234.54309307
|-
|}

IRC analysis suggests the chair transition state has a gauche conformer precursor, and the boat an APP one. This gives the following activation energies (TS energy - reactant energy).

{| class="wikitable"
! Gauche-Chair
! APP-Boat
|-
| 33.70 Kcal/mol
| 43.05 Kcal/mol
|}

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

=== Example 1: Ethylene + Butadiene ===

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|}

=== Finding the Transition State ===

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

=== Example 2: Cyclohexadiene + Maleic Anhydride ===

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|}

'''Locating the Endo Transition State'''

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>FROZEN COORDINATE ENDO2 NEW.mol</uploadedFileContents>
</jmolApplet>
</jmol>

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

'''Locating the Exo Transition State'''

In order to find the exo transition state, the procedure was repeated but with the direction of the maleic anhydride reversed. The result is shown below.

[[File:]]

Rep:Mod:physicalccrossland

2014-11-07T10:25:12Z

Cc3210: /* Optimising the Transition Structure */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 120 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification invlved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
|+ Summary of Transition State Energies
! Chair !! Boat
|-
| E = -234.55698291 || E = -234.54309307
|-
|}

IRC analysis suggests the chair transition state has a gauche conformer precursor, and the boat an APP one. This gives the following activation energies (TS energy - reactant energy).

{| class="wikitable"
! Gauche-Chair
! APP-Boat
|-
| 33.70 Kcal/mol
| 43.05 Kcal/mol
|}

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

=== Example 1: Ethylene + Butadiene ===

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|}

=== Finding the Transition State ===

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

=== Example 2: Cyclohexadiene + Maleic Anhydride ===

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|}

'''Locating the Endo Transition State'''

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>FROZEN COORDINATE ENDO2 NEW.mol</uploadedFileContents>
</jmolApplet>
</jmol>

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

'''Locating the Exo Transition State'''

In order to find the exo transition state, the procedure was repeated but with the direction of the maleic anhydride reversed.

Rep:Mod:physicalccrossland

2014-11-07T10:10:03Z

Cc3210: /* Example 2: Cyclohexadiene + Maleic Anhydride */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 120 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification invlved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
|+ Summary of Transition State Energies
! Chair !! Boat
|-
| E = -234.55698291 || E = -234.54309307
|-
|}

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

=== Example 1: Ethylene + Butadiene ===

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|}

=== Finding the Transition State ===

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

=== Example 2: Cyclohexadiene + Maleic Anhydride ===

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|}

'''Locating the Endo Transition State'''

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>FROZEN COORDINATE ENDO2 NEW.mol</uploadedFileContents>
</jmolApplet>
</jmol>

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

'''Locating the Exo Transition State'''

In order to find the exo transition state, the procedure was repeated but with the direction of the maleic anhydride reversed.

Rep:Mod:physicalccrossland

2014-11-07T10:07:28Z

Cc3210: /* Optimising the Transition Structure */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 120 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification invlved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
|+ Summary of Transition State Energies
! Chair !! Boat
|-
| E = -234.55698291 || E = -234.54309307
|-
|}

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

=== Example 1: Ethylene + Butadiene ===

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|}

=== Finding the Transition State ===

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

=== Example 2: Cyclohexadiene + Maleic Anhydride ===

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|}

'''Locating the Endo Transition State'''

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>FROZEN COORDINATE ENDO2 NEW.mol</uploadedFileContents>
</jmolApplet>
</jmol>

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

'''Locating the Exo Transition State'''

In order to find the ex transition state, the procedure was repeated but with the direction of the malice anhydride reversed.

Rep:Mod:physicalccrossland

2014-11-07T08:49:12Z

Cc3210: /* Finding the Transition State */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 120 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification invlved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

'''Probing Reaction Pathways'''

It is impossible from inspection to observe which transition state serves to interconvert which conformation of reactants and products. This can be achieved by locating the nearest minima to the transition states on the potential energy surface, through the Intrinsic Reaction Coordinate(IRC) method. This works by step-wise deviations from the transition structure in the direction that the energy slope is steepest. Performing this analysis on the chair conformer of the transition state yields the final structure shown below, which closely resembles the gauche conformer.

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

=== Example 1: Ethylene + Butadiene ===

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|}

=== Finding the Transition State ===

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

=== Example 2: Cyclohexadiene + Maleic Anhydride ===

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|}

'''Locating the Endo Transition State'''

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>FROZEN COORDINATE ENDO2 NEW.mol</uploadedFileContents>
</jmolApplet>
</jmol>

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

'''Locating the Exo Transition State'''

In order to find the ex transition state, the procedure was repeated but with the direction of the malice anhydride reversed.

Rep:Mod:physicalccrossland

2014-11-07T08:48:40Z

Cc3210: /* Reaction 2: The Diels-Alder Cycloaddition */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 120 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification invlved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

'''Probing Reaction Pathways'''

It is impossible from inspection to observe which transition state serves to interconvert which conformation of reactants and products. This can be achieved by locating the nearest minima to the transition states on the potential energy surface, through the Intrinsic Reaction Coordinate(IRC) method. This works by step-wise deviations from the transition structure in the direction that the energy slope is steepest. Performing this analysis on the chair conformer of the transition state yields the final structure shown below, which closely resembles the gauche conformer.

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

=== Example 1: Ethylene + Butadiene ===

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|}

=== Finding the Transition State ===

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

'''Cyclohexadiene + Maleic Anhydride'''

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|}

'''Locating the Endo Transition State'''

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>FROZEN COORDINATE ENDO2 NEW.mol</uploadedFileContents>
</jmolApplet>
</jmol>

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

'''Locating the Exo Transition State'''

In order to find the ex transition state, the procedure was repeated but with the direction of the malice anhydride reversed.

Rep:Mod:physicalccrossland

2014-11-07T08:47:39Z

Cc3210: /* Finding the Transition State */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 120 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification invlved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

'''Probing Reaction Pathways'''

It is impossible from inspection to observe which transition state serves to interconvert which conformation of reactants and products. This can be achieved by locating the nearest minima to the transition states on the potential energy surface, through the Intrinsic Reaction Coordinate(IRC) method. This works by step-wise deviations from the transition structure in the direction that the energy slope is steepest. Performing this analysis on the chair conformer of the transition state yields the final structure shown below, which closely resembles the gauche conformer.

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|}

=== Finding the Transition State ===

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

'''Cyclohexadiene + Maleic Anhydride'''

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|}

'''Locating the Endo Transition State'''

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>FROZEN COORDINATE ENDO2 NEW.mol</uploadedFileContents>
</jmolApplet>
</jmol>

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

'''Locating the Exo Transition State'''

In order to find the ex transition state, the procedure was repeated but with the direction of the malice anhydride reversed.

Rep:Mod:physicalccrossland

2014-11-07T08:47:23Z

Cc3210: /* Reaction 2: The Diels-Alder Cycloaddition */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 120 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification invlved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

'''Probing Reaction Pathways'''

It is impossible from inspection to observe which transition state serves to interconvert which conformation of reactants and products. This can be achieved by locating the nearest minima to the transition states on the potential energy surface, through the Intrinsic Reaction Coordinate(IRC) method. This works by step-wise deviations from the transition structure in the direction that the energy slope is steepest. Performing this analysis on the chair conformer of the transition state yields the final structure shown below, which closely resembles the gauche conformer.

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|}

== Finding the Transition State ==

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

'''Cyclohexadiene + Maleic Anhydride'''

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|}

'''Locating the Endo Transition State'''

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>FROZEN COORDINATE ENDO2 NEW.mol</uploadedFileContents>
</jmolApplet>
</jmol>

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

'''Locating the Exo Transition State'''

In order to find the ex transition state, the procedure was repeated but with the direction of the malice anhydride reversed.

Rep:Mod:physicalccrossland

2014-11-07T08:46:34Z

Cc3210: /* Reaction 2: The Diels-Alder Cycloaddition */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 120 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification invlved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

'''Probing Reaction Pathways'''

It is impossible from inspection to observe which transition state serves to interconvert which conformation of reactants and products. This can be achieved by locating the nearest minima to the transition states on the potential energy surface, through the Intrinsic Reaction Coordinate(IRC) method. This works by step-wise deviations from the transition structure in the direction that the energy slope is steepest. Performing this analysis on the chair conformer of the transition state yields the final structure shown below, which closely resembles the gauche conformer.

== Reaction 2: The Diels-Alder Cycloaddition ==

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|}

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

'''Cyclohexadiene + Maleic Anhydride'''

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|}

'''Locating the Endo Transition State'''

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>FROZEN COORDINATE ENDO2 NEW.mol</uploadedFileContents>
</jmolApplet>
</jmol>

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

'''Locating the Exo Transition State'''

In order to find the ex transition state, the procedure was repeated but with the direction of the malice anhydride reversed.

Rep:Mod:physicalccrossland

2014-11-07T08:44:39Z

Cc3210: /* Reaction 2: The Diels-Alder Cycloaddition */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 120 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification invlved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

'''Probing Reaction Pathways'''

It is impossible from inspection to observe which transition state serves to interconvert which conformation of reactants and products. This can be achieved by locating the nearest minima to the transition states on the potential energy surface, through the Intrinsic Reaction Coordinate(IRC) method. This works by step-wise deviations from the transition structure in the direction that the energy slope is steepest. Performing this analysis on the chair conformer of the transition state yields the final structure shown below, which closely resembles the gauche conformer.

=== Reaction 2: The Diels-Alder Cycloaddition ===

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|}

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

'''Cyclohexadiene + Maleic Anhydride'''

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|}

'''Locating the Endo Transition State'''

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Endo Transition State</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>FROZEN COORDINATE ENDO2 NEW.mol</uploadedFileContents>
</jmolApplet>
</jmol>

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

'''Locating the Exo Transition State'''

In order to find the ex transition state, the procedure was repeated but with the direction of the malice anhydride reversed.

Rep:Mod:physicalccrossland

2014-11-07T08:43:50Z

Cc3210: /* Reaction 2: The Diels-Alder Cycloaddition */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 120 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification invlved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

'''Probing Reaction Pathways'''

It is impossible from inspection to observe which transition state serves to interconvert which conformation of reactants and products. This can be achieved by locating the nearest minima to the transition states on the potential energy surface, through the Intrinsic Reaction Coordinate(IRC) method. This works by step-wise deviations from the transition structure in the direction that the energy slope is steepest. Performing this analysis on the chair conformer of the transition state yields the final structure shown below, which closely resembles the gauche conformer.

=== Reaction 2: The Diels-Alder Cycloaddition ===

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|}

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

'''Cyclohexadiene + Maleic Anhydride'''

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|}

'''Locating the Endo Transition State'''

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>FROZEN COORDINATE ENDO2 NEW.mol</uploadedFileContents>
</jmolApplet>
</jmol>

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

'''Locating the Exo Transition State'''

In order to find the ex transition state, the procedure was repeated but with the direction of the malice anhydride reversed.

File:FROZEN COORDINATE ENDO2 NEW.mol

2014-11-07T08:42:00Z

Cc3210:

Rep:Mod:physicalccrossland

2014-11-07T08:34:57Z

Cc3210: /* Reaction 2: The Diels-Alder Cycloaddition */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 120 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
<jmolApplet>
<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification invlved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
</jmolApplet>
</jmol>

<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

'''Probing Reaction Pathways'''

It is impossible from inspection to observe which transition state serves to interconvert which conformation of reactants and products. This can be achieved by locating the nearest minima to the transition states on the potential energy surface, through the Intrinsic Reaction Coordinate(IRC) method. This works by step-wise deviations from the transition structure in the direction that the energy slope is steepest. Performing this analysis on the chair conformer of the transition state yields the final structure shown below, which closely resembles the gauche conformer.

=== Reaction 2: The Diels-Alder Cycloaddition ===

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|}

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

'''Cyclohexadiene + Maleic Anhydride'''

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|}

'''Locating the Endo Transition State'''

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

[[Image:Endo TS 3.gif|center|frame|x300px|Endo Transition State]]

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}

'''Locating the Exo Transition State'''

In order to find the ex transition state, the procedure was repeated but with the direction of the malice anhydride reversed.

Rep:Mod:physicalccrossland

2014-11-07T00:30:26Z

Cc3210: /* Reaction 1: Cope Rearrangement */

== Introduction ==

It is possible to use computational methods to understand the transition structures for many reactions. Gaussian uses quantum mechanical molecular orbital calculations to achieve this.

== Reaction 1: Cope Rearrangement ==

=== Introduction ===

[[File:Cope.jpg|center|Cope Rearrangement]]

The cope rearrangement constitutes the [3,3] sigmatropic (thermal activation, suprafacial) rearrangement of 1,5-hexadiene, as shown.

=== Optimizing Reactants & Products ===

1,5-hexadiene can adopt two principle dihedral angles about its cental C-C bond, antiperiplanar (APP; where the R groups are at 180 degrees) and Gauche (where they are at 120 degrees). To probe the energy of the APP, 1,5-hexadiene was constructed in Gaussian, and the dihedral angle set to 180. Thereafter, the structure was optimised to the Hartree-Fock (HF) 3-21G level of theory, yielding an energy of -231.69253525 Hartrees, with symmetry Ci. Similar analysis with a Gauche conformation yielded an energy of -231.69266122, with C1 symmetry. This showed the Gauche conformation to be the preferred conformer.

The antiperiplanar conformer was further optimised to the B3LYP/6-31G* level, yielding an energy of -234.61170276 hartrees, and identical treatment of the gauche conformer gave an energy of -234.61068499 hartrees.

{| class="wikitable center"
|+ Structures
! Antiperiplanar !! Gauche
|-
| [[Image:Antiperiplanar.png|200px]]||[[Image:Gauche.png|200px| ]]

|-
| E = -231.69253525 (HF) || E = -231.69266122 (HF)
|-
| E = -234.61170276 (B3LYP)|| E = -234.61068499 (B3LYP)
|}

=== Optimising the Transition Structure ===

In order to begin the process of the optimisation of the chair transition state, a simple allyl fragment was constructed and optimised to the HF/3-21G level, yielding the structure shown below.

[[File:Allyl.png|x200px|200px|frame|center|Allyl Fragment]]

Two of these allyl fragments were then aligned as shown below, approximating the separation of the terminal carbons to 2.2 Angstroms.

[[File:chair TS guess.png|x400px|frame|center|Chair Transition State Guess]]

When optimised to the HF/3-21G level, the energy recorded was -231.61932242 hartrees, with point group C1. Further optimisation was carried out using the reaction coordinate freeze method, first by fixing the terminal bond lenghts and then by optimising these, the combination of which yields the fully optimised transition state. The result is shown below.

<jmol>
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<title>Chair Transition Structure Optimised by Frozen Coordinate</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>041114 FREEZE BONDS 2.mol</uploadedFileContents>
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Next, we can optimise the boat transition state, first using the QST2 method. This method involves the input of the reactants and products, which the software interpolates between to find the transition state. An initial computation using 50 iterations yielded the structure below, clearly a distorted chair transition state. Modification of the reactants and products to more closely resemble the anticipated transition state ensured the structure shown next was achieved, resembling how we would expect the transition state to look. This modification invlved setting the central dihedral angle to 0 degrees, and the C-C-C bond angles to 100 degrees.

<jmol>
<jmolApplet>
<title>Distorted Boat Transition Structure by QST2</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ANTI 2 BOAT distorted.mol</uploadedFileContents>
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<jmol>
<jmolApplet>
<title>Boat Transition Structure by QST2 with Bond Angle Adjustment</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti 2 boat wac new mol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

'''Probing Reaction Pathways'''

It is impossible from inspection to observe which transition state serves to interconvert which conformation of reactants and products. This can be achieved by locating the nearest minima to the transition states on the potential energy surface, through the Intrinsic Reaction Coordinate(IRC) method. This works by step-wise deviations from the transition structure in the direction that the energy slope is steepest. Performing this analysis on the chair conformer of the transition state yields the final structure shown below, which closely resembles the gauche conformer.

=== Reaction 2: The Diels-Alder Cycloaddition ===

The Diels-Alder reaction is an example of a pericyclic reaction, whereby two new sigma-bonds are formed from existing pi-bonds, via a concerted reaction. The reactants are a conjugated diene (which must be in the s-cis conformation to react) and a dieneophile. Reaction occurs via the interaction of the HOMO of one species with the LUMO of another. The transition state therefore takes the conformation that achieves most efficient overlap of the orbitals (MOs are shown below for ethylene and butadiene) and can also be influenced by secondary orbital interactions if the reactants are substituted, resulting in differing product stereochemistry. A generic example is shown below, the reaction of butadiene and ethylene.

[[File:Diels-Alder.png|x150px|frame|center|Diels-Alder Cycloaddition]]

{| class="wikitable"
|+ Molecular Orbitals
! !! HOMO !! LUMO
|-
| Cis-Butadiene || [[Image:HOMO-Cis-Butadiene.png|200px]]||[[Image:LUMO-Cis-Butadiene.png|200px]]
|-
| Ethylene || [[Image:HOMO-Ethylene.png|200px]]||[[Image:LUMO-Ethylene.png|200px]]
|}

The transition structure for the Diels-Alder reaction is known to have a structure similar to that shown below. In order to optimise the transition state the structure was constructed in Gaussian and optimised. First, both cis-butadiene and ethylene were independently optimised, then positioned in the same plane as each other and optimised using the AM1 semi-empirical method with the terminal bond lengths frozen. Thereafter the bond lengths were set to derivative and the structure below was found, with the vibration shown as well, the transition structure.

[[Image:Diels-Alder TS.png|center|frame|200px|Diels-Alder Approximate Transition State]]

[[Image:D-A TS 2.gif|300px|center|frame|Diels-Alder Transition State]]

'''Cyclohexadiene + Maleic Anhydride'''

As previously mentioned, substituents upon the reactants cause varying stereochemistry in the products. The following example, of cyclohexadiene and maleic anhydride, forms the endo orientation as the major product. Since this is the thermodynamically less favoured product, the reaction must therefore be under kinetic control with the transition state to the end being the lowest in energy. We will now see if that is indeed the case.

[[Image:Diels-Alder Maleic.png|center|frame|x200px|Reaction Scheme]]

The molecular orbitals of the reactants are as shown below.

{| class="wikitable"
|+ MO's
! !! HOMO !! LUMO
|-
| Cyclohexadiene||[[Image:HOMO-cyclohexadiene.png|200px| ]] || [[Image:LUMO-cyclohexadiene.png|200px| ]]
|-
| Maleic Anhdride||[[Image:HOMO-maleic anhydride.png|200px| ]] || [[Image:LUMO- maleic anhydride.png|200px| ]]
|}

'''Locating the Endo Transition State'''

In order to find the end transition state, both the reactants were optimised by the AM1 method, and positioned such that they looked approximately as expected (with the oxygen of maleic anhydride over the cyclohexadiene molecule). The structure was then optimised using the frozen coordinate method and the result is shown below.

[[Image:Endo TS 3.gif|center|frame|x300px|Endo Transition State]]

This transition state has the MO's as follows.

{| class="wikitable"
|+ MOs- Endo TS
! HOMO !! LUMO
|-
| [[Image:HOMO Endo TS.png|300px| ]] || [[Image:LUMO Endo TS.png|300px]]
|-
|}