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Rep:Mod:Mrh214

2016-12-02T11:33:03Z

Mrh214:

== '''Diels Alder Cycloaddition''' ==
=== Butadiene and Ethene optimization to Cyclohexene via PM6 ===
==== Method ====

1) Butadiene and ethene were optimized to a minimum seperately. Once optimized, they were placed in a similar geometry closely resembling that of the transition state (TS) required for the Diels Alder reaction; with the 4 carbon atoms in the reaction centre being frozen approximately 2.2 angstroms from eachother. This geometry was optimized to a minimum. The optimized geometry was then re-optimized to a TS (Berny), and this was confirmed by the presence of 1 negative frequency in the vibrations. An IRC was run on this TS in both directions with N=100. This geometry was manually displaced and optimized further to a minimum and product confirmation was given by all positive frequencies.

==== Butadiene ====
[[File:Butadiene.jpg|300px]]

==== Ethene ====
[[File:Ethene.jpg|300px]]

The C=C bonds in butadiene are 1.33531 Å; the C-C is 1.46835 Å. The C=C in ethene is 1.32731 Å.

==== TS ====
[[File:TS.jpg|300px]]

[[File:TS vibration 1.gif]]

This is the imaginary vibration at -949.3 icm-1, which corresponds to the TS.

[[File:TS vibration 2.gif]]

And this shows the first positive vibration at 144.91 icm-1. The motions are synchronous, therefore implying that the bond formations are also, synchronous.

In the TS the 2 C=C bonds of butadiene are now 1.37978 and 1.37974 Å. The previous C-C in butadiene is now 1.41114 Å; this has compressed as in the products, it will become a double bond. Similarly, the C=C bonds are now elongated slightly, due to becoming single bonds in the product.

The C=C in ethene for the TS has elongated to 1.38173, as this will be a single bond in the product.

The C atoms involved in the reaction centre for the Diels-Alder mechanism, from butadiene to the ethene carbons are at length 2.11423 and 2.11494 Å.

{| class="wikitable" border="1"
|+ Frontier Orbitals of Reactants
! FMO !! Butadiene !! Ethene
|-
| HOMO || [[File:HOMO Butadiene.jpg|300px]] || [[File:HOMO ethene.jpg|175px]]
|-
| LUMO || [[File:LUMO butadiene.jpg|175px]] || [[File:LUMO ethene.jpg|175px]]
|-
|}

(FMO = Frontier Molecular Orbitals)

{| class="wikitable" border="1"
|+ TS MO's
|-
| [[File:TS MO 16.jpg|175px]] || [[File:TS MO 17.jpg|175px]]
|-
| [[File:TS MO 18.jpg|175px]] || [[File:TS MO 19.jpg|175px]]
|}

==== Cyclohexene ====
[[File:Cyclohexene.jpg|300px]]

==== Bond Distance Variation Over Course of Reaction ====

{| class="wikitable" border="1"
|+ Bond lengths in reactants
! !! Bond lengths Å !!
|-
! Bond Type !! Butadiene !! Ethene
|-
| C-C || 1.46835 || -
|-
| C=C || 1.33531 || 1.32731
|}

{| class="wikitable" border="1"
|+ Bond lengths in TS
! !! Bond lengths Å !!
|-
! Bond Type !! Butadiene fragment !! Ethene fragment
|-
| C-C || 1.41114 || -
|-
| C=C || 1.37978 / 1.37974 || 1.38173
|}

{| class="wikitable" border="1"
|+ 2 C-C lengths in reaction centre
! Reaction centre !! Carbon atom distances Å
|-
| C-C || 2.11423 / 2.11494
|}

{| class="wikitable" border="1"
|+ Bond lengths in Cyclohexene product
! !! Cyclohexene
|-
! Bond type !! Bond lengths Å
|-
| C-C || 1.50085 / 1.50087
|-
| C-C || 1.53714 / 1.53704
|-
| C-C (opposite C=C) || 1.53453
|-
| C=C || 1.33698
|}

In the final product, the C=C is 1.33698 Å, the neighboring C-C on either side to the double bond are 1.50085 and 1.50087 Å. The adjacent C-C to these bonds are 1.53714 and 1.53704 Å. And the C-C directly opposite the C=C is 1.53453 Å.

Typical C-C sp3 length is 1.54 Å and the corresponding sp2 length is 1.34 Å. The Van der Waals radius of carbon is 1.70 Å. The sum of Van der Waals radii for 2 carbon atoms is 3.4 Å. The bond distances displayed in the above tables, are all less than this, and so there is bonding interaction. The key aspect here is for the 4 C atoms in the reaction centre, with both being approximately 2.114 Å distance between each C-C pair, this shows progressive bonding interaction, as these distances are far less than the Van der Waals radius for 2 C atoms.[1][2]

==== The Diels-Alder MO Diagram[3] ====
[[File:DA MO.jpg|400px]]

The MO diagram shows that the HOMO for the diene is closer in energy to the LUMO of the dienophile, hence will allow more efficient/constructive overlap (and lower energy antibonding MO) than the opposite case; which would be the LUMO of the diene with the HOMO of the dienophile.

==== The Symmetry Conditions[5] ====
Let g = gerade (symmetric) and u = ungerade (antisymmetric).

Orbitals of the same symmetry may combine, ie. g-g, u-u, which is an allowed reaction. However, orbitals of mis-matched symmetry may not, ie. g-u / u-g, and so is a forbidden reaction.

The orbital overlap integral is non-zero for g-g / u-u, but zero for g-u / u-g.

== '''A Comparison of Endo- and Exo- Products''' ==
=== The Reaction of Cyclohexadiene and 1,3-Dioxole by PM6 ===
==== Method ====

Both reactants were optimized, and subsequently placed in the endo TS conformation with the 4 C atoms involved in the reaction centre being frozen from eachother at a distance of 2.2 Å. An optimization to a minimum was carried out, followed by an optimization to a TS (Berny). An IRC was done on this TS structure, which ran in both directions, at N=20. The geometry obtained at the start of the reaction profile from the IRC was optimized to a minimum and no imaginary frequencies confirmed this to be the product.

The same procedure was carried out for the exo-conformer.

==== B3LYP frequency pictures for exo and endo ====

A B3LYP/6-31G(d) calculation was run on both TS geometries and the presence of 1 imaginary frequency in both TS structures confirmed them to be the TS. These frequencies were 520.86 and 528.8icm-1 for the endo and exo TS's respectively.

{| class="wikitable" border="1"
|+ B3LYP Vibrations and TS
! Endo !! Exo
|-
| [[File:Endo B3LYP TS.jpg|275px]] || [[File:Exo B3LYP TS.jpg|275px]]
|-
| [[File:Endo B3LYP Vib.jpg|275px]] || [[File:Exo B3LYP Vib.jpg|275px]]
|}

==== The releveant FMOs for Diels-Alder by symmetry ====

From the MO diagram for Diels-Alder, the same orbitals come into play for these reactions; combining g symmetry with g, and u with u.

{| class="wikitable" border="1"
|+ endo-TS MO's
|-
| Bonding Orbitals || [[File:EndoTS MO 29.jpg|175px]] || [[File:EndoTS MO 30.jpg|175px]]
|-
| Antibonding Orbitals ||[[File:EndoTS MO 31.jpg|175px]] || [[File:EndoTS MO 32.jpg|175px]]
|}

{| class="wikitable" border="1"
|+ exo-TS MO's
|-
| Bonding Orbitals || [[File:Exo TS MO 29.jpg|175px]] || [[File:Exo TS MO 30.jpg|175px]]
|-
| Antibonding Orbitals || [[File:Exo TS MO 31.jpg|175px]] || [[File:Exo TS MO 32.jpg|175px]]
|}

{| class="wikitable" border="1"
|+ Endo vs Exo TS's
! !! Endo !! Exo
|-
| TS vibrations || [[File:Endo TS Vibrations.jpg|275px]] || [[File:Exo TS Vibrations.jpg|275px]]
|-
| TS Geometry || [[File:Endo TS Geometry.jpg|275px]] || [[File:Exo TS Geometry.jpg|275px]]
|-
|}

The presence of 1 imaginary negative frequency shows that these are the TS structures for the 2 reactions.

{| class="wikitable" border="1"
|+ Endo and Exo Product Formation from IRC
! !! Endo !! Exo
|-
| IRC || [[File:Endo product.gif|750px|]] || [[File:Exo product.gif|750px]]
|-
| Reaction coordinate || [[File:Endo Reaction Coordinate.jpg|750px]] || [[File:Exo Reaction Coordinate.jpg|750px]]
|}

=== Thermochemistry of Exo- vs Endo- ===

{| class="wikitable" border="1"
|+ Endo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.130081 || 20.64 || -
|-
| TS || 0.137942 || - || -
|-
| Product || 0.244570 || - || 300.59
|}

{| class="wikitable" border="1"
|+ Exo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.136771 || 5.60 || -
|-
| TS || 0.138905 || - || -
|-
| Product || 0.037977 || - || -259.38
|}

==== Secondary Orbital Interactions ====

{| class="wikitable" border="1"
|+ HOMO of exo and endo TS
! TS !! HOMO
|-
| endo || [[File:Endo TS HOMO 2ndary orbital interaction.jpg|450px]]
|-
| exo || [[File:Exo TS HOMO no 2ndary interaction.jpg|200px]]
|}

Primary orbital interactions lead to sigma bond formation. The dienophile, in this case the 1,3 Dioxole, is pointing away from the diene which does not allow for any further orbital interactions; and so only has primary orbital interactions, and forms the exo-product.

In the endo conformation, the dienophile is positioned such that the lobes of the C-O and the back orbitals in the cyclohexadiene can form a favourable bonding interaction, which lowers the energy of the TS, and in turn, is the kinetic product. Such an interaction is a secondary orbital interaction. A point to note is that no such bonds are formed in this case.4

This such reaction is a normal demand Diels-Alder reaction, as the diene is electron rich whereas the dienophile, has electronegative oxygen atoms making it electron poor.5

== '''Diels-Alder and Chelotropic Pathways''' ==
=== o-Xylylene and SO2 optimization to adducts of both reaction types ===
==== Method ====

==== Diels-Alder ====

The product was drawn and optimized to a minimum using the PM6 method. The C-S and C-O bonds in the resulting structure were removed and separated by 2.4 and 2.0 Å respectively, and frozen. This was then optimized to a TS (Berny). An IRC was then run on this TS geometry, and the lowest energy conformation from the resulting reaction profile was optimized to a minimum.

This gave the exo product; so the TS geometry was altered by manually displacing the O atom of the SO2 into an approximate endo geometry for TS. This was then optimized to a TS (Berny), after which an IRC was run and a subsequent optimization to a minimum on the product to obtain the energies. Using this method, allowed for both reaction paths to be analysed.

==== Chelotropic ====

The chelotropic product was drawn and optimized to a minimum. The C-S bonds of this resulting geometry were broken and the coordinates were frozen at approximately 2.2 Å apart. This structure was then optimized to a minimum, and the subsequent geometry reoptimized to a TS (Berny). An IRC was run on this TS with N=200, forward only, to obtain a reaction path.

{| class="wikitable" border="1"
|+ Diels-Alder & Chelotropic Reactions
! !! Endo !! Exo !! Chelotropic
|-
| TS || [[File:Endo Xyl TS.jpg|650px]] || [[File:Exo Xyl TS.jpg|650px]] || [[File:Chelotropic TS.jpg|650px]]
|-
| IRC || [[File:Endo Xyl IRC.gif]] || [[File:Exo Xyl IRC.gif]] || [[File:Chelotropic IRC.gif]]
|-
| Reaction Profile || [[File:Endo Xyl Reaction Profile.jpg|650px]] || [[File:Exo Xyl Reaction Coordinate.jpg|650px]] || [[File:Chelotropic Reaction Coordinate.jpg|650px]]
|}

During the course of all 3 reactions, xylylene's 6 membered ring becomes aromatized, which gives it extra thermodynamic stability due to the lowering in energy. This extra energy provides the driving force(ΔG) of the reaction. The stabilization of the TS in this way allows the o-xylylene reaction to progress at a faster rate. This is very true for the Diels-Alder reaction.

=== Thermochemistry of o-Xylylene and SO2 ===

{| class="wikitable" border="1"
|+ Endo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.090737 || -0.47 || -
|-
| TS || 0.090559 || - || -
|-
| Product || 0.021693 || - || -181.28
|}

{| class="wikitable" border="1"
|+ Exo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.092130 || -0.000053 || -
|-
| TS || 0.092077 || - || -
|-
| Product || 0.021455 || - || -185.56
|}

{| class="wikitable" border="1"
|+ Chelotropic
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.097953 || 2.9 || -
|-
| TS || 0.099059 || - || -
|-
| Product || -0.000002 || - || -257.18
|}

=== '''A Comparison of Reaction Profiles''' ===

[[File:All 3 Reaction Profiles.jpg|930px]]

It can be seen that the chelotropic product has the lowest energy and is the most thermodynamically stable product. It also has the highest activation energy out of all 3 reactions, suggesting it may have the largest kinetic stability in comparison to the other reactions. The endo and exo products are very close in energy suggesting similar thermodynamic stability, however, the secondary orbital interactions which occur in the endo TS conformation from the lobes of the oxgeyn atom as the dienophile SO2 approaches will allow lowering of the TS activation barrier, thus allowing the endo product to be the kinetic product and form faster than the exo product.

==== '''References''' ====

1. Allen, F.H., Kennard, O., Watson, D.G., Brammer, L., Orpen, G.A. and Taylor, R.(1987) ‘Tables of bond lengths determined by x-ray and neutron diffraction. Part 1. Bond lengths in organic compounds’, Journal of the Chemical Society, Perkin Transactions 2, (12), pp. 1–19. doi: 10.1039/P298700000S1.

2. Inorganic Materials, Vol. 37, No. 9, 2001, pp. 871–885. Translated from Neorganicheskie Materialy, Vol. 37, No. 9, 2001, pp. 1031–1046. Original Russian Text Copyright © 2001 by Batsanov.

3. Clayden, J., Greeves, N., Warren, S. and Claydon, J. (2000) Organic chemistry. New York: Oxford University Press.

4. Gheorghiu, M.D. (no date) Diels Alder Reactions. Available at: https://ocw.mit.edu/courses/chemistry/5-32-intermediate-chemical-experimentation-spring-2003/labs/Appendix_1_Diels_Alder_Reactions_03.pdf.

5. Prof Sue Gibson, Pericyclics Lecture Course 2016, Imperial College Chemistry Department.

'''''By Riashat Hossain'''''

Rep:Mod:Mrh214

2016-12-02T11:30:55Z

Mrh214:

Rep:Mod:Mrh214

2016-12-02T11:19:32Z

Mrh214:

== '''Diels Alder Cycloaddition''' ==
=== Butadiene and Ethene optimization to Cyclohexene via PM6 ===
==== Method ====

1) Butadiene and ethene were optimized to a minimum seperately. Once optimized, they were placed in a similar geometry closely resembling that of the transition state (TS) required for the Diels Alder reaction; with the 4 carbon atoms in the reaction centre being frozen approximately 2.2 angstroms from eachother. This geometry was optimized to a minimum. The optimized geometry was then re-optimized to a TS (Berny), and this was confirmed by the presence of 1 negative frequency in the vibrations. An IRC was run on this TS in both directions with N=100. This geometry was manually displaced and optimized further to a minimum and product confirmation was given by all positive frequencies.

==== Butadiene ====
[[File:Butadiene.jpg|300px]]

==== Ethene ====
[[File:Ethene.jpg|300px]]

The C=C bonds in butadiene are 1.33531 Å; the C-C is 1.46835 Å. The C=C in ethene is 1.32731 Å.

==== TS ====
[[File:TS.jpg|300px]]

[[File:TS vibration 1.gif]]

This is the imaginary vibration at -949.3 icm-1, which corresponds to the TS.

[[File:TS vibration 2.gif]]

And this shows the first positive vibration at 144.91 icm-1. The motions are synchronous, therefore implying that the bond formations are also, synchronous.

In the TS the 2 C=C bonds of butadiene are now 1.37978 and 1.37974 Å. The previous C-C in butadiene is now 1.41114 Å; this has compressed as in the products, it will become a double bond. Similarly, the C=C bonds are now elongated slightly, due to becoming single bonds in the product.

The C=C in ethene for the TS has elongated to 1.38173, as this will be a single bond in the product.

The C atoms involved in the reaction centre for the Diels-Alder mechanism, from butadiene to the ethene carbons are at length 2.11423 and 2.11494 Å.

{| class="wikitable" border="1"
|+ Frontier Orbitals of Reactants
! FMO !! Butadiene !! Ethene
|-
| HOMO || [[File:HOMO Butadiene.jpg|300px]] || [[File:HOMO ethene.jpg|175px]]
|-
| LUMO || [[File:LUMO butadiene.jpg|175px]] || [[File:LUMO ethene.jpg|175px]]
|-
|}

(FMO = Frontier Molecular Orbitals)

{| class="wikitable" border="1"
|+ TS MO's
|-
| [[File:TS MO 16.jpg|175px]] || [[File:TS MO 17.jpg|175px]]
|-
| [[File:TS MO 18.jpg|175px]] || [[File:TS MO 19.jpg|175px]]
|}

==== Cyclohexene ====
[[File:Cyclohexene.jpg|300px]]

==== Bond Distance Variation Over Course of Reaction ====

{| class="wikitable" border="1"
|+ Bond lengths in reactants
! !! Bond lengths Å !!
|-
! Bond Type !! Butadiene !! Ethene
|-
| C-C || 1.46835 || -
|-
| C=C || 1.33531 || 1.32731
|}

{| class="wikitable" border="1"
|+ Bond lengths in TS
! !! Bond lengths Å !!
|-
! Bond Type !! Butadiene fragment !! Ethene fragment
|-
| C-C || 1.41114 || -
|-
| C=C || 1.37978 / 1.37974 || 1.38173
|}

{| class="wikitable" border="1"
|+ 2 C-C lengths in reaction centre
! Reaction centre !! Carbon atom distances Å
|-
| C-C || 2.11423 / 2.11494
|}

{| class="wikitable" border="1"
|+ Bond lengths in Cyclohexene product
! !! Cyclohexene
|-
! Bond type !! Bond lengths Å
|-
| C-C || 1.50085 / 1.50087
|-
| C-C || 1.53714 / 1.53704
|-
| C-C (opposite C=C) || 1.53453
|-
| C=C || 1.33698
|}

In the final product, the C=C is 1.33698 Å, the neighboring C-C on either side to the double bond are 1.50085 and 1.50087 Å. The adjacent C-C to these bonds are 1.53714 and 1.53704 Å. And the C-C directly opposite the C=C is 1.53453 Å.

Typical C-C sp3 length is 1.54 Å and the corresponding sp2 length is 1.34 Å. The Van der Waals radius of carbon is 1.70 Å. The sum of Van der Waals radii for 2 carbon atoms is 3.4 Å. The bond distances displayed in the above tables, are all less than this, and so there is bonding interaction. The key aspect here is for the 4 C atoms in the reaction centre, with both being approximately 2.114 Å distance between each C-C pair, this shows progressive bonding interaction, as these distances are far less than the Van der Waals radius for 2 C atoms.[1][2]

==== The Diels-Alder MO Diagram[3] ====
[[File:DA MO.jpg|400px]]

The MO diagram shows that the HOMO for the diene is closer in energy to the LUMO of the dienophile, hence will allow more efficient/constructive overlap (and lower energy antibonding MO) than the opposite case; which would be the LUMO of the diene with the HOMO of the dienophile.

==== The Symmetry Conditions5 ====
Let g = gerade (symmetric) and u = ungerade (antisymmetric).

Orbitals of the same symmetry may combine, ie. g-g, u-u, which is an allowed reaction. However, orbitals of mis-matched symmetry may not, ie. g-u / u-g, and so is a forbidden reaction.

The orbital overlap integral is non-zero for g-g / u-u, but zero for g-u / u-g.

== '''A Comparison of Endo- and Exo- Products''' ==
=== The Reaction of Cyclohexadiene and 1,3-Dioxole by PM6 ===
==== Method ====

Both reactants were optimized, and subsequently placed in the endo TS conformation with the 4 C atoms involved in the reaction centre being frozen from eachother at a distance of 2.2 Å. An optimization to a minimum was carried out, followed by an optimization to a TS (Berny). An IRC was done on this TS structure, which ran in both directions, at N=20. The geometry obtained at the start of the reaction profile from the IRC was optimized to a minimum and no imaginary frequencies confirmed this to be the product.

The same procedure was carried out for the exo-conformer.

==== B3LYP frequency pictures for exo and endo ====

A B3LYP/6-31G(d) calculation was run on both TS geometries and the presence of 1 imaginary frequency in both TS structures confirmed them to be the TS. These frequencies were 520.86 and 528.8icm-1 for the endo and exo TS's respectively.

{| class="wikitable" border="1"
|+ B3LYP Vibrations and TS
! Endo !! Exo
|-
| [[File:Endo B3LYP TS.jpg|275px]] || [[File:Exo B3LYP TS.jpg|275px]]
|-
| [[File:Endo B3LYP Vib.jpg|275px]] || [[File:Exo B3LYP Vib.jpg|275px]]
|}

==== The releveant FMOs for Diels-Alder by symmetry ====

From the MO diagram for Diels-Alder, the same orbitals come into play for these reactions.

{| class="wikitable" border="1"
|+ endo-TS MO's
|-
| Bonding Orbitals || [[File:EndoTS MO 29.jpg|175px]] || [[File:EndoTS MO 30.jpg|175px]]
|-
| Antibonding Orbitals ||[[File:EndoTS MO 31.jpg|175px]] || [[File:EndoTS MO 32.jpg|175px]]
|}

{| class="wikitable" border="1"
|+ exo-TS MO's
|-
| Bonding Orbitals || [[File:Exo TS MO 29.jpg|175px]] || [[File:Exo TS MO 30.jpg|175px]]
|-
| Antibonding Orbitals || [[File:Exo TS MO 31.jpg|175px]] || [[File:Exo TS MO 32.jpg|175px]]
|}

{| class="wikitable" border="1"
|+ Endo vs Exo TS's
! !! Endo !! Exo
|-
| TS vibrations || [[File:Endo TS Vibrations.jpg|275px]] || [[File:Exo TS Vibrations.jpg|275px]]
|-
| TS Geometry || [[File:Endo TS Geometry.jpg|275px]] || [[File:Exo TS Geometry.jpg|275px]]
|-
|}

The presence of 1 imaginary negative frequency shows that these are the TS structures for the 2 reactions.

{| class="wikitable" border="1"
|+ Endo and Exo Product Formation from IRC
! !! Endo !! Exo
|-
| IRC || [[File:Endo product.gif|750px|]] || [[File:Exo product.gif|750px]]
|-
| Reaction coordinate || [[File:Endo Reaction Coordinate.jpg|750px]] || [[File:Exo Reaction Coordinate.jpg|750px]]
|}

=== Thermochemistry of Exo- vs Endo- ===

{| class="wikitable" border="1"
|+ Endo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.130081 || 20.64 || -
|-
| TS || 0.137942 || - || -
|-
| Product || 0.244570 || - || 300.59
|}

{| class="wikitable" border="1"
|+ Exo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.136771 || 5.60 || -
|-
| TS || 0.138905 || - || -
|-
| Product || 0.037977 || - || -259.38
|}

==== Secondary Orbital Interactions ====

{| class="wikitable" border="1"
|+ HOMO of exo and endo TS
! TS !! HOMO
|-
| endo || [[File:Endo TS HOMO 2ndary orbital interaction.jpg|450px]]
|-
| exo || [[File:Exo TS HOMO no 2ndary interaction.jpg|200px]]
|}

Primary orbital interactions lead to sigma bond formation. The dienophile, in this case the 1,3 Dioxole, is pointing away from the diene which does not allow for any further orbital interactions; and so only has primary orbital interactions, and forms the exo-product.

In the endo conformation, the dienophile is positioned such that the lobes of the C-O and the back orbitals in the cyclohexadiene can form a favourable bonding interaction, which lowers the energy of the TS, and in turn, is the kinetic product. Such an interaction is a secondary orbital interaction. A point to note is that no such bonds are formed in this case.4

This such reaction is a normal demand Diels-Alder reaction, as the diene is electron rich whereas the dienophile, has electronegative oxygen atoms making it electron poor.5

== '''Diels-Alder and Chelotropic Pathways''' ==
=== o-Xylylene and SO2 optimization to adducts of both reaction types ===
==== Method ====

==== Diels-Alder ====

The product was drawn and optimized to a minimum using the PM6 method. The C-S and C-O bonds in the resulting structure were removed and separated by 2.4 and 2.0 Å respectively, and frozen. This was then optimized to a TS (Berny). An IRC was then run on this TS geometry, and the lowest energy conformation from the resulting reaction profile was optimized to a minimum.

This gave the exo product; so the TS geometry was altered by manually displacing the O atom of the SO2 into an approximate endo geometry for TS. This was then optimized to a TS (Berny), after which an IRC was run and a subsequent optimization to a minimum on the product to obtain the energies. Using this method, allowed for both reaction paths to be analysed.

==== Chelotropic ====

The chelotropic product was drawn and optimized to a minimum. The C-S bonds of this resulting geometry were broken and the coordinates were frozen at approximately 2.2 Å apart. This structure was then optimized to a minimum, and the subsequent geometry reoptimized to a TS (Berny). An IRC was run on this TS with N=200, forward only, to obtain a reaction path.

{| class="wikitable" border="1"
|+ Diels-Alder & Chelotropic Reactions
! !! Endo !! Exo !! Chelotropic
|-
| TS || [[File:Endo Xyl TS.jpg|650px]] || [[File:Exo Xyl TS.jpg|650px]] || [[File:Chelotropic TS.jpg|650px]]
|-
| IRC || [[File:Endo Xyl IRC.gif]] || [[File:Exo Xyl IRC.gif]] || [[File:Chelotropic IRC.gif]]
|-
| Reaction Profile || [[File:Endo Xyl Reaction Profile.jpg|650px]] || [[File:Exo Xyl Reaction Coordinate.jpg|650px]] || [[File:Chelotropic Reaction Coordinate.jpg|650px]]
|}

During the course of all 3 reactions, xylylene's 6 membered ring becomes aromatized, which gives it extra thermodynamic stability due to the lowering in energy. This extra energy provides the driving force(ΔG) of the reaction. The stabilization of the TS in this way allows the o-xylylene reaction to progress at a faster rate. This is very true for the Diels-Alder reaction.

=== Thermochemistry of o-Xylylene and SO2 ===

{| class="wikitable" border="1"
|+ Endo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.090737 || -0.47 || -
|-
| TS || 0.090559 || - || -
|-
| Product || 0.021693 || - || -181.28
|}

{| class="wikitable" border="1"
|+ Exo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.092130 || -0.000053 || -
|-
| TS || 0.092077 || - || -
|-
| Product || 0.021455 || - || -185.56
|}

{| class="wikitable" border="1"
|+ Chelotropic
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.097953 || 2.9 || -
|-
| TS || 0.099059 || - || -
|-
| Product || -0.000002 || - || -257.18
|}

=== '''A Comparison of Reaction Profiles''' ===

[[File:All 3 Reaction Profiles.jpg|930px]]

It can be seen that the chelotropic product has the lowest energy and is the most thermodynamically stable product. The endo and exo products are very close in energy suggesting similar thermodynamic stability, however, the secondary orbital interactions which occur in the endo TS conformation from the lobes of the oxgeyn atom as the dienophile SO2 approaches will allow lowering of the TS activation barrier, thus allowing the endo product to be the kinetic product and form faster than the exo product.

==== '''References''' ====

1. Allen, F.H., Kennard, O., Watson, D.G., Brammer, L., Orpen, G.A. and Taylor, R.(1987) ‘Tables of bond lengths determined by x-ray and neutron diffraction. Part 1. Bond lengths in organic compounds’, Journal of the Chemical Society, Perkin Transactions 2, (12), pp. 1–19. doi: 10.1039/P298700000S1.

2. Inorganic Materials, Vol. 37, No. 9, 2001, pp. 871–885. Translated from Neorganicheskie Materialy, Vol. 37, No. 9, 2001, pp. 1031–1046. Original Russian Text Copyright © 2001 by Batsanov.

3. Clayden, J., Greeves, N., Warren, S. and Claydon, J. (2000) Organic chemistry. New York: Oxford University Press.

4. Gheorghiu, M.D. (no date) Diels Alder Reactions. Available at: https://ocw.mit.edu/courses/chemistry/5-32-intermediate-chemical-experimentation-spring-2003/labs/Appendix_1_Diels_Alder_Reactions_03.pdf.

5. Prof Sue Gibson, Pericyclics Lecture Course 2016, Imperial College Chemistry Department.

Rep:Mod:Mrh214

2016-12-02T11:04:45Z

Mrh214:

== '''Diels Alder Cycloaddition''' ==
=== Butadiene and Ethene optimization to Cyclohexene via PM6 ===
==== Method ====

1) Butadiene and ethene were optimized to a minimum seperately. Once optimized, they were placed in a similar geometry closely resembling that of the transition state (TS) required for the Diels Alder reaction; with the 4 carbon atoms in the reaction centre being frozen approximately 2.2 angstroms from eachother. This geometry was optimized to a minimum. The optimized geometry was then re-optimized to a TS (Berny), and this was confirmed by the presence of 1 negative frequency in the vibrations. An IRC was run on this TS in both directions with N=100. This geometry was manually displaced and optimized further to a minimum and product confirmation was given by all positive frequencies.

==== Butadiene ====
[[File:Butadiene.jpg|300px]]

==== Ethene ====
[[File:Ethene.jpg|300px]]

The C=C bonds in butadiene are 1.33531 Å; the C-C is 1.46835 Å. The C=C in ethene is 1.32731 Å.

==== TS ====
[[File:TS.jpg|300px]]

[[File:TS vibration 1.gif]]

This is the imaginary vibration at -949.3 icm-1, which corresponds to the TS.

[[File:TS vibration 2.gif]]

And this shows the first positive vibration at 144.91 icm-1. The motions are synchronous, therefore implying that the bond formations are also, synchronous.

In the TS the 2 C=C bonds of butadiene are now 1.37978 and 1.37974 Å. The previous C-C in butadiene is now 1.41114 Å; this has compressed as in the products, it will become a double bond. Similarly, the C=C bonds are now elongated slightly, due to becoming single bonds in the product.

The C=C in ethene for the TS has elongated to 1.38173, as this will be a single bond in the product.

The C atoms involved in the reaction centre for the Diels-Alder mechanism, from butadiene to the ethene carbons are at length 2.11423 and 2.11494 Å.

{| class="wikitable" border="1"
|+ Frontier Orbitals of Reactants
! FMO !! Butadiene !! Ethene
|-
| HOMO || [[File:HOMO Butadiene.jpg|300px]] || [[File:HOMO ethene.jpg|175px]]
|-
| LUMO || [[File:LUMO butadiene.jpg|175px]] || [[File:LUMO ethene.jpg|175px]]
|-
|}

(FMO = Frontier Molecular Orbitals)

{| class="wikitable" border="1"
|+ TS MO's
|-
| [[File:TS MO 16.jpg|175px]] || [[File:TS MO 17.jpg|175px]]
|-
| [[File:TS MO 18.jpg|175px]] || [[File:TS MO 19.jpg|175px]]
|}

==== Cyclohexene ====
[[File:Cyclohexene.jpg|300px]]

==== Bond Distance Variation Over Course of Reaction ====

{| class="wikitable" border="1"
|+ Bond lengths in reactants
! !! Bond lengths Å !!
|-
! Bond Type !! Butadiene !! Ethene
|-
| C-C || 1.46835 || -
|-
| C=C || 1.33531 || 1.32731
|}

{| class="wikitable" border="1"
|+ Bond lengths in TS
! !! Bond lengths Å !!
|-
! Bond Type !! Butadiene fragment !! Ethene fragment
|-
| C-C || 1.41114 || -
|-
| C=C || 1.37978 / 1.37974 || 1.38173
|}

{| class="wikitable" border="1"
|+ 2 C-C lengths in reaction centre
! Reaction centre !! Carbon atom distances Å
|-
| C-C || 2.11423 / 2.11494
|}

{| class="wikitable" border="1"
|+ Bond lengths in Cyclohexene product
! !! Cyclohexene
|-
! Bond type !! Bond lengths Å
|-
| C-C || 1.50085 / 1.50087
|-
| C-C || 1.53714 / 1.53704
|-
| C-C (opposite C=C) || 1.53453
|-
| C=C || 1.33698
|}

In the final product, the C=C is 1.33698 Å, the neighboring C-C on either side to the double bond are 1.50085 and 1.50087 Å. The adjacent C-C to these bonds are 1.53714 and 1.53704 Å. And the C-C directly opposite the C=C is 1.53453 Å.

Typical C-C sp3 length is 1.54 Å and the corresponding sp2 length is 1.34 Å. The Van der Waals radius of carbon is 1.70 Å. The sum of Van der Waals radii for 2 carbon atoms is 3.4 Å. The bond distances displayed in the above tables, are all less than this, and so there is bonding interaction. The key aspect here is for the 4 C atoms in the reaction centre, with both being approximately 2.114 Å distance between each C-C pair, this shows progressive bonding interaction, as these distances are far less than the Van der Waals radius for 2 C atoms.[1][2]

==== The Diels-Alder MO Diagram[3] ====
[[File:DA MO.jpg|400px]]

The MO diagram shows that the HOMO for the diene is closer in energy to the LUMO of the dienophile, hence will allow more efficient/constructive overlap (and lower energy antibonding MO) than the opposite case; which would be the LUMO of the diene with the HOMO of the dienophile.

==== The Symmetry Conditions ====
Let g = gerade (symmetric) and u = ungerade (antisymmetric).

Orbitals of the same symmetry may combine, ie. g-g, u-u. However, orbitals of mis-matched symmetry may not, ie. g-u / u-g.

The orbital overlap integral is non-zero for g-g / u-u, but zero for g-u / u-g.

DIELS-ALDER REACTIONS, Mircea D. Gherghiu

== '''A Comparison of Endo- and Exo- Products''' ==
=== The Reaction of Cyclohexadiene and 1,3-Dioxole by PM6 ===
==== Method ====

Both reactants were optimized, and subsequently placed in the endo TS conformation with the 4 C atoms involved in the reaction centre being frozen from eachother at a distance of 2.2 Å. An optimization to a minimum was carried out, followed by an optimization to a TS (Berny). An IRC was done on this TS structure, which ran in both directions, at N=20. The geometry obtained at the start of the reaction profile from the IRC was optimized to a minimum and no imaginary frequencies confirmed this to be the product.

The same procedure was carried out for the exo-conformer.

==== B3LYP frequency pictures for exo and endo ====

A B3LYP/6-31G(d) calculation was run on both TS geometries and the presence of 1 imaginary frequency in both TS structures confirmed them to be the TS. These frequencies were 520.86 and 528.8icm-1 for the endo and exo TS's respectively.

{| class="wikitable" border="1"
|+ B3LYP Vibrations and TS
! Endo !! Exo
|-
| [[File:Endo B3LYP TS.jpg|275px]] || [[File:Exo B3LYP TS.jpg|275px]]
|-
| [[File:Endo B3LYP Vib.jpg|275px]] || [[File:Exo B3LYP Vib.jpg|275px]]
|}

==== The releveant FMOs for Diels-Alder by symmetry ====

From the MO diagram for Diels-Alder, the same orbitals come into play for these reactions.

{| class="wikitable" border="1"
|+ endo-TS MO's
|-
| Bonding Orbitals || [[File:EndoTS MO 29.jpg|175px]] || [[File:EndoTS MO 30.jpg|175px]]
|-
| Antibonding Orbitals ||[[File:EndoTS MO 31.jpg|175px]] || [[File:EndoTS MO 32.jpg|175px]]
|}

{| class="wikitable" border="1"
|+ exo-TS MO's
|-
| Bonding Orbitals || [[File:Exo TS MO 29.jpg|175px]] || [[File:Exo TS MO 30.jpg|175px]]
|-
| Antibonding Orbitals || [[File:Exo TS MO 31.jpg|175px]] || [[File:Exo TS MO 32.jpg|175px]]
|}

{| class="wikitable" border="1"
|+ Endo vs Exo TS's
! !! Endo !! Exo
|-
| TS vibrations || [[File:Endo TS Vibrations.jpg|275px]] || [[File:Exo TS Vibrations.jpg|275px]]
|-
| TS Geometry || [[File:Endo TS Geometry.jpg|275px]] || [[File:Exo TS Geometry.jpg|275px]]
|-
|}

The presence of 1 imaginary negative frequency shows that these are the TS structures for the 2 reactions.

{| class="wikitable" border="1"
|+ Endo and Exo Product Formation from IRC
! !! Endo !! Exo
|-
| IRC || [[File:Endo product.gif|750px|]] || [[File:Exo product.gif|750px]]
|-
| Reaction coordinate || [[File:Endo Reaction Coordinate.jpg|750px]] || [[File:Exo Reaction Coordinate.jpg|750px]]
|}

=== Thermochemistry of Exo- vs Endo- ===

{| class="wikitable" border="1"
|+ Endo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.130081 || 20.64 || -
|-
| TS || 0.137942 || - || -
|-
| Product || 0.244570 || - || 300.59
|}

{| class="wikitable" border="1"
|+ Exo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.136771 || 5.60 || -
|-
| TS || 0.138905 || - || -
|-
| Product || 0.037977 || - || -259.38
|}

==== Secondary Orbital Interactions ====

{| class="wikitable" border="1"
|+ HOMO of exo and endo TS
! TS !! HOMO
|-
| endo || [[File:Endo TS HOMO 2ndary orbital interaction.jpg|450px]]
|-
| exo || [[File:Exo TS HOMO no 2ndary interaction.jpg|200px]]
|}

Primary orbital interactions lead to sigma bond formation. The dienophile, in this case the 1,3 Dioxole, is pointing away from the diene which does not allow for any further orbital interactions; and so only has primary orbital interactions, and forms the exo-product.

In the endo conformation, the dienophile is positioned such that the lobes of the C-O and the back orbitals in the cyclohexadiene can form a favourable bonding interaction, which lowers the energy of the TS, and in turn, is the kinetic product. Such an interaction is a secondary orbital interaction. A point to note is that no such bonds are formed in this case.4

== '''Diels-Alder and Chelotropic Pathways''' ==
=== o-Xylylene and SO2 optimization to adducts of both reaction types ===
==== Method ====

==== Diels-Alder ====

The product was drawn and optimized to a minimum using the PM6 method. The C-S and C-O bonds in the resulting structure were removed and separated by 2.4 and 2.0 Å respectively, and frozen. This was then optimized to a TS (Berny). An IRC was then run on this TS geometry, and the lowest energy conformation from the resulting reaction profile was optimized to a minimum.

This gave the exo product; so the TS geometry was altered by manually displacing the O atom of the SO2 into an approximate endo geometry for TS. This was then optimized to a TS (Berny), after which an IRC was run and a subsequent optimization to a minimum on the product to obtain the energies. Using this method, allowed for both reaction paths to be analysed.

==== Chelotropic ====

The chelotropic product was drawn and optimized to a minimum. The C-S bonds of this resulting geometry were broken and the coordinates were frozen at approximately 2.2 Å apart. This structure was then optimized to a minimum, and the subsequent geometry reoptimized to a TS (Berny). An IRC was run on this TS with N=200, forward only, to obtain a reaction path.

{| class="wikitable" border="1"
|+ Diels-Alder & Chelotropic Reactions
! !! Endo !! Exo !! Chelotropic
|-
| TS || [[File:Endo Xyl TS.jpg|650px]] || [[File:Exo Xyl TS.jpg|650px]] || [[File:Chelotropic TS.jpg|650px]]
|-
| IRC || [[File:Endo Xyl IRC.gif]] || [[File:Exo Xyl IRC.gif]] || [[File:Chelotropic IRC.gif]]
|-
| Reaction Profile || [[File:Endo Xyl Reaction Profile.jpg|650px]] || [[File:Exo Xyl Reaction Coordinate.jpg|650px]] || [[File:Chelotropic Reaction Coordinate.jpg|650px]]
|}

During the course of all 3 reactions, xylylene's 6 membered ring becomes aromatized, which gives it extra thermodynamic stability due to the lowering in energy. This extra energy provides the driving force(ΔG) of the reaction. The stabilization of the TS in this way allows the o-xylylene reaction to progress at a faster rate. This is very true for the Diels-Alder reaction.

=== Thermochemistry of o-Xylylene and SO2 ===

{| class="wikitable" border="1"
|+ Endo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.090737 || -0.47 || -
|-
| TS || 0.090559 || - || -
|-
| Product || 0.021693 || - || -181.28
|}

{| class="wikitable" border="1"
|+ Exo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.092130 || -0.000053 || -
|-
| TS || 0.092077 || - || -
|-
| Product || 0.021455 || - || -185.56
|}

{| class="wikitable" border="1"
|+ Chelotropic
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.097953 || 2.9 || -
|-
| TS || 0.099059 || - || -
|-
| Product || -0.000002 || - || -257.18
|}

=== '''A Comparison of Reaction Profiles''' ===

[[File:All 3 Reaction Profiles.jpg|930px]]

It can be seen that the chelotropic product has the lowest energy and is the most thermodynamically stable product. The endo and exo products are very close in energy suggesting similar thermodynamic stability, however, the secondary orbital interactions which occur in the endo TS conformation from the lobes of the oxgeyn atom as the dienophile SO2 approaches will allow lowering of the TS activation barrier, thus allowing the endo product to be the kinetic product and form faster than the exo product.

==== '''References''' ====

1. Allen, F.H., Kennard, O., Watson, D.G., Brammer, L., Orpen, G.A. and Taylor, R.(1987) ‘Tables of bond lengths determined by x-ray and neutron diffraction. Part 1. Bond lengths in organic compounds’, Journal of the Chemical Society, Perkin Transactions 2, (12), pp. 1–19. doi: 10.1039/P298700000S1.

2. Inorganic Materials, Vol. 37, No. 9, 2001, pp. 871–885. Translated from Neorganicheskie Materialy, Vol. 37, No. 9, 2001, pp. 1031–1046. Original Russian Text Copyright © 2001 by Batsanov.

3. Clayden, J., Greeves, N., Warren, S. and Claydon, J. (2000) Organic chemistry. New York: Oxford University Press.

4. Gheorghiu, M.D. (no date) Diels Alder Reactions. Available at: https://ocw.mit.edu/courses/chemistry/5-32-intermediate-chemical-experimentation-spring-2003/labs/Appendix_1_Diels_Alder_Reactions_03.pdf.

Rep:Mod:Mrh214

2016-12-02T10:50:45Z

Mrh214:

== '''Diels Alder Cycloaddition''' ==
=== Butadiene and Ethene optimization to Cyclohexene via PM6 ===
==== Method ====

1) Butadiene and ethene were optimized to a minimum seperately. Once optimized, they were placed in a similar geometry closely resembling that of the transition state (TS) required for the Diels Alder reaction; with the 4 carbon atoms in the reaction centre being frozen approximately 2.2 angstroms from eachother. This geometry was optimized to a minimum. The optimized geometry was then re-optimized to a TS (Berny), and this was confirmed by the presence of 1 negative frequency in the vibrations. An IRC was run on this TS in both directions with N=100. This geometry was manually displaced and optimized further to a minimum and product confirmation was given by all positive frequencies.

==== Butadiene ====
[[File:Butadiene.jpg|300px]]

==== Ethene ====
[[File:Ethene.jpg|300px]]

The C=C bonds in butadiene are 1.33531 Å; the C-C is 1.46835 Å. The C=C in ethene is 1.32731 Å.

==== TS ====
[[File:TS.jpg|300px]]

[[File:TS vibration 1.gif]]

This is the imaginary vibration at -949.3 icm-1, which corresponds to the TS.

[[File:TS vibration 2.gif]]

And this shows the first positive vibration at 144.91 icm-1. The motions are synchronous, therefore implying that the bond formations are also, synchronous.

In the TS the 2 C=C bonds of butadiene are now 1.37978 and 1.37974 Å. The previous C-C in butadiene is now 1.41114 Å; this has compressed as in the products, it will become a double bond. Similarly, the C=C bonds are now elongated slightly, due to becoming single bonds in the product.

The C=C in ethene for the TS has elongated to 1.38173, as this will be a single bond in the product.

The C atoms involved in the reaction centre for the Diels-Alder mechanism, from butadiene to the ethene carbons are at length 2.11423 and 2.11494 Å.

{| class="wikitable" border="1"
|+ Frontier Orbitals of Reactants
! FMO !! Butadiene !! Ethene
|-
| HOMO || [[File:HOMO Butadiene.jpg|300px]] || [[File:HOMO ethene.jpg|175px]]
|-
| LUMO || [[File:LUMO butadiene.jpg|175px]] || [[File:LUMO ethene.jpg|175px]]
|-
|}

(FMO = Frontier Molecular Orbitals)

{| class="wikitable" border="1"
|+ TS MO's
|-
| [[File:TS MO 16.jpg|175px]] || [[File:TS MO 17.jpg|175px]]
|-
| [[File:TS MO 18.jpg|175px]] || [[File:TS MO 19.jpg|175px]]
|}

==== Cyclohexene ====
[[File:Cyclohexene.jpg|300px]]

==== Bond Distance Variation Over Course of Reaction ====

{| class="wikitable" border="1"
|+ Bond lengths in reactants
! !! Bond lengths Å !!
|-
! Bond Type !! Butadiene !! Ethene
|-
| C-C || 1.46835 || -
|-
| C=C || 1.33531 || 1.32731
|}

{| class="wikitable" border="1"
|+ Bond lengths in TS
! !! Bond lengths Å !!
|-
! Bond Type !! Butadiene fragment !! Ethene fragment
|-
| C-C || 1.41114 || -
|-
| C=C || 1.37978 / 1.37974 || 1.38173
|}

{| class="wikitable" border="1"
|+ 2 C-C lengths in reaction centre
! Reaction centre !! Carbon atom distances Å
|-
| C-C || 2.11423 / 2.11494
|}

{| class="wikitable" border="1"
|+ Bond lengths in Cyclohexene product
! !! Cyclohexene
|-
! Bond type !! Bond lengths Å
|-
| C-C || 1.50085 / 1.50087
|-
| C-C || 1.53714 / 1.53704
|-
| C-C (opposite C=C) || 1.53453
|-
| C=C || 1.33698
|}

In the final product, the C=C is 1.33698 Å, the neighboring C-C on either side to the double bond are 1.50085 and 1.50087 Å. The adjacent C-C to these bonds are 1.53714 and 1.53704 Å. And the C-C directly opposite the C=C is 1.53453 Å.

Typical C-C sp3 length is 1.54 Å and the corresponding sp2 length is 1.34 Å. The Van der Waals radius of carbon is 1.70 Å. The sum of Van der Waals radii for 2 carbon atoms is 3.4 Å. The bond distances displayed in the above tables, are all less than this, and so there is bonding interaction. The key aspect here is for the 4 C atoms in the reaction centre, with both being approximately 2.114 Å distance between each C-C pair, this shows progressive bonding interaction, as these distances are far less than the Van der Waals radius for 2 C atoms.[1][2]

==== The Diels-Alder MO Diagram[3] ====
[[File:DA MO.jpg|400px]]

The MO diagram shows that the HOMO for the diene is closer in energy to the LUMO of the dienophile, hence will allow more efficient/constructive overlap (and lower energy antibonding MO) than the opposite case; which would be the LUMO of the diene with the HOMO of the dienophile.

==== The Symmetry Conditions ====
Let g = gerade (symmetric) and u = ungerade (antisymmetric).

Orbitals of the same symmetry may combine, ie. g-g, u-u. However, orbitals of mis-matched symmetry may not, ie. g-u / u-g.

The orbital overlap integral is non-zero for g-g / u-u, but zero for g-u / u-g.

==== Reference ====
Clayden (MO diagram)
DIELS-ALDER REACTIONS, Mircea D. Gherghiu

== '''A Comparison of Endo- and Exo- Products''' ==
=== The Reaction of Cyclohexadiene and 1,3-Dioxole by PM6 ===
==== Method ====

Both reactants were optimized, and subsequently placed in the endo TS conformation with the 4 C atoms involved in the reaction centre being frozen from eachother at a distance of 2.2 Å. An optimization to a minimum was carried out, followed by an optimization to a TS (Berny). An IRC was done on this TS structure, which ran in both directions, at N=20. The geometry obtained at the start of the reaction profile from the IRC was optimized to a minimum and no imaginary frequencies confirmed this to be the product.

The same procedure was carried out for the exo-conformer.

==== B3LYP frequency pictures for exo and endo ====

A B3LYP/6-31G(d) calculation was run on both TS geometries and the presence of 1 imaginary frequency in both TS structures confirmed them to be the TS. These frequencies were 520.86 and 528.8icm-1 for the endo and exo TS's respectively.

{| class="wikitable" border="1"
|+ B3LYP Vibrations and TS
! Endo !! Exo
|-
| [[File:Endo B3LYP TS.jpg|275px]] || [[File:Exo B3LYP TS.jpg|275px]]
|-
| [[File:Endo B3LYP Vib.jpg|275px]] || [[File:Exo B3LYP Vib.jpg|275px]]
|}

==== The releveant FMOs for Diels-Alder by symmetry ====

From the MO diagram for Diels-Alder, the same orbitals come into play for these reactions.

{| class="wikitable" border="1"
|+ endo-TS MO's
|-
| Bonding Orbitals || [[File:EndoTS MO 29.jpg|175px]] || [[File:EndoTS MO 30.jpg|175px]]
|-
| Antibonding Orbitals ||[[File:EndoTS MO 31.jpg|175px]] || [[File:EndoTS MO 32.jpg|175px]]
|}

{| class="wikitable" border="1"
|+ exo-TS MO's
|-
| Bonding Orbitals || [[File:Exo TS MO 29.jpg|175px]] || [[File:Exo TS MO 30.jpg|175px]]
|-
| Antibonding Orbitals || [[File:Exo TS MO 31.jpg|175px]] || [[File:Exo TS MO 32.jpg|175px]]
|}

{| class="wikitable" border="1"
|+ Endo vs Exo TS's
! !! Endo !! Exo
|-
| TS vibrations || [[File:Endo TS Vibrations.jpg|275px]] || [[File:Exo TS Vibrations.jpg|275px]]
|-
| TS Geometry || [[File:Endo TS Geometry.jpg|275px]] || [[File:Exo TS Geometry.jpg|275px]]
|-
|}

The presence of 1 imaginary negative frequency shows that these are the TS structures for the 2 reactions.

{| class="wikitable" border="1"
|+ Endo and Exo Product Formation from IRC
! !! Endo !! Exo
|-
| IRC || [[File:Endo product.gif|750px|]] || [[File:Exo product.gif|750px]]
|-
| Reaction coordinate || [[File:Endo Reaction Coordinate.jpg|750px]] || [[File:Exo Reaction Coordinate.jpg|750px]]
|}

=== Thermochemistry of Exo- vs Endo- ===

{| class="wikitable" border="1"
|+ Endo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.130081 || 20.64 || -
|-
| TS || 0.137942 || - || -
|-
| Product || 0.244570 || - || 300.59
|}

{| class="wikitable" border="1"
|+ Exo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.136771 || 5.60 || -
|-
| TS || 0.138905 || - || -
|-
| Product || 0.037977 || - || -259.38
|}

==== Secondary Orbital Interactions ====

{| class="wikitable" border="1"
|+ HOMO of exo and endo TS
! TS !! HOMO
|-
| endo || [[File:Endo TS HOMO 2ndary orbital interaction.jpg|450px]]
|-
| exo || [[File:Exo TS HOMO no 2ndary interaction.jpg|200px]]
|}

Primary orbital interactions lead to sigma bond formation. The dienophile, in this case the 1,3 Dioxole, is pointing away from the diene which does not allow for any further orbital interactions; and so only has primary orbital interactions, and forms the exo-product.

In the endo conformation, the dienophile is positioned such that the lobes of the C-O and the back orbitals in the cyclohexadiene can form a favourable bonding interaction, which lowers the energy of the TS, and in turn, is the kinetic product. Such an interaction is a secondary orbital interaction. A point to note is that no such bonds are formed in this case.

== '''Diels-Alder and Chelotropic Pathways''' ==
=== o-Xylylene and SO2 optimization to adducts of both reaction types ===
==== Method ====

==== Diels-Alder ====

The product was drawn and optimized to a minimum using the PM6 method. The C-S and C-O bonds in the resulting structure were removed and separated by 2.4 and 2.0 Å respectively, and frozen. This was then optimized to a TS (Berny). An IRC was then run on this TS geometry, and the lowest energy conformation from the resulting reaction profile was optimized to a minimum.

This gave the exo product; so the TS geometry was altered by manually displacing the O atom of the SO2 into an approximate endo geometry for TS. This was then optimized to a TS (Berny), after which an IRC was run and a subsequent optimization to a minimum on the product to obtain the energies. Using this method, allowed for both reaction paths to be analysed.

==== Chelotropic ====

The chelotropic product was drawn and optimized to a minimum. The C-S bonds of this resulting geometry were broken and the coordinates were frozen at approximately 2.2 Å apart. This structure was then optimized to a minimum, and the subsequent geometry reoptimized to a TS (Berny). An IRC was run on this TS with N=200, forward only, to obtain a reaction path.

==== Diels Alder ====

{| class="wikitable" border="1"
|+ Diels-Alder & Chelotropic Reactions
! !! Endo !! Exo !! Chelotropic
|-
| TS || [[File:Endo Xyl TS.jpg|650px]] || [[File:Exo Xyl TS.jpg|650px]] || [[File:Chelotropic TS.jpg|650px]]
|-
| IRC || [[File:Endo Xyl IRC.gif]] || [[File:Exo Xyl IRC.gif]] || [[File:Chelotropic IRC.gif]]
|-
| Reaction Profile || [[File:Endo Xyl Reaction Profile.jpg|650px]] || [[File:Exo Xyl Reaction Coordinate.jpg|650px]] || [[File:Chelotropic Reaction Coordinate.jpg|650px]]
|}

During the course of all 3 reactions, xylylene's 6 membered ring becomes aromatized, which gives it extra thermodynamic stability due to the lowering in energy. This extra energy provides the driving force(ΔG) of the reaction. The stabilization of the TS in this way allows the o-xylylene reaction to progress at a faster rate. This is very true for the Diels-Alder reaction.

=== Thermochemistry of o-Xylylene and SO2 ===

{| class="wikitable" border="1"
|+ Endo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.090737 || -0.47 || -
|-
| TS || 0.090559 || - || -
|-
| Product || 0.021693 || - || -181.28
|}

{| class="wikitable" border="1"
|+ Exo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.092130 || -0.000053 || -
|-
| TS || 0.092077 || - || -
|-
| Product || 0.021455 || - || -185.56
|}

{| class="wikitable" border="1"
|+ Chelotropic
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.097953 || 2.9 || -
|-
| TS || 0.099059 || - || -
|-
| Product || -0.000002 || - || -257.18
|}

=== '''A Comparison of Reaction Profiles''' ===

[[File:All 3 Reaction Profiles.jpg|930px]]

==== '''References''' ====

1. Allen, F.H., Kennard, O., Watson, D.G., Brammer, L., Orpen, G.A. and Taylor, R.(1987) ‘Tables of bond lengths determined by x-ray and neutron diffraction. Part 1. Bond lengths in organic compounds’, Journal of the Chemical Society, Perkin Transactions 2, (12), pp. 1–19. doi: 10.1039/P298700000S1.

2. Inorganic Materials, Vol. 37, No. 9, 2001, pp. 871–885. Translated from Neorganicheskie Materialy, Vol. 37, No. 9, 2001, pp. 1031–1046. Original Russian Text Copyright © 2001 by Batsanov.

3. Clayden, J., Greeves, N., Warren, S. and Claydon, J. (2000) Organic chemistry. New York: Oxford University Press.

Rep:Mod:Mrh214

2016-12-02T10:43:31Z

Mrh214:

== '''Diels Alder Cycloaddition''' ==
=== Butadiene and Ethene optimization to Cyclohexene via PM6 ===
==== Method ====

1) Butadiene and ethene were optimized to a minimum seperately. Once optimized, they were placed in a similar geometry closely resembling that of the transition state (TS) required for the Diels Alder reaction; with the 4 carbon atoms in the reaction centre being frozen approximately 2.2 angstroms from eachother. This geometry was optimized to a minimum. The optimized geometry was then re-optimized to a TS (Berny), and this was confirmed by the presence of 1 negative frequency in the vibrations. An IRC was run on this TS in both directions with N=100. This geometry was manually displaced and optimized further to a minimum and product confirmation was given by all positive frequencies.

==== Butadiene ====
[[File:Butadiene.jpg|300px]]

==== Ethene ====
[[File:Ethene.jpg|300px]]

The C=C bonds in butadiene are 1.33531 Å; the C-C is 1.46835 Å. The C=C in ethene is 1.32731 Å.

==== TS ====
[[File:TS.jpg|300px]]

[[File:TS vibration 1.gif]]

This is the imaginary vibration at -949.3 icm-1, which corresponds to the TS.

[[File:TS vibration 2.gif]]

And this shows the first positive vibration at 144.91 icm-1. The motions are synchronous, therefore implying that the bond formations are also, synchronous.

In the TS the 2 C=C bonds of butadiene are now 1.37978 and 1.37974 Å. The previous C-C in butadiene is now 1.41114 Å; this has compressed as in the products, it will become a double bond. Similarly, the C=C bonds are now elongated slightly, due to becoming single bonds in the product.

The C=C in ethene for the TS has elongated to 1.38173, as this will be a single bond in the product.

The C atoms involved in the reaction centre for the Diels-Alder mechanism, from butadiene to the ethene carbons are at length 2.11423 and 2.11494 Å.

{| class="wikitable" border="1"
|+ Frontier Orbitals of Reactants
! FMO !! Butadiene !! Ethene
|-
| HOMO || [[File:HOMO Butadiene.jpg|300px]] || [[File:HOMO ethene.jpg|175px]]
|-
| LUMO || [[File:LUMO butadiene.jpg|175px]] || [[File:LUMO ethene.jpg|175px]]
|-
|}

(FMO = Frontier Molecular Orbitals)

{| class="wikitable" border="1"
|+ TS MO's
|-
| [[File:TS MO 16.jpg|175px]] || [[File:TS MO 17.jpg|175px]]
|-
| [[File:TS MO 18.jpg|175px]] || [[File:TS MO 19.jpg|175px]]
|}

==== Cyclohexene ====
[[File:Cyclohexene.jpg|300px]]

==== Bond Distance Variation Over Course of Reaction ====

{| class="wikitable" border="1"
|+ Bond lengths in reactants
! !! Bond lengths Å !!
|-
! Bond Type !! Butadiene !! Ethene
|-
| C-C || 1.46835 || -
|-
| C=C || 1.33531 || 1.32731
|}

{| class="wikitable" border="1"
|+ Bond lengths in TS
! !! Bond lengths Å !!
|-
! Bond Type !! Butadiene fragment !! Ethene fragment
|-
| C-C || 1.41114 || -
|-
| C=C || 1.37978 / 1.37974 || 1.38173
|}

{| class="wikitable" border="1"
|+ 2 C-C lengths in reaction centre
! Reaction centre !! Carbon atom distances Å
|-
| C-C || 2.11423 / 2.11494
|}

{| class="wikitable" border="1"
|+ Bond lengths in Cyclohexene product
! !! Cyclohexene
|-
! Bond type !! Bond lengths Å
|-
| C-C || 1.50085 / 1.50087
|-
| C-C || 1.53714 / 1.53704
|-
| C-C (opposite C=C) || 1.53453
|-
| C=C || 1.33698
|}

In the final product, the C=C is 1.33698 Å, the neighboring C-C on either side to the double bond are 1.50085 and 1.50087 Å. The adjacent C-C to these bonds are 1.53714 and 1.53704 Å. And the C-C directly opposite the C=C is 1.53453 Å.

Typical C-C sp3 length is 1.54 Å and the corresponding sp2 length is 1.34 Å. (ADD REFERENCE)!!! '''ADD VDW RADIII'''

The C-C bonds formed in TS have lengths less than the combined Van der Waals radius of 2 C atoms, which implies a bonding interaction is occuring.

==== The Diels-Alder MO Diagram ====
[[File:DA MO.jpg|400px]]

The MO diagram shows that the HOMO for the diene is closer in energy to the LUMO of the dienophile, hence will allow more efficient/constructive overlap (and lower energy antibonding MO) than the opposite case; which would be the LUMO of the diene with the HOMO of the dienophile.

==== The Symmetry Conditions ====
Let g = gerade (symmetric) and u = ungerade (antisymmetric).

Orbitals of the same symmetry may combine, ie. g-g, u-u. However, orbitals of mis-matched symmetry may not, ie. g-u / u-g.

The orbital overlap integral is non-zero for g-g / u-u, but zero for g-u / u-g.

==== Reference ====
Clayden (MO diagram)
DIELS-ALDER REACTIONS, Mircea D. Gherghiu

== '''A Comparison of Endo- and Exo- Products''' ==
=== The Reaction of Cyclohexadiene and 1,3-Dioxole by PM6 ===
==== Method ====

Both reactants were optimized, and subsequently placed in the endo TS conformation with the 4 C atoms involved in the reaction centre being frozen from eachother at a distance of 2.2 Å. An optimization to a minimum was carried out, followed by an optimization to a TS (Berny). An IRC was done on this TS structure, which ran in both directions, at N=20. The geometry obtained at the start of the reaction profile from the IRC was optimized to a minimum and no imaginary frequencies confirmed this to be the product.

The same procedure was carried out for the exo-conformer.

==== B3LYP frequency pictures for exo and endo ====

A B3LYP/6-31G(d) calculation was run on both TS geometries and the presence of 1 imaginary frequency in both TS structures confirmed them to be the TS. These frequencies were 520.86 and 528.8icm-1 for the endo and exo TS's respectively.

{| class="wikitable" border="1"
|+ B3LYP Vibrations and TS
! Endo !! Exo
|-
| [[File:Endo B3LYP TS.jpg|275px]] || [[File:Exo B3LYP TS.jpg|275px]]
|-
| [[File:Endo B3LYP Vib.jpg|275px]] || [[File:Exo B3LYP Vib.jpg|275px]]
|}

==== The releveant FMOs for Diels-Alder by symmetry ====

From the MO diagram for Diels-Alder, the same orbitals come into play for these reactions.

{| class="wikitable" border="1"
|+ endo-TS MO's
|-
| Bonding Orbitals || [[File:EndoTS MO 29.jpg|175px]] || [[File:EndoTS MO 30.jpg|175px]]
|-
| Antibonding Orbitals ||[[File:EndoTS MO 31.jpg|175px]] || [[File:EndoTS MO 32.jpg|175px]]
|}

{| class="wikitable" border="1"
|+ exo-TS MO's
|-
| Bonding Orbitals || [[File:Exo TS MO 29.jpg|175px]] || [[File:Exo TS MO 30.jpg|175px]]
|-
| Antibonding Orbitals || [[File:Exo TS MO 31.jpg|175px]] || [[File:Exo TS MO 32.jpg|175px]]
|}

{| class="wikitable" border="1"
|+ Endo vs Exo TS's
! !! Endo !! Exo
|-
| TS vibrations || [[File:Endo TS Vibrations.jpg|275px]] || [[File:Exo TS Vibrations.jpg|275px]]
|-
| TS Geometry || [[File:Endo TS Geometry.jpg|275px]] || [[File:Exo TS Geometry.jpg|275px]]
|-
|}

The presence of 1 imaginary negative frequency shows that these are the TS structures for the 2 reactions.

{| class="wikitable" border="1"
|+ Endo and Exo Product Formation from IRC
! !! Endo !! Exo
|-
| IRC || [[File:Endo product.gif|750px|]] || [[File:Exo product.gif|750px]]
|-
| Reaction coordinate || [[File:Endo Reaction Coordinate.jpg|750px]] || [[File:Exo Reaction Coordinate.jpg|750px]]
|}

=== Thermochemistry of Exo- vs Endo- ===

{| class="wikitable" border="1"
|+ Endo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.130081 || 20.64 || -
|-
| TS || 0.137942 || - || -
|-
| Product || 0.244570 || - || 300.59
|}

{| class="wikitable" border="1"
|+ Exo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.136771 || 5.60 || -
|-
| TS || 0.138905 || - || -
|-
| Product || 0.037977 || - || -259.38
|}

==== Secondary Orbital Interactions ====

{| class="wikitable" border="1"
|+ HOMO of exo and endo TS
! TS !! HOMO
|-
| endo || [[File:Endo TS HOMO 2ndary orbital interaction.jpg|450px]]
|-
| exo || [[File:Exo TS HOMO no 2ndary interaction.jpg|200px]]
|}

Primary orbital interactions lead to sigma bond formation. The dienophile, in this case the 1,3 Dioxole, is pointing away from the diene which does not allow for any further orbital interactions; and so only has primary orbital interactions, and forms the exo-product.

In the endo conformation, the dienophile is positioned such that the lobes of the C-O and the back orbitals in the cyclohexadiene can form a favourable bonding interaction, which lowers the energy of the TS, and in turn, is the kinetic product. Such an interaction is a secondary orbital interaction. A point to note is that no such bonds are formed in this case.

== '''Diels-Alder and Chelotropic Pathways''' ==
=== o-Xylylene and SO2 optimization to adducts of both reaction types ===
==== Method ====

==== Diels-Alder ====

The product was drawn and optimized to a minimum using the PM6 method. The C-S and C-O bonds in the resulting structure were removed and separated by 2.4 and 2.0 Å respectively, and frozen. This was then optimized to a TS (Berny). An IRC was then run on this TS geometry, and the lowest energy conformation from the resulting reaction profile was optimized to a minimum.

This gave the exo product; so the TS geometry was altered by manually displacing the O atom of the SO2 into an approximate endo geometry for TS. This was then optimized to a TS (Berny), after which an IRC was run and a subsequent optimization to a minimum on the product to obtain the energies. Using this method, allowed for both reaction paths to be analysed.

==== Chelotropic ====

The chelotropic product was drawn and optimized to a minimum. The C-S bonds of this resulting geometry were broken and the coordinates were frozen at approximately 2.2 Å apart. This structure was then optimized to a minimum, and the subsequent geometry reoptimized to a TS (Berny). An IRC was run on this TS with N=200, forward only, to obtain a reaction path.

==== Diels Alder ====

{| class="wikitable" border="1"
|+ Diels-Alder & Chelotropic Reactions
! !! Endo !! Exo !! Chelotropic
|-
| TS || [[File:Endo Xyl TS.jpg|650px]] || [[File:Exo Xyl TS.jpg|650px]] || [[File:Chelotropic TS.jpg|650px]]
|-
| IRC || [[File:Endo Xyl IRC.gif]] || [[File:Exo Xyl IRC.gif]] || [[File:Chelotropic IRC.gif]]
|-
| Reaction Profile || [[File:Endo Xyl Reaction Profile.jpg|650px]] || [[File:Exo Xyl Reaction Coordinate.jpg|650px]] || [[File:Chelotropic Reaction Coordinate.jpg|650px]]
|}

During the course of all 3 reactions, xylylene's 6 membered ring becomes aromatized, which gives it extra thermodynamic stability due to the lowering in energy. This extra energy provides the driving force(ΔG) of the reaction. The stabilization of the TS in this way allows the o-xylylene reaction to progress at a faster rate. This is very true for the Diels-Alder reaction.

=== Thermochemistry of o-Xylylene and SO2 ===

{| class="wikitable" border="1"
|+ Endo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.090737 || -0.47 || -
|-
| TS || 0.090559 || - || -
|-
| Product || 0.021693 || - || -181.28
|}

{| class="wikitable" border="1"
|+ Exo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.092130 || -0.000053 || -
|-
| TS || 0.092077 || - || -
|-
| Product || 0.021455 || - || -185.56
|}

{| class="wikitable" border="1"
|+ Chelotropic
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.097953 || 2.9 || -
|-
| TS || 0.099059 || - || -
|-
| Product || -0.000002 || - || -257.18
|}

=== '''A Comparison of Reaction Profiles''' ===

[[File:All 3 Reaction Profiles.jpg|930px]]

==== '''References''' ====

1. Allen, F.H., Kennard, O., Watson, D.G., Brammer, L., Orpen, G.A. and Taylor, R.(1987) ‘Tables of bond lengths determined by x-ray and neutron diffraction. Part 1. Bond lengths in organic compounds’, Journal of the Chemical Society, Perkin Transactions 2, (12), pp. 1–19. doi: 10.1039/P298700000S1.

2. Inorganic Materials, Vol. 37, No. 9, 2001, pp. 871–885. Translated from Neorganicheskie Materialy, Vol. 37, No. 9, 2001, pp. 1031–1046. Original Russian Text Copyright © 2001 by Batsanov.

3. Clayden, J., Greeves, N., Warren, S. and Claydon, J. (2000) Organic chemistry. New York: Oxford University Press.

Rep:Mod:Mrh214

2016-12-02T10:34:20Z

Mrh214: /* Bond Distance Variation Over Course of Reaction */

== '''Diels Alder Cycloaddition''' ==
=== Butadiene and Ethene optimization to Cyclohexene via PM6 ===
==== Method ====

1) Butadiene and ethene were optimized to a minimum seperately. Once optimized, they were placed in a similar geometry closely resembling that of the transition state (TS) required for the Diels Alder reaction; with the 4 carbon atoms in the reaction centre being frozen approximately 2.2 angstroms from eachother. This geometry was optimized to a minimum. The optimized geometry was then re-optimized to a TS (Berny), and this was confirmed by the presence of 1 negative frequency in the vibrations. An IRC was run on this TS in both directions with N=100. This geometry was manually displaced and optimized further to a minimum and product confirmation was given by all positive frequencies.

==== Butadiene ====
[[File:Butadiene.jpg|300px]]

==== Ethene ====
[[File:Ethene.jpg|300px]]

The C=C bonds in butadiene are 1.33531 Å; the C-C is 1.46835 Å. The C=C in ethene is 1.32731 Å.

==== TS ====
[[File:TS.jpg|300px]]

[[File:TS vibration 1.gif]]

This is the imaginary vibration at -949.3 icm-1, which corresponds to the TS.

[[File:TS vibration 2.gif]]

And this shows the first positive vibration at 144.91 icm-1. The motions are synchronous, therefore implying that the bond formations are also, synchronous.

In the TS the 2 C=C bonds of butadiene are now 1.37978 and 1.37974 Å. The previous C-C in butadiene is now 1.41114 Å; this has compressed as in the products, it will become a double bond. Similarly, the C=C bonds are now elongated slightly, due to becoming single bonds in the product.

The C=C in ethene for the TS has elongated to 1.38173, as this will be a single bond in the product.

The C atoms involved in the reaction centre for the Diels-Alder mechanism, from butadiene to the ethene carbons are at length 2.11423 and 2.11494 Å.

{| class="wikitable" border="1"
|+ Frontier Orbitals of Reactants
! FMO !! Butadiene !! Ethene
|-
| HOMO || [[File:HOMO Butadiene.jpg|300px]] || [[File:HOMO ethene.jpg|175px]]
|-
| LUMO || [[File:LUMO butadiene.jpg|175px]] || [[File:LUMO ethene.jpg|175px]]
|-
|}

(FMO = Frontier Molecular Orbitals)

{| class="wikitable" border="1"
|+ TS MO's
|-
| [[File:TS MO 16.jpg|175px]] || [[File:TS MO 17.jpg|175px]]
|-
| [[File:TS MO 18.jpg|175px]] || [[File:TS MO 19.jpg|175px]]
|}

==== Cyclohexene ====
[[File:Cyclohexene.jpg|300px]]

==== Bond Distance Variation Over Course of Reaction ====

{| class="wikitable" border="1"
|+ Bond lengths in reactants
! !! Bond lengths Å !!
|-
! Bond Type !! Butadiene !! Ethene
|-
| C-C || 1.46835 || -
|-
| C=C || 1.33531 || 1.32731
|}

{| class="wikitable" border="1"
|+ Bond lengths in TS
! !! Bond lengths Å !!
|-
! Bond Type !! Butadiene fragment !! Ethene fragment
|-
| C-C || 1.41114 || -
|-
| C=C || 1.37978 / 1.37974 || 1.38173
|}

{| class="wikitable" border="1"
|+ 2 C-C lengths in reaction centre
! Reaction centre !! Carbon atom distances Å
|-
| C-C || 2.11423 / 2.11494
|}

{| class="wikitable" border="1"
|+ Bond lengths in Cyclohexene product
! !! Cyclohexene
|-
! Bond type !! Bond lengths Å
|-
| C-C || 1.50085 / 1.50087
|-
| C-C || 1.53714 / 1.53704
|-
| C-C (opposite C=C) || 1.53453
|-
| C=C || 1.33698
|}

In the final product, the C=C is 1.33698 Å, the neighboring C-C on either side to the double bond are 1.50085 and 1.50087 Å. The adjacent C-C to these bonds are 1.53714 and 1.53704 Å. And the C-C directly opposite the C=C is 1.53453 Å.

Typical C-C sp3 length is 1.54 Å and the corresponding sp2 length is 1.34 Å. (ADD REFERENCE)!!! '''ADD VDW RADIII'''

The C-C bonds formed in TS have lengths less than the combined Van der Waals radius of 2 C atoms, which implies a bonding interaction is occuring.

==== The Diels-Alder MO Diagram ====
[[File:DA MO.jpg|400px]]

The MO diagram shows that the HOMO for the diene is closer in energy to the LUMO of the dienophile, hence will allow more efficient/constructive overlap (and lower energy antibonding MO) than the opposite case; which would be the LUMO of the diene with the HOMO of the dienophile.

==== The Symmetry Conditions ====
Let g = gerade (symmetric) and u = ungerade (antisymmetric).

Orbitals of the same symmetry may combine, ie. g-g, u-u. However, orbitals of mis-matched symmetry may not, ie. g-u / u-g.

The orbital overlap integral is non-zero for g-g / u-u, but zero for g-u / u-g.

==== Reference ====
Clayden (MO diagram)
DIELS-ALDER REACTIONS, Mircea D. Gherghiu

== '''A Comparison of Endo- and Exo- Products''' ==
=== The Reaction of Cyclohexadiene and 1,3-Dioxole by PM6 ===
==== Method ====

Both reactants were optimized, and subsequently placed in the endo TS conformation with the 4 C atoms involved in the reaction centre being frozen from eachother at a distance of 2.2 Å. An optimization to a minimum was carried out, followed by an optimization to a TS (Berny). An IRC was done on this TS structure, which ran in both directions, at N=20. The geometry obtained at the start of the reaction profile from the IRC was optimized to a minimum and no imaginary frequencies confirmed this to be the product.

The same procedure was carried out for the exo-conformer.

==== B3LYP frequency pictures for exo and endo ====

A B3LYP/6-31G(d) calculation was run on both TS geometries and the presence of 1 imaginary frequency in both TS structures confirmed them to be the TS. These frequencies were 520.86 and 528.8icm-1 for the endo and exo TS's respectively.

{| class="wikitable" border="1"
|+ B3LYP Vibrations and TS
! Endo !! Exo
|-
| [[File:Endo B3LYP TS.jpg|275px]] || [[File:Exo B3LYP TS.jpg|275px]]
|-
| [[File:Endo B3LYP Vib.jpg|275px]] || [[File:Exo B3LYP Vib.jpg|275px]]
|}

==== The releveant FMOs for Diels-Alder by symmetry ====

From the MO diagram for Diels-Alder, the same orbitals come into play for these reactions.

{| class="wikitable" border="1"
|+ endo-TS MO's
|-
| Bonding Orbitals || [[File:EndoTS MO 29.jpg|175px]] || [[File:EndoTS MO 30.jpg|175px]]
|-
| Antibonding Orbitals ||[[File:EndoTS MO 31.jpg|175px]] || [[File:EndoTS MO 32.jpg|175px]]
|}

{| class="wikitable" border="1"
|+ exo-TS MO's
|-
| Bonding Orbitals || [[File:Exo TS MO 29.jpg|175px]] || [[File:Exo TS MO 30.jpg|175px]]
|-
| Antibonding Orbitals || [[File:Exo TS MO 31.jpg|175px]] || [[File:Exo TS MO 32.jpg|175px]]
|}

{| class="wikitable" border="1"
|+ Endo vs Exo TS's
! !! Endo !! Exo
|-
| TS vibrations || [[File:Endo TS Vibrations.jpg|275px]] || [[File:Exo TS Vibrations.jpg|275px]]
|-
| TS Geometry || [[File:Endo TS Geometry.jpg|275px]] || [[File:Exo TS Geometry.jpg|275px]]
|-
|}

The presence of 1 imaginary negative frequency shows that these are the TS structures for the 2 reactions.

{| class="wikitable" border="1"
|+ Endo and Exo Product Formation from IRC
! !! Endo !! Exo
|-
| IRC || [[File:Endo product.gif|750px|]] || [[File:Exo product.gif|750px]]
|-
| Reaction coordinate || [[File:Endo Reaction Coordinate.jpg|750px]] || [[File:Exo Reaction Coordinate.jpg|750px]]
|}

=== Thermochemistry of Exo- vs Endo- ===

{| class="wikitable" border="1"
|+ Endo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.130081 || 20.64 || -
|-
| TS || 0.137942 || - || -
|-
| Product || 0.244570 || - || 300.59
|}

{| class="wikitable" border="1"
|+ Exo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.136771 || 5.60 || -
|-
| TS || 0.138905 || - || -
|-
| Product || 0.037977 || - || -259.38
|}

==== Secondary Orbital Interactions ====

{| class="wikitable" border="1"
|+ HOMO of exo and endo TS
! TS !! HOMO
|-
| endo || [[File:Endo TS HOMO 2ndary orbital interaction.jpg|450px]]
|-
| exo || [[File:Exo TS HOMO no 2ndary interaction.jpg|200px]]
|}

Primary orbital interactions lead to sigma bond formation. The dienophile, in this case the 1,3 Dioxole, is pointing away from the diene which does not allow for any further orbital interactions; and so only has primary orbital interactions, and forms the exo-product.

In the endo conformation, the dienophile is positioned such that the lobes of the C-O and the back orbitals in the cyclohexadiene can form a favourable bonding interaction, which lowers the energy of the TS, and in turn, is the kinetic product. Such an interaction is a secondary orbital interaction. A point to note is that no such bonds are formed in this case.

== '''Diels-Alder and Chelotropic Pathways''' ==
=== o-Xylylene and SO2 optimization to adducts of both reaction types ===
==== Method ====

==== Diels-Alder ====

The product was drawn and optimized to a minimum using the PM6 method. The C-S and C-O bonds in the resulting structure were removed and separated by 2.4 and 2.0 Å respectively, and frozen. This was then optimized to a TS (Berny). An IRC was then run on this TS geometry, and the lowest energy conformation from the resulting reaction profile was optimized to a minimum.

This gave the exo product; so the TS geometry was altered by manually displacing the O atom of the SO2 into an approximate endo geometry for TS. This was then optimized to a TS (Berny), after which an IRC was run and a subsequent optimization to a minimum on the product to obtain the energies. Using this method, allowed for both reaction paths to be analysed.

==== Chelotropic ====

The chelotropic product was drawn and optimized to a minimum. The C-S bonds of this resulting geometry were broken and the coordinates were frozen at approximately 2.2 Å apart. This structure was then optimized to a minimum, and the subsequent geometry reoptimized to a TS (Berny). An IRC was run on this TS with N=200, forward only, to obtain a reaction path.

==== Diels Alder ====

{| class="wikitable" border="1"
|+ Diels-Alder & Chelotropic Reactions
! !! Endo !! Exo !! Chelotropic
|-
| TS || [[File:Endo Xyl TS.jpg|650px]] || [[File:Exo Xyl TS.jpg|650px]] || [[File:Chelotropic TS.jpg|650px]]
|-
| IRC || [[File:Endo Xyl IRC.gif]] || [[File:Exo Xyl IRC.gif]] || [[File:Chelotropic IRC.gif]]
|-
| Reaction Profile || [[File:Endo Xyl Reaction Profile.jpg|650px]] || [[File:Exo Xyl Reaction Coordinate.jpg|650px]] || [[File:Chelotropic Reaction Coordinate.jpg|650px]]
|}

During the course of all 3 reactions, xylylene's 6 membered ring becomes aromatized, which gives it extra thermodynamic stability due to the lowering in energy. This extra energy provides the driving force(ΔG) of the reaction. The stabilization of the TS in this way allows the o-xylylene reaction to progress at a faster rate. This is very true for the Diels-Alder reaction.

=== Thermochemistry of o-Xylylene and SO2 ===

{| class="wikitable" border="1"
|+ Endo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.090737 || -0.47 || -
|-
| TS || 0.090559 || - || -
|-
| Product || 0.021693 || - || -181.28
|}

{| class="wikitable" border="1"
|+ Exo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.092130 || -0.000053 || -
|-
| TS || 0.092077 || - || -
|-
| Product || 0.021455 || - || -185.56
|}

{| class="wikitable" border="1"
|+ Chelotropic
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.097953 || 2.9 || -
|-
| TS || 0.099059 || - || -
|-
| Product || -0.000002 || - || -257.18
|}

=== '''A Comparison of Reaction Profiles''' ===

==== '''References'''

File:All 3 Reaction Profiles.jpg

2016-12-02T10:23:32Z

Mrh214:

Rep:Mod:Mrh214

2016-12-02T10:20:24Z

Mrh214: /* Thermochemistry of o-Xylylene and SO2 */

== '''Diels Alder Cycloaddition''' ==
=== Butadiene and Ethene optimization to Cyclohexene via PM6 ===
==== Method ====

1) Butadiene and ethene were optimized to a minimum seperately. Once optimized, they were placed in a similar geometry closely resembling that of the transition state (TS) required for the Diels Alder reaction; with the 4 carbon atoms in the reaction centre being frozen approximately 2.2 angstroms from eachother. This geometry was optimized to a minimum. The optimized geometry was then re-optimized to a TS (Berny), and this was confirmed by the presence of 1 negative frequency in the vibrations. An IRC was run on this TS in both directions with N=100. This geometry was manually displaced and optimized further to a minimum and product confirmation was given by all positive frequencies.

==== Butadiene ====
[[File:Butadiene.jpg|300px]]

==== Ethene ====
[[File:Ethene.jpg|300px]]

The C=C bonds in butadiene are 1.33531 Å; the C-C is 1.46835 Å. The C=C in ethene is 1.32731 Å.

==== TS ====
[[File:TS.jpg|300px]]

[[File:TS vibration 1.gif]]

This is the imaginary vibration at -949.3 icm-1, which corresponds to the TS.

[[File:TS vibration 2.gif]]

And this shows the first positive vibration at 144.91 icm-1. The motions are synchronous, therefore implying that the bond formations are also, synchronous.

In the TS the 2 C=C bonds of butadiene are now 1.37978 and 1.37974 Å. The previous C-C in butadiene is now 1.41114 Å; this has compressed as in the products, it will become a double bond. Similarly, the C=C bonds are now elongated slightly, due to becoming single bonds in the product.

The C=C in ethene for the TS has elongated to 1.38173, as this will be a single bond in the product.

The C atoms involved in the reaction centre for the Diels-Alder mechanism, from butadiene to the ethene carbons are at length 2.11423 and 2.11494 Å.

{| class="wikitable" border="1"
|+ Frontier Orbitals of Reactants
! FMO !! Butadiene !! Ethene
|-
| HOMO || [[File:HOMO Butadiene.jpg|300px]] || [[File:HOMO ethene.jpg|175px]]
|-
| LUMO || [[File:LUMO butadiene.jpg|175px]] || [[File:LUMO ethene.jpg|175px]]
|-
|}

(FMO = Frontier Molecular Orbitals)

{| class="wikitable" border="1"
|+ TS MO's
|-
| [[File:TS MO 16.jpg|175px]] || [[File:TS MO 17.jpg|175px]]
|-
| [[File:TS MO 18.jpg|175px]] || [[File:TS MO 19.jpg|175px]]
|}

==== Cyclohexene ====
[[File:Cyclohexene.jpg|300px]]

==== Bond Distance Variation Over Course of Reaction ====

{| class="wikitable" border="1"
|+ Bond lengths in reactants
! !! Bond lengths Å !!
|-
! Bond Type !! Butadiene !! Ethene
|-
| C-C || 1.46835 || -
|-
| C=C || 1.33531 || 1.32731
|}

{| class="wikitable" border="1"
|+ Bond lengths in TS
! !! Bond lengths Å !!
|-
! Bond Type !! Butadiene fragment !! Ethene fragment
|-
| C-C || 1.41114 || -
|-
| C=C || 1.37978 / 1.37974 || 1.38173
|}

{| class="wikitable" border="1"
|+ 2 C-C lengths in reaction centre
! Reaction centre !! Carbon atom distances Å
|-
| C-C || 2.11423 / 2.11494
|}

{| class="wikitable" border="1"
|+ Bond lengths in Cyclohexene product
! !! Cyclohexene
|-
! Bond type !! Bond lengths Å
|-
| C-C || 1.50085 / 1.50087
|-
| C-C || 1.53714 / 1.53704
|-
| C-C (opposite C=C) || 1.53453
|-
| C=C || 1.33698
|}

In the final product, the C=C is 1.33698 Å, the neighboring C-C on either side to the double bond are 1.50085 and 1.50087 Å. The adjacent C-C to these bonds are 1.53714 and 1.53704 Å. And the C-C directly opposite the C=C is 1.53453 Å.

Typical C-C sp3 length is 1.54 Å and the corresponding sp2 length is 1.34 Å. (ADD REFERENCE)!!! '''ADD VDW RADIII'''

The C-C bonds formed in TS have lengths less than the combined Van der Waals radius of 2 C atoms, which implies a bonding interaction is occuring.

==== The Diels-Alder MO Diagram ====
[[File:DA MO.jpg|400px]]

The MO diagram shows that the HOMO for the diene is closer in energy to the LUMO of the dienophile, hence will allow more efficient/constructive overlap (and lower energy antibonding MO) than the opposite case; which would be the LUMO of the diene with the HOMO of the dienophile.

==== The Symmetry Conditions ====
Let g = gerade (symmetric) and u = ungerade (antisymmetric).

Orbitals of the same symmetry may combine, ie. g-g, u-u. However, orbitals of mis-matched symmetry may not, ie. g-u / u-g.

The orbital overlap integral is non-zero for g-g / u-u, but zero for g-u / u-g.

==== Reference ====
Clayden (MO diagram)
DIELS-ALDER REACTIONS, Mircea D. Gherghiu

== '''A Comparison of Endo- and Exo- Products''' ==
=== The Reaction of Cyclohexadiene and 1,3-Dioxole by PM6 ===
==== Method ====

Both reactants were optimized, and subsequently placed in the endo TS conformation with the 4 C atoms involved in the reaction centre being frozen from eachother at a distance of 2.2 Å. An optimization to a minimum was carried out, followed by an optimization to a TS (Berny). An IRC was done on this TS structure, which ran in both directions, at N=20. The geometry obtained at the start of the reaction profile from the IRC was optimized to a minimum and no imaginary frequencies confirmed this to be the product.

The same procedure was carried out for the exo-conformer.

==== B3LYP frequency pictures for exo and endo ====

A B3LYP/6-31G(d) calculation was run on both TS geometries and the presence of 1 imaginary frequency in both TS structures confirmed them to be the TS. These frequencies were 520.86 and 528.8icm-1 for the endo and exo TS's respectively.

{| class="wikitable" border="1"
|+ B3LYP Vibrations and TS
! Endo !! Exo
|-
| [[File:Endo B3LYP TS.jpg|275px]] || [[File:Exo B3LYP TS.jpg|275px]]
|-
| [[File:Endo B3LYP Vib.jpg|275px]] || [[File:Exo B3LYP Vib.jpg|275px]]
|}

==== The releveant FMOs for Diels-Alder by symmetry ====

From the MO diagram for Diels-Alder, the same orbitals come into play for these reactions.

{| class="wikitable" border="1"
|+ endo-TS MO's
|-
| Bonding Orbitals || [[File:EndoTS MO 29.jpg|175px]] || [[File:EndoTS MO 30.jpg|175px]]
|-
| Antibonding Orbitals ||[[File:EndoTS MO 31.jpg|175px]] || [[File:EndoTS MO 32.jpg|175px]]
|}

{| class="wikitable" border="1"
|+ exo-TS MO's
|-
| Bonding Orbitals || [[File:Exo TS MO 29.jpg|175px]] || [[File:Exo TS MO 30.jpg|175px]]
|-
| Antibonding Orbitals || [[File:Exo TS MO 31.jpg|175px]] || [[File:Exo TS MO 32.jpg|175px]]
|}

{| class="wikitable" border="1"
|+ Endo vs Exo TS's
! !! Endo !! Exo
|-
| TS vibrations || [[File:Endo TS Vibrations.jpg|275px]] || [[File:Exo TS Vibrations.jpg|275px]]
|-
| TS Geometry || [[File:Endo TS Geometry.jpg|275px]] || [[File:Exo TS Geometry.jpg|275px]]
|-
|}

The presence of 1 imaginary negative frequency shows that these are the TS structures for the 2 reactions.

{| class="wikitable" border="1"
|+ Endo and Exo Product Formation from IRC
! !! Endo !! Exo
|-
| IRC || [[File:Endo product.gif|750px|]] || [[File:Exo product.gif|750px]]
|-
| Reaction coordinate || [[File:Endo Reaction Coordinate.jpg|750px]] || [[File:Exo Reaction Coordinate.jpg|750px]]
|}

=== Thermochemistry of Exo- vs Endo- ===

{| class="wikitable" border="1"
|+ Endo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.130081 || 20.64 || -
|-
| TS || 0.137942 || - || -
|-
| Product || 0.244570 || - || 300.59
|}

{| class="wikitable" border="1"
|+ Exo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.136771 || 5.60 || -
|-
| TS || 0.138905 || - || -
|-
| Product || 0.037977 || - || -259.38
|}

==== Secondary Orbital Interactions ====

{| class="wikitable" border="1"
|+ HOMO of exo and endo TS
! TS !! HOMO
|-
| endo || [[File:Endo TS HOMO 2ndary orbital interaction.jpg|450px]]
|-
| exo || [[File:Exo TS HOMO no 2ndary interaction.jpg|200px]]
|}

Primary orbital interactions lead to sigma bond formation. The dienophile, in this case the 1,3 Dioxole, is pointing away from the diene which does not allow for any further orbital interactions; and so only has primary orbital interactions, and forms the exo-product.

In the endo conformation, the dienophile is positioned such that the lobes of the C-O and the back orbitals in the cyclohexadiene can form a favourable bonding interaction, which lowers the energy of the TS, and in turn, is the kinetic product. Such an interaction is a secondary orbital interaction. A point to note is that no such bonds are formed in this case.

== '''Diels-Alder and Chelotropic Pathways''' ==
=== o-Xylylene and SO2 optimization to adducts of both reaction types ===
==== Method ====

==== Diels-Alder ====

The product was drawn and optimized to a minimum using the PM6 method. The C-S and C-O bonds in the resulting structure were removed and separated by 2.4 and 2.0 Å respectively, and frozen. This was then optimized to a TS (Berny). An IRC was then run on this TS geometry, and the lowest energy conformation from the resulting reaction profile was optimized to a minimum.

This gave the exo product; so the TS geometry was altered by manually displacing the O atom of the SO2 into an approximate endo geometry for TS. This was then optimized to a TS (Berny), after which an IRC was run and a subsequent optimization to a minimum on the product to obtain the energies. Using this method, allowed for both reaction paths to be analysed.

==== Chelotropic ====

The chelotropic product was drawn and optimized to a minimum. The C-S bonds of this resulting geometry were broken and the coordinates were frozen at approximately 2.2 Å apart. This structure was then optimized to a minimum, and the subsequent geometry reoptimized to a TS (Berny). An IRC was run on this TS with N=200, forward only, to obtain a reaction path.

==== Diels Alder ====

{| class="wikitable" border="1"
|+ Diels-Alder & Chelotropic Reactions
! !! Endo !! Exo !! Chelotropic
|-
| TS || [[File:Endo Xyl TS.jpg|650px]] || [[File:Exo Xyl TS.jpg|650px]] || [[File:Chelotropic TS.jpg|650px]]
|-
| IRC || [[File:Endo Xyl IRC.gif]] || [[File:Exo Xyl IRC.gif]] || [[File:Chelotropic IRC.gif]]
|-
| Reaction Profile || [[File:Endo Xyl Reaction Profile.jpg|650px]] || [[File:Exo Xyl Reaction Coordinate.jpg|650px]] || [[File:Chelotropic Reaction Coordinate.jpg|650px]]
|}

During the course of all 3 reactions, xylylene's 6 membered ring becomes aromatized, which gives it extra thermodynamic stability due to the lowering in energy. This extra energy provides the driving force(ΔG) of the reaction. The stabilization of the TS in this way allows the o-xylylene reaction to progress at a faster rate. This is very true for the Diels-Alder reaction.

=== Thermochemistry of o-Xylylene and SO2 ===

{| class="wikitable" border="1"
|+ Endo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.090737 || -0.47 || -
|-
| TS || 0.090559 || - || -
|-
| Product || 0.021693 || - || -181.28
|}

{| class="wikitable" border="1"
|+ Exo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.092130 || -0.000053 || -
|-
| TS || 0.092077 || - || -
|-
| Product || 0.021455 || - || -185.56
|}

{| class="wikitable" border="1"
|+ Chelotropic
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.097953 || 2.9 || -
|-
| TS || 0.099059 || - || -
|-
| Product || -0.000002 || - || -257.18
|}

=== '''A Comparison of Reaction Profiles''' ===

==== '''References'''

Rep:Mod:Mrh214

2016-12-02T10:18:08Z

Mrh214:

== '''Diels Alder Cycloaddition''' ==
=== Butadiene and Ethene optimization to Cyclohexene via PM6 ===
==== Method ====

1) Butadiene and ethene were optimized to a minimum seperately. Once optimized, they were placed in a similar geometry closely resembling that of the transition state (TS) required for the Diels Alder reaction; with the 4 carbon atoms in the reaction centre being frozen approximately 2.2 angstroms from eachother. This geometry was optimized to a minimum. The optimized geometry was then re-optimized to a TS (Berny), and this was confirmed by the presence of 1 negative frequency in the vibrations. An IRC was run on this TS in both directions with N=100. This geometry was manually displaced and optimized further to a minimum and product confirmation was given by all positive frequencies.

==== Butadiene ====
[[File:Butadiene.jpg|300px]]

==== Ethene ====
[[File:Ethene.jpg|300px]]

The C=C bonds in butadiene are 1.33531 Å; the C-C is 1.46835 Å. The C=C in ethene is 1.32731 Å.

==== TS ====
[[File:TS.jpg|300px]]

[[File:TS vibration 1.gif]]

This is the imaginary vibration at -949.3 icm-1, which corresponds to the TS.

[[File:TS vibration 2.gif]]

And this shows the first positive vibration at 144.91 icm-1. The motions are synchronous, therefore implying that the bond formations are also, synchronous.

In the TS the 2 C=C bonds of butadiene are now 1.37978 and 1.37974 Å. The previous C-C in butadiene is now 1.41114 Å; this has compressed as in the products, it will become a double bond. Similarly, the C=C bonds are now elongated slightly, due to becoming single bonds in the product.

The C=C in ethene for the TS has elongated to 1.38173, as this will be a single bond in the product.

The C atoms involved in the reaction centre for the Diels-Alder mechanism, from butadiene to the ethene carbons are at length 2.11423 and 2.11494 Å.

{| class="wikitable" border="1"
|+ Frontier Orbitals of Reactants
! FMO !! Butadiene !! Ethene
|-
| HOMO || [[File:HOMO Butadiene.jpg|300px]] || [[File:HOMO ethene.jpg|175px]]
|-
| LUMO || [[File:LUMO butadiene.jpg|175px]] || [[File:LUMO ethene.jpg|175px]]
|-
|}

(FMO = Frontier Molecular Orbitals)

{| class="wikitable" border="1"
|+ TS MO's
|-
| [[File:TS MO 16.jpg|175px]] || [[File:TS MO 17.jpg|175px]]
|-
| [[File:TS MO 18.jpg|175px]] || [[File:TS MO 19.jpg|175px]]
|}

==== Cyclohexene ====
[[File:Cyclohexene.jpg|300px]]

==== Bond Distance Variation Over Course of Reaction ====

{| class="wikitable" border="1"
|+ Bond lengths in reactants
! !! Bond lengths Å !!
|-
! Bond Type !! Butadiene !! Ethene
|-
| C-C || 1.46835 || -
|-
| C=C || 1.33531 || 1.32731
|}

{| class="wikitable" border="1"
|+ Bond lengths in TS
! !! Bond lengths Å !!
|-
! Bond Type !! Butadiene fragment !! Ethene fragment
|-
| C-C || 1.41114 || -
|-
| C=C || 1.37978 / 1.37974 || 1.38173
|}

{| class="wikitable" border="1"
|+ 2 C-C lengths in reaction centre
! Reaction centre !! Carbon atom distances Å
|-
| C-C || 2.11423 / 2.11494
|}

{| class="wikitable" border="1"
|+ Bond lengths in Cyclohexene product
! !! Cyclohexene
|-
! Bond type !! Bond lengths Å
|-
| C-C || 1.50085 / 1.50087
|-
| C-C || 1.53714 / 1.53704
|-
| C-C (opposite C=C) || 1.53453
|-
| C=C || 1.33698
|}

In the final product, the C=C is 1.33698 Å, the neighboring C-C on either side to the double bond are 1.50085 and 1.50087 Å. The adjacent C-C to these bonds are 1.53714 and 1.53704 Å. And the C-C directly opposite the C=C is 1.53453 Å.

Typical C-C sp3 length is 1.54 Å and the corresponding sp2 length is 1.34 Å. (ADD REFERENCE)!!! '''ADD VDW RADIII'''

The C-C bonds formed in TS have lengths less than the combined Van der Waals radius of 2 C atoms, which implies a bonding interaction is occuring.

==== The Diels-Alder MO Diagram ====
[[File:DA MO.jpg|400px]]

The MO diagram shows that the HOMO for the diene is closer in energy to the LUMO of the dienophile, hence will allow more efficient/constructive overlap (and lower energy antibonding MO) than the opposite case; which would be the LUMO of the diene with the HOMO of the dienophile.

==== The Symmetry Conditions ====
Let g = gerade (symmetric) and u = ungerade (antisymmetric).

Orbitals of the same symmetry may combine, ie. g-g, u-u. However, orbitals of mis-matched symmetry may not, ie. g-u / u-g.

The orbital overlap integral is non-zero for g-g / u-u, but zero for g-u / u-g.

==== Reference ====
Clayden (MO diagram)
DIELS-ALDER REACTIONS, Mircea D. Gherghiu

== '''A Comparison of Endo- and Exo- Products''' ==
=== The Reaction of Cyclohexadiene and 1,3-Dioxole by PM6 ===
==== Method ====

Both reactants were optimized, and subsequently placed in the endo TS conformation with the 4 C atoms involved in the reaction centre being frozen from eachother at a distance of 2.2 Å. An optimization to a minimum was carried out, followed by an optimization to a TS (Berny). An IRC was done on this TS structure, which ran in both directions, at N=20. The geometry obtained at the start of the reaction profile from the IRC was optimized to a minimum and no imaginary frequencies confirmed this to be the product.

The same procedure was carried out for the exo-conformer.

==== B3LYP frequency pictures for exo and endo ====

A B3LYP/6-31G(d) calculation was run on both TS geometries and the presence of 1 imaginary frequency in both TS structures confirmed them to be the TS. These frequencies were 520.86 and 528.8icm-1 for the endo and exo TS's respectively.

{| class="wikitable" border="1"
|+ B3LYP Vibrations and TS
! Endo !! Exo
|-
| [[File:Endo B3LYP TS.jpg|275px]] || [[File:Exo B3LYP TS.jpg|275px]]
|-
| [[File:Endo B3LYP Vib.jpg|275px]] || [[File:Exo B3LYP Vib.jpg|275px]]
|}

==== The releveant FMOs for Diels-Alder by symmetry ====

From the MO diagram for Diels-Alder, the same orbitals come into play for these reactions.

{| class="wikitable" border="1"
|+ endo-TS MO's
|-
| Bonding Orbitals || [[File:EndoTS MO 29.jpg|175px]] || [[File:EndoTS MO 30.jpg|175px]]
|-
| Antibonding Orbitals ||[[File:EndoTS MO 31.jpg|175px]] || [[File:EndoTS MO 32.jpg|175px]]
|}

{| class="wikitable" border="1"
|+ exo-TS MO's
|-
| Bonding Orbitals || [[File:Exo TS MO 29.jpg|175px]] || [[File:Exo TS MO 30.jpg|175px]]
|-
| Antibonding Orbitals || [[File:Exo TS MO 31.jpg|175px]] || [[File:Exo TS MO 32.jpg|175px]]
|}

{| class="wikitable" border="1"
|+ Endo vs Exo TS's
! !! Endo !! Exo
|-
| TS vibrations || [[File:Endo TS Vibrations.jpg|275px]] || [[File:Exo TS Vibrations.jpg|275px]]
|-
| TS Geometry || [[File:Endo TS Geometry.jpg|275px]] || [[File:Exo TS Geometry.jpg|275px]]
|-
|}

The presence of 1 imaginary negative frequency shows that these are the TS structures for the 2 reactions.

{| class="wikitable" border="1"
|+ Endo and Exo Product Formation from IRC
! !! Endo !! Exo
|-
| IRC || [[File:Endo product.gif|750px|]] || [[File:Exo product.gif|750px]]
|-
| Reaction coordinate || [[File:Endo Reaction Coordinate.jpg|750px]] || [[File:Exo Reaction Coordinate.jpg|750px]]
|}

=== Thermochemistry of Exo- vs Endo- ===

{| class="wikitable" border="1"
|+ Endo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.130081 || 20.64 || -
|-
| TS || 0.137942 || - || -
|-
| Product || 0.244570 || - || 300.59
|}

{| class="wikitable" border="1"
|+ Exo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.136771 || 5.60 || -
|-
| TS || 0.138905 || - || -
|-
| Product || 0.037977 || - || -259.38
|}

==== Secondary Orbital Interactions ====

{| class="wikitable" border="1"
|+ HOMO of exo and endo TS
! TS !! HOMO
|-
| endo || [[File:Endo TS HOMO 2ndary orbital interaction.jpg|450px]]
|-
| exo || [[File:Exo TS HOMO no 2ndary interaction.jpg|200px]]
|}

Primary orbital interactions lead to sigma bond formation. The dienophile, in this case the 1,3 Dioxole, is pointing away from the diene which does not allow for any further orbital interactions; and so only has primary orbital interactions, and forms the exo-product.

In the endo conformation, the dienophile is positioned such that the lobes of the C-O and the back orbitals in the cyclohexadiene can form a favourable bonding interaction, which lowers the energy of the TS, and in turn, is the kinetic product. Such an interaction is a secondary orbital interaction. A point to note is that no such bonds are formed in this case.

== '''Diels-Alder and Chelotropic Pathways''' ==
=== o-Xylylene and SO2 optimization to adducts of both reaction types ===
==== Method ====

==== Diels-Alder ====

The product was drawn and optimized to a minimum using the PM6 method. The C-S and C-O bonds in the resulting structure were removed and separated by 2.4 and 2.0 Å respectively, and frozen. This was then optimized to a TS (Berny). An IRC was then run on this TS geometry, and the lowest energy conformation from the resulting reaction profile was optimized to a minimum.

This gave the exo product; so the TS geometry was altered by manually displacing the O atom of the SO2 into an approximate endo geometry for TS. This was then optimized to a TS (Berny), after which an IRC was run and a subsequent optimization to a minimum on the product to obtain the energies. Using this method, allowed for both reaction paths to be analysed.

==== Chelotropic ====

The chelotropic product was drawn and optimized to a minimum. The C-S bonds of this resulting geometry were broken and the coordinates were frozen at approximately 2.2 Å apart. This structure was then optimized to a minimum, and the subsequent geometry reoptimized to a TS (Berny). An IRC was run on this TS with N=200, forward only, to obtain a reaction path.

==== Diels Alder ====

{| class="wikitable" border="1"
|+ Diels-Alder & Chelotropic Reactions
! !! Endo !! Exo !! Chelotropic
|-
| TS || [[File:Endo Xyl TS.jpg|650px]] || [[File:Exo Xyl TS.jpg|650px]] || [[File:Chelotropic TS.jpg|650px]]
|-
| IRC || [[File:Endo Xyl IRC.gif]] || [[File:Exo Xyl IRC.gif]] || [[File:Chelotropic IRC.gif]]
|-
| Reaction Profile || [[File:Endo Xyl Reaction Profile.jpg|650px]] || [[File:Exo Xyl Reaction Coordinate.jpg|650px]] || [[File:Chelotropic Reaction Coordinate.jpg|650px]]
|}

During the course of all 3 reactions, xylylene's 6 membered ring becomes aromatized, which gives it extra thermodynamic stability due to the lowering in energy. This extra energy provides the driving force(ΔG) of the reaction. The stabilization of the TS in this way allows the o-xylylene reaction to progress at a faster rate. This is very true for the Diels-Alder reaction.

=== Thermochemistry of o-Xylylene and SO2 ===

{| class="wikitable" border="1"
|+ Endo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.090737 || -0.47 || -
|-
| TS || 0.090559 || - || -
|-
| Product || 0.021693 || - || -181.28
|}

{| class="wikitable" border="1"
|+ Exo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.130081 || 20.64 || -
|-
| TS || 0.137942 || - || -
|-
| Product || 0.244570 || - || 300.59
|}

{| class="wikitable" border="1"
|+ Chelotropic
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.097953 || 2.9 || -
|-
| TS || 0.099059 || - || -
|-
| Product || -0.000002 || - || -257.18
|}

=== '''A Comparison of Reaction Profiles''' ===

==== '''References'''

Rep:Mod:Mrh214

2016-12-02T02:30:16Z

Mrh214: /* Method */

== '''Diels Alder Cycloaddition''' ==
=== Butadiene and Ethene optimization to Cyclohexene via PM6 ===
==== Method ====

1) Butadiene and ethene were optimized to a minimum seperately. Once optimized, they were placed in a similar geometry closely resembling that of the transition state (TS) required for the Diels Alder reaction; with the 4 carbon atoms in the reaction centre being frozen approximately 2.2 angstroms from eachother. This geometry was optimized to a minimum. The optimized geometry was then re-optimized to a TS (Berny), and this was confirmed by the presence of 1 negative frequency in the vibrations. An IRC was run on this TS in both directions with N=100. This geometry was manually displaced and optimized further to a minimum and product confirmation was given by all positive frequencies.

==== Butadiene ====
[[File:Butadiene.jpg|300px]]

==== Ethene ====
[[File:Ethene.jpg|300px]]

The C=C bonds in butadiene are 1.33531 Å; the C-C is 1.46835 Å. The C=C in ethene is 1.32731 Å.

==== TS ====
[[File:TS.jpg|300px]]

[[File:TS vibration 1.gif]]

This is the imaginary vibration at -949.3 icm-1, which corresponds to the TS.

[[File:TS vibration 2.gif]]

And this shows the first positive vibration at 144.91 icm-1. The motions are synchronous, therefore implying that the bond formations are also, synchronous.

In the TS the 2 C=C bonds of butadiene are now 1.37978 and 1.37974 Å. The previous C-C in butadiene is now 1.41114 Å; this has compressed as in the products, it will become a double bond. Similarly, the C=C bonds are now elongated slightly, due to becoming single bonds in the product.

The C=C in ethene for the TS has elongated to 1.38173, as this will be a single bond in the product.

The C atoms involved in the reaction centre for the Diels-Alder mechanism, from butadiene to the ethene carbons are at length 2.11423 and 2.11494 Å.

{| class="wikitable" border="1"
|+ Frontier Orbitals of Reactants
! FMO !! Butadiene !! Ethene
|-
| HOMO || [[File:HOMO Butadiene.jpg|300px]] || [[File:HOMO ethene.jpg|175px]]
|-
| LUMO || [[File:LUMO butadiene.jpg|175px]] || [[File:LUMO ethene.jpg|175px]]
|-
|}

(FMO = Frontier Molecular Orbitals)

{| class="wikitable" border="1"
|+ TS MO's
|-
| [[File:TS MO 16.jpg|175px]] || [[File:TS MO 17.jpg|175px]]
|-
| [[File:TS MO 18.jpg|175px]] || [[File:TS MO 19.jpg|175px]]
|}

==== Cyclohexene ====
[[File:Cyclohexene.jpg|300px]]

==== Bond Distance Variation Over Course of Reaction ====

{| class="wikitable" border="1"
|+ Bond lengths in reactants
! !! Bond lengths Å !!
|-
! Bond Type !! Butadiene !! Ethene
|-
| C-C || 1.46835 || -
|-
| C=C || 1.33531 || 1.32731
|}

{| class="wikitable" border="1"
|+ Bond lengths in TS
! !! Bond lengths Å !!
|-
! Bond Type !! Butadiene fragment !! Ethene fragment
|-
| C-C || 1.41114 || -
|-
| C=C || 1.37978 / 1.37974 || 1.38173
|}

{| class="wikitable" border="1"
|+ 2 C-C lengths in reaction centre
! Reaction centre !! Carbon atom distances Å
|-
| C-C || 2.11423 / 2.11494
|}

{| class="wikitable" border="1"
|+ Bond lengths in Cyclohexene product
! !! Cyclohexene
|-
! Bond type !! Bond lengths Å
|-
| C-C || 1.50085 / 1.50087
|-
| C-C || 1.53714 / 1.53704
|-
| C-C (opposite C=C) || 1.53453
|-
| C=C || 1.33698
|}

In the final product, the C=C is 1.33698 Å, the neighboring C-C on either side to the double bond are 1.50085 and 1.50087 Å. The adjacent C-C to these bonds are 1.53714 and 1.53704 Å. And the C-C directly opposite the C=C is 1.53453 Å.

Typical C-C sp3 length is 1.54 Å and the corresponding sp2 length is 1.34 Å. (ADD REFERENCE)!!! '''ADD VDW RADIII'''

The C-C bonds formed in TS have lengths less than the combined Van der Waals radius of 2 C atoms, which implies a bonding interaction is occuring.

==== The Diels-Alder MO Diagram ====
[[File:DA MO.jpg|400px]]

The MO diagram shows that the HOMO for the diene is closer in energy to the LUMO of the dienophile, hence will allow more efficient/constructive overlap (and lower energy antibonding MO) than the opposite case; which would be the LUMO of the diene with the HOMO of the dienophile.

==== The Symmetry Conditions ====
Let g = gerade (symmetric) and u = ungerade (antisymmetric).

Orbitals of the same symmetry may combine, ie. g-g, u-u. However, orbitals of mis-matched symmetry may not, ie. g-u / u-g.

The orbital overlap integral is non-zero for g-g / u-u, but zero for g-u / u-g.

==== Reference ====
Clayden (MO diagram)
DIELS-ALDER REACTIONS, Mircea D. Gherghiu

== '''A Comparison of Endo- and Exo- Products''' ==
=== The Reaction of Cyclohexadiene and 1,3-Dioxole by PM6 ===
==== Method ====

Both reactants were optimized, and subsequently placed in the endo TS conformation with the 4 C atoms involved in the reaction centre being frozen from eachother at a distance of 2.2 Å. An optimization to a minimum was carried out, followed by an optimization to a TS (Berny). An IRC was done on this TS structure, which ran in both directions, at N=20. The geometry obtained at the start of the reaction profile from the IRC was optimized to a minimum and no imaginary frequencies confirmed this to be the product.

The same procedure was carried out for the exo-conformer.

==== B3LYP frequency pictures for exo and endo ====

A B3LYP/6-31G(d) calculation was run on both TS geometries and the presence of 1 imaginary frequency in both TS structures confirmed them to be the TS. These frequencies were 520.86 and 528.8icm-1 for the endo and exo TS's respectively.

{| class="wikitable" border="1"
|+ B3LYP Vibrations and TS
! Endo !! Exo
|-
| [[File:Endo B3LYP TS.jpg|275px]] || [[File:Exo B3LYP TS.jpg|275px]]
|-
| [[File:Endo B3LYP Vib.jpg|275px]] || [[File:Exo B3LYP Vib.jpg|275px]]
|}

==== The releveant FMOs for Diels-Alder by symmetry ====

From the MO diagram for Diels-Alder, the same orbitals come into play for these reactions.

{| class="wikitable" border="1"
|+ endo-TS MO's
|-
| Bonding Orbitals || [[File:EndoTS MO 29.jpg|175px]] || [[File:EndoTS MO 30.jpg|175px]]
|-
| Antibonding Orbitals ||[[File:EndoTS MO 31.jpg|175px]] || [[File:EndoTS MO 32.jpg|175px]]
|}

{| class="wikitable" border="1"
|+ exo-TS MO's
|-
| Bonding Orbitals || [[File:Exo TS MO 29.jpg|175px]] || [[File:Exo TS MO 30.jpg|175px]]
|-
| Antibonding Orbitals || [[File:Exo TS MO 31.jpg|175px]] || [[File:Exo TS MO 32.jpg|175px]]
|}

{| class="wikitable" border="1"
|+ Endo vs Exo TS's
! !! Endo !! Exo
|-
| TS vibrations || [[File:Endo TS Vibrations.jpg|275px]] || [[File:Exo TS Vibrations.jpg|275px]]
|-
| TS Geometry || [[File:Endo TS Geometry.jpg|275px]] || [[File:Exo TS Geometry.jpg|275px]]
|-
|}

The presence of 1 imaginary negative frequency shows that these are the TS structures for the 2 reactions.

{| class="wikitable" border="1"
|+ Endo and Exo Product Formation from IRC
! !! Endo !! Exo
|-
| IRC || [[File:Endo product.gif|750px|]] || [[File:Exo product.gif|750px]]
|-
| Reaction coordinate || [[File:Endo Reaction Coordinate.jpg|750px]] || [[File:Exo Reaction Coordinate.jpg|750px]]
|}

=== Thermochemistry of Exo- vs Endo- ===

{| class="wikitable" border="1"
|+ Endo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.130081 || 20.64 || -
|-
| TS || 0.137942 || - || -
|-
| Product || 0.244570 || - || 300.59
|}

{| class="wikitable" border="1"
|+ Exo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.136771 || 5.60 || -
|-
| TS || 0.138905 || - || -
|-
| Product || 0.037977 || - || -259.38
|}

==== Secondary Orbital Interactions ====

{| class="wikitable" border="1"
|+ HOMO of exo and endo TS
! TS !! HOMO
|-
| endo || [[File:Endo TS HOMO 2ndary orbital interaction.jpg|450px]]
|-
| exo || [[File:Exo TS HOMO no 2ndary interaction.jpg|200px]]
|}

Primary orbital interactions lead to sigma bond formation. The dienophile, in this case the 1,3 Dioxole, is pointing away from the diene which does not allow for any further orbital interactions; and so only has primary orbital interactions, and forms the exo-product.

In the endo conformation, the dienophile is positioned such that the lobes of the C-O and the back orbitals in the cyclohexadiene can form a favourable bonding interaction, which lowers the energy of the TS, and in turn, is the kinetic product. Such an interaction is a secondary orbital interaction. A point to note is that no such bonds are formed in this case.

== '''Diels-Alder and Chelotropic Pathways''' ==
=== o-Xylylene and SO2 optimization to adducts of both reaction types ===
==== Method ====

==== Diels-Alder ====

The product was drawn and optimized to a minimum using the PM6 method. The C-S and C-O bonds in the resulting structure were removed and separated by 2.4 and 2.0 Å respectively, and frozen. This was then optimized to a TS (Berny). An IRC was then run on this TS geometry, and the lowest energy conformation from the resulting reaction profile was optimized to a minimum.

This gave the exo product; so the TS geometry was altered by manually displacing the O atom of the SO2 into an approximate endo geometry for TS. This was then optimized to a TS (Berny), after which an IRC was run and a subsequent optimization to a minimum on the product to obtain the energies. Using this method, allowed for both reaction paths to be analysed.

==== Chelotropic ====

The chelotropic product was drawn and optimized to a minimum. The C-S bonds of this resulting geometry were broken and the coordinates were frozen at approximately 2.2 Å apart. This structure was then optimized to a minimum, and the subsequent geometry reoptimized to a TS (Berny). An IRC was run on this TS with N=200, forward only, to obtain a reaction path.

==== Diels Alder ====

{| class="wikitable" border="1"
|+ Diels-Alder & Chelotropic Reactions
! !! Endo !! Exo !! Chelotropic
|-
| TS || [[File:Endo Xyl TS.jpg|650px]] || [[File:Exo Xyl TS.jpg|650px]] || [[File:Chelotropic TS.jpg|650px]]
|-
| IRC || [[File:Endo Xyl IRC.gif]] || [[File:Exo Xyl IRC.gif]] || [[File:Chelotropic IRC.gif]]
|-
| Reaction Profile || [[File:Endo Xyl Reaction Profile.jpg|650px]] || [[File:Exo Xyl Reaction Coordinate.jpg|650px]] || [[File:Chelotropic Reaction Coordinate.jpg|650px]]
|}

During the course of all 3 reactions, xylylene's 6 membered ring becomes aromatized, which gives it extra thermodynamic stability due to the lowering in energy. This extra energy provides the driving force(ΔG) of the reaction. The stabilization of the TS in this way allows the o-xylylene reaction to progress at a faster rate. This is very true for the Diels-Alder reaction.

=== Thermochemistry of o-Xylylene and SO2 ===

{| class="wikitable" border="1"
|+ Endo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.130081 || 20.64 || -
|-
| TS || 0.137942 || - || -
|-
| Product || 0.244570 || - || 300.59
|}

{| class="wikitable" border="1"
|+ Exo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.130081 || 20.64 || -
|-
| TS || 0.137942 || - || -
|-
| Product || 0.244570 || - || 300.59
|}

{| class="wikitable" border="1"
|+ Chelotropic
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.130081 || 20.64 || -
|-
| TS || 0.137942 || - || -
|-
| Product || 0.244570 || - || 300.59
|}

Rep:Mod:Mrh214

2016-12-02T02:06:08Z

Mrh214: /* Diels Alder and Chelotropic Pathways */

== '''Diels Alder Cycloaddition''' ==
=== Butadiene and Ethene optimization to Cyclohexene via PM6 ===
==== Method ====

1) Butadiene and ethene were optimized to a minimum seperately. Once optimized, they were placed in a similar geometry closely resembling that of the transition state (TS) required for the Diels Alder reaction; with the 4 carbon atoms in the reaction centre being frozen approximately 2.2 angstroms from eachother. This geometry was optimized to a minimum. The optimized geometry was then re-optimized to a TS (Berny), and this was confirmed by the presence of 1 negative frequency in the vibrations. An IRC was run on this TS in both directions with N=100. This geometry was manually displaced and optimized further to a minimum and product confirmation was given by all positive frequencies.

==== Butadiene ====
[[File:Butadiene.jpg|300px]]

==== Ethene ====
[[File:Ethene.jpg|300px]]

The C=C bonds in butadiene are 1.33531 Å; the C-C is 1.46835 Å. The C=C in ethene is 1.32731 Å.

==== TS ====
[[File:TS.jpg|300px]]

[[File:TS vibration 1.gif]]

This is the imaginary vibration at -949.3 icm-1, which corresponds to the TS.

[[File:TS vibration 2.gif]]

And this shows the first positive vibration at 144.91 icm-1. The motions are synchronous, therefore implying that the bond formations are also, synchronous.

In the TS the 2 C=C bonds of butadiene are now 1.37978 and 1.37974 Å. The previous C-C in butadiene is now 1.41114 Å; this has compressed as in the products, it will become a double bond. Similarly, the C=C bonds are now elongated slightly, due to becoming single bonds in the product.

The C=C in ethene for the TS has elongated to 1.38173, as this will be a single bond in the product.

The C atoms involved in the reaction centre for the Diels-Alder mechanism, from butadiene to the ethene carbons are at length 2.11423 and 2.11494 Å.

{| class="wikitable" border="1"
|+ Frontier Orbitals of Reactants
! FMO !! Butadiene !! Ethene
|-
| HOMO || [[File:HOMO Butadiene.jpg|300px]] || [[File:HOMO ethene.jpg|175px]]
|-
| LUMO || [[File:LUMO butadiene.jpg|175px]] || [[File:LUMO ethene.jpg|175px]]
|-
|}

(FMO = Frontier Molecular Orbitals)

{| class="wikitable" border="1"
|+ TS MO's
|-
| [[File:TS MO 16.jpg|175px]] || [[File:TS MO 17.jpg|175px]]
|-
| [[File:TS MO 18.jpg|175px]] || [[File:TS MO 19.jpg|175px]]
|}

==== Cyclohexene ====
[[File:Cyclohexene.jpg|300px]]

==== Bond Distance Variation Over Course of Reaction ====

{| class="wikitable" border="1"
|+ Bond lengths in reactants
! !! Bond lengths Å !!
|-
! Bond Type !! Butadiene !! Ethene
|-
| C-C || 1.46835 || -
|-
| C=C || 1.33531 || 1.32731
|}

{| class="wikitable" border="1"
|+ Bond lengths in TS
! !! Bond lengths Å !!
|-
! Bond Type !! Butadiene fragment !! Ethene fragment
|-
| C-C || 1.41114 || -
|-
| C=C || 1.37978 / 1.37974 || 1.38173
|}

{| class="wikitable" border="1"
|+ 2 C-C lengths in reaction centre
! Reaction centre !! Carbon atom distances Å
|-
| C-C || 2.11423 / 2.11494
|}

{| class="wikitable" border="1"
|+ Bond lengths in Cyclohexene product
! !! Cyclohexene
|-
! Bond type !! Bond lengths Å
|-
| C-C || 1.50085 / 1.50087
|-
| C-C || 1.53714 / 1.53704
|-
| C-C (opposite C=C) || 1.53453
|-
| C=C || 1.33698
|}

In the final product, the C=C is 1.33698 Å, the neighboring C-C on either side to the double bond are 1.50085 and 1.50087 Å. The adjacent C-C to these bonds are 1.53714 and 1.53704 Å. And the C-C directly opposite the C=C is 1.53453 Å.

Typical C-C sp3 length is 1.54 Å and the corresponding sp2 length is 1.34 Å. (ADD REFERENCE)!!! '''ADD VDW RADIII'''

The C-C bonds formed in TS have lengths less than the combined Van der Waals radius of 2 C atoms, which implies a bonding interaction is occuring.

==== The Diels-Alder MO Diagram ====
[[File:DA MO.jpg|400px]]

The MO diagram shows that the HOMO for the diene is closer in energy to the LUMO of the dienophile, hence will allow more efficient/constructive overlap (and lower energy antibonding MO) than the opposite case; which would be the LUMO of the diene with the HOMO of the dienophile.

==== The Symmetry Conditions ====
Let g = gerade (symmetric) and u = ungerade (antisymmetric).

Orbitals of the same symmetry may combine, ie. g-g, u-u. However, orbitals of mis-matched symmetry may not, ie. g-u / u-g.

The orbital overlap integral is non-zero for g-g / u-u, but zero for g-u / u-g.

==== Reference ====
Clayden (MO diagram)
DIELS-ALDER REACTIONS, Mircea D. Gherghiu

== '''A Comparison of Endo- and Exo- Products''' ==
=== The Reaction of Cyclohexadiene and 1,3-Dioxole by PM6 ===
==== Method ====

Both reactants were optimized, and subsequently placed in the endo TS conformation with the 4 C atoms involved in the reaction centre being frozen from eachother at a distance of 2.2 Å. An optimization to a minimum was carried out, followed by an optimization to a TS (Berny). An IRC was done on this TS structure, which ran in both directions, at N=20. The geometry obtained at the start of the reaction profile from the IRC was optimized to a minimum and no imaginary frequencies confirmed this to be the product.

The same procedure was carried out for the exo-conformer.

==== B3LYP frequency pictures for exo and endo ====

A B3LYP/6-31G(d) calculation was run on both TS geometries and the presence of 1 imaginary frequency in both TS structures confirmed them to be the TS. These frequencies were 520.86 and 528.8icm-1 for the endo and exo TS's respectively.

{| class="wikitable" border="1"
|+ B3LYP Vibrations and TS
! Endo !! Exo
|-
| [[File:Endo B3LYP TS.jpg|275px]] || [[File:Exo B3LYP TS.jpg|275px]]
|-
| [[File:Endo B3LYP Vib.jpg|275px]] || [[File:Exo B3LYP Vib.jpg|275px]]
|}

==== The releveant FMOs for Diels-Alder by symmetry ====

From the MO diagram for Diels-Alder, the same orbitals come into play for these reactions.

{| class="wikitable" border="1"
|+ endo-TS MO's
|-
| Bonding Orbitals || [[File:EndoTS MO 29.jpg|175px]] || [[File:EndoTS MO 30.jpg|175px]]
|-
| Antibonding Orbitals ||[[File:EndoTS MO 31.jpg|175px]] || [[File:EndoTS MO 32.jpg|175px]]
|}

{| class="wikitable" border="1"
|+ exo-TS MO's
|-
| Bonding Orbitals || [[File:Exo TS MO 29.jpg|175px]] || [[File:Exo TS MO 30.jpg|175px]]
|-
| Antibonding Orbitals || [[File:Exo TS MO 31.jpg|175px]] || [[File:Exo TS MO 32.jpg|175px]]
|}

{| class="wikitable" border="1"
|+ Endo vs Exo TS's
! !! Endo !! Exo
|-
| TS vibrations || [[File:Endo TS Vibrations.jpg|275px]] || [[File:Exo TS Vibrations.jpg|275px]]
|-
| TS Geometry || [[File:Endo TS Geometry.jpg|275px]] || [[File:Exo TS Geometry.jpg|275px]]
|-
|}

The presence of 1 imaginary negative frequency shows that these are the TS structures for the 2 reactions.

{| class="wikitable" border="1"
|+ Endo and Exo Product Formation from IRC
! !! Endo !! Exo
|-
| IRC || [[File:Endo product.gif|750px|]] || [[File:Exo product.gif|750px]]
|-
| Reaction coordinate || [[File:Endo Reaction Coordinate.jpg|750px]] || [[File:Exo Reaction Coordinate.jpg|750px]]
|}

=== Thermochemistry of Exo- vs Endo- ===

{| class="wikitable" border="1"
|+ Endo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.130081 || 20.64 || -
|-
| TS || 0.137942 || - || -
|-
| Product || 0.244570 || - || 300.59
|}

{| class="wikitable" border="1"
|+ Exo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.136771 || 5.60 || -
|-
| TS || 0.138905 || - || -
|-
| Product || 0.037977 || - || -259.38
|}

==== Secondary Orbital Interactions ====

{| class="wikitable" border="1"
|+ HOMO of exo and endo TS
! TS !! HOMO
|-
| endo || [[File:Endo TS HOMO 2ndary orbital interaction.jpg|450px]]
|-
| exo || [[File:Exo TS HOMO no 2ndary interaction.jpg|200px]]
|}

Primary orbital interactions lead to sigma bond formation. The dienophile, in this case the 1,3 Dioxole, is pointing away from the diene which does not allow for any further orbital interactions; and so only has primary orbital interactions, and forms the exo-product.

In the endo conformation, the dienophile is positioned such that the lobes of the C-O and the back orbitals in the cyclohexadiene can form a favourable bonding interaction, which lowers the energy of the TS, and in turn, is the kinetic product. Such an interaction is a secondary orbital interaction. A point to note is that no such bonds are formed in this case.

== '''Diels-Alder and Chelotropic Pathways''' ==
=== o-Xylylene and SO2 optimization to adducts of both reaction types ===
==== Method ====

==== Chelotropic ====

The chelotropic product was drawn and optimized to a minimum. The C-S bonds of this resulting geometry were broken and the coordinates were frozen at approximately 2.2 Å apart. This structure was then optimized to a minimum, and the subsequent geometry reoptimized to a TS (Berny). An IRC was run on this TS with N=200, forward only, to obtain a reaction path.

==== Diels Alder ====

{| class="wikitable" border="1"
|+ Diels-Alder & Chelotropic Reactions
! !! Endo !! Exo !! Chelotropic
|-
| TS || [[File:Endo Xyl TS.jpg|650px]] || [[File:Exo Xyl TS.jpg|650px]] || [[File:Chelotropic TS.jpg|650px]]
|-
| IRC || [[File:Endo Xyl IRC.gif]] || [[File:Exo Xyl IRC.gif]] || [[File:Chelotropic IRC.gif]]
|-
| Reaction Profile || [[File:Endo Xyl Reaction Profile.jpg|650px]] || [[File:Exo Xyl Reaction Coordinate.jpg|650px]] || [[File:Chelotropic Reaction Coordinate.jpg|650px]]
|}

During the course of all 3 reactions, xylylene's 6 membered ring becomes aromatized, which gives it extra thermodynamic stability due to the lowering in energy. This extra energy provides the driving force(ΔG) of the reaction. The stabilization of the TS in this way allows the o-xylylene reaction to progress at a faster rate. This is very true for the Diels-Alder reaction.

=== Thermochemistry of o-Xylylene and SO2 ===

{| class="wikitable" border="1"
|+ Endo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.130081 || 20.64 || -
|-
| TS || 0.137942 || - || -
|-
| Product || 0.244570 || - || 300.59
|}

{| class="wikitable" border="1"
|+ Exo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.130081 || 20.64 || -
|-
| TS || 0.137942 || - || -
|-
| Product || 0.244570 || - || 300.59
|}

{| class="wikitable" border="1"
|+ Chelotropic
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.130081 || 20.64 || -
|-
| TS || 0.137942 || - || -
|-
| Product || 0.244570 || - || 300.59
|}

Rep:Mod:Mrh214

2016-12-02T02:04:02Z

Mrh214:

== '''Diels Alder Cycloaddition''' ==
=== Butadiene and Ethene optimization to Cyclohexene via PM6 ===
==== Method ====

1) Butadiene and ethene were optimized to a minimum seperately. Once optimized, they were placed in a similar geometry closely resembling that of the transition state (TS) required for the Diels Alder reaction; with the 4 carbon atoms in the reaction centre being frozen approximately 2.2 angstroms from eachother. This geometry was optimized to a minimum. The optimized geometry was then re-optimized to a TS (Berny), and this was confirmed by the presence of 1 negative frequency in the vibrations. An IRC was run on this TS in both directions with N=100. This geometry was manually displaced and optimized further to a minimum and product confirmation was given by all positive frequencies.

==== Butadiene ====
[[File:Butadiene.jpg|300px]]

==== Ethene ====
[[File:Ethene.jpg|300px]]

The C=C bonds in butadiene are 1.33531 Å; the C-C is 1.46835 Å. The C=C in ethene is 1.32731 Å.

==== TS ====
[[File:TS.jpg|300px]]

[[File:TS vibration 1.gif]]

This is the imaginary vibration at -949.3 icm-1, which corresponds to the TS.

[[File:TS vibration 2.gif]]

And this shows the first positive vibration at 144.91 icm-1. The motions are synchronous, therefore implying that the bond formations are also, synchronous.

In the TS the 2 C=C bonds of butadiene are now 1.37978 and 1.37974 Å. The previous C-C in butadiene is now 1.41114 Å; this has compressed as in the products, it will become a double bond. Similarly, the C=C bonds are now elongated slightly, due to becoming single bonds in the product.

The C=C in ethene for the TS has elongated to 1.38173, as this will be a single bond in the product.

The C atoms involved in the reaction centre for the Diels-Alder mechanism, from butadiene to the ethene carbons are at length 2.11423 and 2.11494 Å.

{| class="wikitable" border="1"
|+ Frontier Orbitals of Reactants
! FMO !! Butadiene !! Ethene
|-
| HOMO || [[File:HOMO Butadiene.jpg|300px]] || [[File:HOMO ethene.jpg|175px]]
|-
| LUMO || [[File:LUMO butadiene.jpg|175px]] || [[File:LUMO ethene.jpg|175px]]
|-
|}

(FMO = Frontier Molecular Orbitals)

{| class="wikitable" border="1"
|+ TS MO's
|-
| [[File:TS MO 16.jpg|175px]] || [[File:TS MO 17.jpg|175px]]
|-
| [[File:TS MO 18.jpg|175px]] || [[File:TS MO 19.jpg|175px]]
|}

==== Cyclohexene ====
[[File:Cyclohexene.jpg|300px]]

==== Bond Distance Variation Over Course of Reaction ====

{| class="wikitable" border="1"
|+ Bond lengths in reactants
! !! Bond lengths Å !!
|-
! Bond Type !! Butadiene !! Ethene
|-
| C-C || 1.46835 || -
|-
| C=C || 1.33531 || 1.32731
|}

{| class="wikitable" border="1"
|+ Bond lengths in TS
! !! Bond lengths Å !!
|-
! Bond Type !! Butadiene fragment !! Ethene fragment
|-
| C-C || 1.41114 || -
|-
| C=C || 1.37978 / 1.37974 || 1.38173
|}

{| class="wikitable" border="1"
|+ 2 C-C lengths in reaction centre
! Reaction centre !! Carbon atom distances Å
|-
| C-C || 2.11423 / 2.11494
|}

{| class="wikitable" border="1"
|+ Bond lengths in Cyclohexene product
! !! Cyclohexene
|-
! Bond type !! Bond lengths Å
|-
| C-C || 1.50085 / 1.50087
|-
| C-C || 1.53714 / 1.53704
|-
| C-C (opposite C=C) || 1.53453
|-
| C=C || 1.33698
|}

In the final product, the C=C is 1.33698 Å, the neighboring C-C on either side to the double bond are 1.50085 and 1.50087 Å. The adjacent C-C to these bonds are 1.53714 and 1.53704 Å. And the C-C directly opposite the C=C is 1.53453 Å.

Typical C-C sp3 length is 1.54 Å and the corresponding sp2 length is 1.34 Å. (ADD REFERENCE)!!! '''ADD VDW RADIII'''

The C-C bonds formed in TS have lengths less than the combined Van der Waals radius of 2 C atoms, which implies a bonding interaction is occuring.

==== The Diels-Alder MO Diagram ====
[[File:DA MO.jpg|400px]]

The MO diagram shows that the HOMO for the diene is closer in energy to the LUMO of the dienophile, hence will allow more efficient/constructive overlap (and lower energy antibonding MO) than the opposite case; which would be the LUMO of the diene with the HOMO of the dienophile.

==== The Symmetry Conditions ====
Let g = gerade (symmetric) and u = ungerade (antisymmetric).

Orbitals of the same symmetry may combine, ie. g-g, u-u. However, orbitals of mis-matched symmetry may not, ie. g-u / u-g.

The orbital overlap integral is non-zero for g-g / u-u, but zero for g-u / u-g.

==== Reference ====
Clayden (MO diagram)
DIELS-ALDER REACTIONS, Mircea D. Gherghiu

== '''A Comparison of Endo- and Exo- Products''' ==
=== The Reaction of Cyclohexadiene and 1,3-Dioxole by PM6 ===
==== Method ====

Both reactants were optimized, and subsequently placed in the endo TS conformation with the 4 C atoms involved in the reaction centre being frozen from eachother at a distance of 2.2 Å. An optimization to a minimum was carried out, followed by an optimization to a TS (Berny). An IRC was done on this TS structure, which ran in both directions, at N=20. The geometry obtained at the start of the reaction profile from the IRC was optimized to a minimum and no imaginary frequencies confirmed this to be the product.

The same procedure was carried out for the exo-conformer.

==== B3LYP frequency pictures for exo and endo ====

A B3LYP/6-31G(d) calculation was run on both TS geometries and the presence of 1 imaginary frequency in both TS structures confirmed them to be the TS. These frequencies were 520.86 and 528.8icm-1 for the endo and exo TS's respectively.

{| class="wikitable" border="1"
|+ B3LYP Vibrations and TS
! Endo !! Exo
|-
| [[File:Endo B3LYP TS.jpg|275px]] || [[File:Exo B3LYP TS.jpg|275px]]
|-
| [[File:Endo B3LYP Vib.jpg|275px]] || [[File:Exo B3LYP Vib.jpg|275px]]
|}

==== The releveant FMOs for Diels-Alder by symmetry ====

From the MO diagram for Diels-Alder, the same orbitals come into play for these reactions.

{| class="wikitable" border="1"
|+ endo-TS MO's
|-
| Bonding Orbitals || [[File:EndoTS MO 29.jpg|175px]] || [[File:EndoTS MO 30.jpg|175px]]
|-
| Antibonding Orbitals ||[[File:EndoTS MO 31.jpg|175px]] || [[File:EndoTS MO 32.jpg|175px]]
|}

{| class="wikitable" border="1"
|+ exo-TS MO's
|-
| Bonding Orbitals || [[File:Exo TS MO 29.jpg|175px]] || [[File:Exo TS MO 30.jpg|175px]]
|-
| Antibonding Orbitals || [[File:Exo TS MO 31.jpg|175px]] || [[File:Exo TS MO 32.jpg|175px]]
|}

{| class="wikitable" border="1"
|+ Endo vs Exo TS's
! !! Endo !! Exo
|-
| TS vibrations || [[File:Endo TS Vibrations.jpg|275px]] || [[File:Exo TS Vibrations.jpg|275px]]
|-
| TS Geometry || [[File:Endo TS Geometry.jpg|275px]] || [[File:Exo TS Geometry.jpg|275px]]
|-
|}

The presence of 1 imaginary negative frequency shows that these are the TS structures for the 2 reactions.

{| class="wikitable" border="1"
|+ Endo and Exo Product Formation from IRC
! !! Endo !! Exo
|-
| IRC || [[File:Endo product.gif|750px|]] || [[File:Exo product.gif|750px]]
|-
| Reaction coordinate || [[File:Endo Reaction Coordinate.jpg|750px]] || [[File:Exo Reaction Coordinate.jpg|750px]]
|}

=== Thermochemistry of Exo- vs Endo- ===

{| class="wikitable" border="1"
|+ Endo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.130081 || 20.64 || -
|-
| TS || 0.137942 || - || -
|-
| Product || 0.244570 || - || 300.59
|}

{| class="wikitable" border="1"
|+ Exo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.136771 || 5.60 || -
|-
| TS || 0.138905 || - || -
|-
| Product || 0.037977 || - || -259.38
|}

==== Secondary Orbital Interactions ====

{| class="wikitable" border="1"
|+ HOMO of exo and endo TS
! TS !! HOMO
|-
| endo || [[File:Endo TS HOMO 2ndary orbital interaction.jpg|450px]]
|-
| exo || [[File:Exo TS HOMO no 2ndary interaction.jpg|200px]]
|}

Primary orbital interactions lead to sigma bond formation. The dienophile, in this case the 1,3 Dioxole, is pointing away from the diene which does not allow for any further orbital interactions; and so only has primary orbital interactions, and forms the exo-product.

In the endo conformation, the dienophile is positioned such that the lobes of the C-O and the back orbitals in the cyclohexadiene can form a favourable bonding interaction, which lowers the energy of the TS, and in turn, is the kinetic product. Such an interaction is a secondary orbital interaction. A point to note is that no such bonds are formed in this case.

== '''Diels Alder and Chelotropic Pathways''' ==
=== o-Xylylene and SO2 optimization to adducts of both reaction types ===
==== Method ====

==== Chelotropic ====

The chelotropic product was drawn and optimized to a minimum. The C-S bonds of this resulting geometry were broken and the coordinates were frozen at approximately 2.2 Å apart. This structure was then optimized to a minimum, and the subsequent geometry reoptimized to a TS (Berny). An IRC was run on this TS with N=200, forward only, to obtain a reaction path.

==== Diels Alder ====

{| class="wikitable" border="1"
|+ Diels-Alder & Chelotropic Reactions
! !! Endo !! Exo !! Chelotropic
|-
| TS || [[File:Endo Xyl TS.jpg|650px]] || [[File:Exo Xyl TS.jpg|650px]] || [[File:Chelotropic TS.jpg|650px]]
|-
| IRC || [[File:Endo Xyl IRC.gif]] || [[File:Exo Xyl IRC.gif]] || [[File:Chelotropic IRC.gif]]
|-
| Reaction Profile || [[File:Endo Xyl Reaction Profile.jpg|650px]] || [[File:Exo Xyl Reaction Coordinate.jpg|650px]] || [[File:Chelotropic Reaction Coordinate.jpg|650px]]
|}

During the course of all 3 reactions, xylylene's 6 membered ring becomes aromatized, which gives it extra thermodynamic stability due to the lowering in energy. This extra energy provides the driving force(ΔG) of the reaction. The stabilization of the TS in this way allows the o-xylylene reaction to progress at a faster rate. This is very true for the Diels-Alder reaction.

=== Thermochemistry of o-Xylylene and SO2 ===

{| class="wikitable" border="1"
|+ Endo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.130081 || 20.64 || -
|-
| TS || 0.137942 || - || -
|-
| Product || 0.244570 || - || 300.59
|}

{| class="wikitable" border="1"
|+ Exo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.130081 || 20.64 || -
|-
| TS || 0.137942 || - || -
|-
| Product || 0.244570 || - || 300.59
|}

{| class="wikitable" border="1"
|+ Chelotropic
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.130081 || 20.64 || -
|-
| TS || 0.137942 || - || -
|-
| Product || 0.244570 || - || 300.59
|}

Rep:Mod:Mrh214

2016-12-02T01:22:40Z

Mrh214: /* Secondary Orbital Interactions */

== '''Diels Alder Cycloaddition''' ==
=== Butadiene and Ethene optimization to Cyclohexene via PM6 ===
==== Method ====

1) Butadiene and ethene were optimized to a minimum seperately. Once optimized, they were placed in a similar geometry closely resembling that of the transition state (TS) required for the Diels Alder reaction; with the 4 carbon atoms in the reaction centre being frozen approximately 2.2 angstroms from eachother. This geometry was optimized to a minimum. The optimized geometry was then re-optimized to a TS (Berny), and this was confirmed by the presence of 1 negative frequency in the vibrations. An IRC was run on this TS in both directions with N=100. This geometry was manually displaced and optimized further to a minimum and product confirmation was given by all positive frequencies.

==== Butadiene ====
[[File:Butadiene.jpg|300px]]

==== Ethene ====
[[File:Ethene.jpg|300px]]

The C=C bonds in butadiene are 1.33531 Å; the C-C is 1.46835 Å. The C=C in ethene is 1.32731 Å.

==== TS ====
[[File:TS.jpg|300px]]

[[File:TS vibration 1.gif]]

This is the imaginary vibration at -949.3 icm-1, which corresponds to the TS.

[[File:TS vibration 2.gif]]

And this shows the first positive vibration at 144.91 icm-1. The motions are synchronous, therefore implying that the bond formations are also, synchronous.

In the TS the 2 C=C bonds of butadiene are now 1.37978 and 1.37974 Å. The previous C-C in butadiene is now 1.41114 Å; this has compressed as in the products, it will become a double bond. Similarly, the C=C bonds are now elongated slightly, due to becoming single bonds in the product.

The C=C in ethene for the TS has elongated to 1.38173, as this will be a single bond in the product.

The C atoms involved in the reaction centre for the Diels-Alder mechanism, from butadiene to the ethene carbons are at length 2.11423 and 2.11494 Å.

{| class="wikitable" border="1"
|+ Frontier Orbitals of Reactants
! FMO !! Butadiene !! Ethene
|-
| HOMO || [[File:HOMO Butadiene.jpg|300px]] || [[File:HOMO ethene.jpg|175px]]
|-
| LUMO || [[File:LUMO butadiene.jpg|175px]] || [[File:LUMO ethene.jpg|175px]]
|-
|}

(FMO = Frontier Molecular Orbitals)

{| class="wikitable" border="1"
|+ TS MO's
|-
| [[File:TS MO 16.jpg|175px]] || [[File:TS MO 17.jpg|175px]]
|-
| [[File:TS MO 18.jpg|175px]] || [[File:TS MO 19.jpg|175px]]
|}

==== Cyclohexene ====
[[File:Cyclohexene.jpg|300px]]

==== Bond Distance Variation Over Course of Reaction ====

{| class="wikitable" border="1"
|+ Bond lengths in reactants
! !! Bond lengths Å !!
|-
! Bond Type !! Butadiene !! Ethene
|-
| C-C || 1.46835 || -
|-
| C=C || 1.33531 || 1.32731
|}

{| class="wikitable" border="1"
|+ Bond lengths in TS
! !! Bond lengths Å !!
|-
! Bond Type !! Butadiene fragment !! Ethene fragment
|-
| C-C || 1.41114 || -
|-
| C=C || 1.37978 / 1.37974 || 1.38173
|}

{| class="wikitable" border="1"
|+ 2 C-C lengths in reaction centre
! Reaction centre !! Carbon atom distances Å
|-
| C-C || 2.11423 / 2.11494
|}

{| class="wikitable" border="1"
|+ Bond lengths in Cyclohexene product
! !! Cyclohexene
|-
! Bond type !! Bond lengths Å
|-
| C-C || 1.50085 / 1.50087
|-
| C-C || 1.53714 / 1.53704
|-
| C-C (opposite C=C) || 1.53453
|-
| C=C || 1.33698
|}

In the final product, the C=C is 1.33698 Å, the neighboring C-C on either side to the double bond are 1.50085 and 1.50087 Å. The adjacent C-C to these bonds are 1.53714 and 1.53704 Å. And the C-C directly opposite the C=C is 1.53453 Å.

Typical C-C sp3 length is 1.54 Å and the corresponding sp2 length is 1.34 Å. (ADD REFERENCE)!!! '''ADD VDW RADIII'''

The C-C bonds formed in TS have lengths less than the combined Van der Waals radius of 2 C atoms, which implies a bonding interaction is occuring.

==== The Diels-Alder MO Diagram ====
[[File:DA MO.jpg|400px]]

The MO diagram shows that the HOMO for the diene is closer in energy to the LUMO of the dienophile, hence will allow more efficient/constructive overlap (and lower energy antibonding MO) than the opposite case; which would be the LUMO of the diene with the HOMO of the dienophile.

==== The Symmetry Conditions ====
Let g = gerade (symmetric) and u = ungerade (antisymmetric).

Orbitals of the same symmetry may combine, ie. g-g, u-u. However, orbitals of mis-matched symmetry may not, ie. g-u / u-g.

The orbital overlap integral is non-zero for g-g / u-u, but zero for g-u / u-g.

==== Reference ====
Clayden (MO diagram)
DIELS-ALDER REACTIONS, Mircea D. Gherghiu

== '''A Comparison of Endo- and Exo- Products''' ==
=== The Reaction of Cyclohexadiene and 1,3-Dioxole by PM6 ===
==== Method ====

Both reactants were optimized, and subsequently placed in the endo TS conformation with the 4 C atoms involved in the reaction centre being frozen from eachother at a distance of 2.2 Å. An optimization to a minimum was carried out, followed by an optimization to a TS (Berny). An IRC was done on this TS structure, which ran in both directions, at N=20. The geometry obtained at the start of the reaction profile from the IRC was optimized to a minimum and no imaginary frequencies confirmed this to be the product.

The same procedure was carried out for the exo-conformer.

==== B3LYP frequency pictures for exo and endo ====

A B3LYP/6-31G(d) calculation was run on both TS geometries and the presence of 1 imaginary frequency in both TS structures confirmed them to be the TS. These frequencies were 520.86 and 528.8icm-1 for the endo and exo TS's respectively.

{| class="wikitable" border="1"
|+ B3LYP Vibrations and TS
! Endo !! Exo
|-
| [[File:Endo B3LYP TS.jpg|275px]] || [[File:Exo B3LYP TS.jpg|275px]]
|-
| [[File:Endo B3LYP Vib.jpg|275px]] || [[File:Exo B3LYP Vib.jpg|275px]]
|}

==== The releveant FMOs for Diels-Alder by symmetry ====

From the MO diagram for Diels-Alder, the same orbitals come into play for these reactions.

{| class="wikitable" border="1"
|+ endo-TS MO's
|-
| Bonding Orbitals || [[File:EndoTS MO 29.jpg|175px]] || [[File:EndoTS MO 30.jpg|175px]]
|-
| Antibonding Orbitals ||[[File:EndoTS MO 31.jpg|175px]] || [[File:EndoTS MO 32.jpg|175px]]
|}

{| class="wikitable" border="1"
|+ exo-TS MO's
|-
| Bonding Orbitals || [[File:Exo TS MO 29.jpg|175px]] || [[File:Exo TS MO 30.jpg|175px]]
|-
| Antibonding Orbitals || [[File:Exo TS MO 31.jpg|175px]] || [[File:Exo TS MO 32.jpg|175px]]
|}

{| class="wikitable" border="1"
|+ Endo vs Exo TS's
! !! Endo !! Exo
|-
| TS vibrations || [[File:Endo TS Vibrations.jpg|275px]] || [[File:Exo TS Vibrations.jpg|275px]]
|-
| TS Geometry || [[File:Endo TS Geometry.jpg|275px]] || [[File:Exo TS Geometry.jpg|275px]]
|-
|}

The presence of 1 imaginary negative frequency shows that these are the TS structures for the 2 reactions.

{| class="wikitable" border="1"
|+ Endo and Exo Product Formation from IRC
! !! Endo !! Exo
|-
| IRC || [[File:Endo product.gif|750px|]] || [[File:Exo product.gif|750px]]
|-
| Reaction coordinate || [[File:Endo Reaction Coordinate.jpg|750px]] || [[File:Exo Reaction Coordinate.jpg|750px]]
|}

=== Thermochemistry of Exo- vs Endo- ===

{| class="wikitable" border="1"
|+ Endo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.130081 || 20.64 || -
|-
| TS || 0.137942 || - || -
|-
| Product || 0.244570 || - || 300.59
|}

{| class="wikitable" border="1"
|+ Exo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.136771 || 5.60 || -
|-
| TS || 0.138905 || - || -
|-
| Product || 0.037977 || - || -259.38
|}

==== Secondary Orbital Interactions ====

{| class="wikitable" border="1"
|+ HOMO of exo and endo TS
! TS !! HOMO
|-
| endo || [[File:Endo TS HOMO 2ndary orbital interaction.jpg|450px]]
|-
| exo || [[File:Exo TS HOMO no 2ndary interaction.jpg|200px]]
|}

Primary orbital interactions lead to sigma bond formation. The dienophile, in this case the 1,3 Dioxole, is pointing away from the diene which does not allow for any further orbital interactions; and so only has primary orbital interactions, and forms the exo-product.

In the endo conformation, the dienophile is positioned such that the lobes of the C-O and the back orbitals in the cyclohexadiene can form a favourable bonding interaction, which lowers the energy of the TS, and in turn, is the kinetic product. Such an interaction is a secondary orbital interaction. A point to note is that no such bonds are formed in this case.

== '''Diels Alder and Chelotropic Pathways''' ==
=== o-Xylylene and SO2 optimization to adducts of both reaction types ===
==== Method ====

==== Chelotropic ====

The chelotropic product was drawn and optimized to a minimum. The C-S bonds of this resulting geometry were broken and the coordinates were frozen at approximately 2.2 Å apart. This structure was then optimized to a minimum, and the subsequent geometry reoptimized to a TS (Berny). An IRC was run on this TS with N=200, forward only, to obtain a reaction path.

==== Diels Alder ====

{| class="wikitable" border="1"
|+ Diels-Alder & Chelotropic Reactions
! !! Endo !! Exo !! Chelotropic
|-
| TS || [[File:Endo Xyl TS.jpg|650px]] || [[File:Exo Xyl TS.jpg|650px]] || [[File:Chelotropic TS.jpg|650px]]
|-
| IRC || [[File:Endo Xyl IRC.gif]] || [[File:Exo Xyl IRC.gif]] || [[File:Chelotropic IRC.gif]]
|-
| Reaction Profile || [[File:Endo Xyl Reaction Profile.jpg|650px]] || [[File:Exo Xyl Reaction Coordinate.jpg|650px]] || [[File:Chelotropic Reaction Coordinate.jpg|650px]]
|}

=== Thermochemistry of o-Xylylene and SO2 ===

{| class="wikitable" border="1"
|+ Endo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.130081 || 20.64 || -
|-
| TS || 0.137942 || - || -
|-
| Product || 0.244570 || - || 300.59
|}

{| class="wikitable" border="1"
|+ Exo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.130081 || 20.64 || -
|-
| TS || 0.137942 || - || -
|-
| Product || 0.244570 || - || 300.59
|}

{| class="wikitable" border="1"
|+ Chelotropic
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.130081 || 20.64 || -
|-
| TS || 0.137942 || - || -
|-
| Product || 0.244570 || - || 300.59
|}

Rep:Mod:Mrh214

2016-12-02T01:03:01Z

Mrh214:

== '''Diels Alder Cycloaddition''' ==
=== Butadiene and Ethene optimization to Cyclohexene via PM6 ===
==== Method ====

1) Butadiene and ethene were optimized to a minimum seperately. Once optimized, they were placed in a similar geometry closely resembling that of the transition state (TS) required for the Diels Alder reaction; with the 4 carbon atoms in the reaction centre being frozen approximately 2.2 angstroms from eachother. This geometry was optimized to a minimum. The optimized geometry was then re-optimized to a TS (Berny), and this was confirmed by the presence of 1 negative frequency in the vibrations. An IRC was run on this TS in both directions with N=100. This geometry was manually displaced and optimized further to a minimum and product confirmation was given by all positive frequencies.

==== Butadiene ====
[[File:Butadiene.jpg|300px]]

==== Ethene ====
[[File:Ethene.jpg|300px]]

The C=C bonds in butadiene are 1.33531 Å; the C-C is 1.46835 Å. The C=C in ethene is 1.32731 Å.

==== TS ====
[[File:TS.jpg|300px]]

[[File:TS vibration 1.gif]]

This is the imaginary vibration at -949.3 icm-1, which corresponds to the TS.

[[File:TS vibration 2.gif]]

And this shows the first positive vibration at 144.91 icm-1. The motions are synchronous, therefore implying that the bond formations are also, synchronous.

In the TS the 2 C=C bonds of butadiene are now 1.37978 and 1.37974 Å. The previous C-C in butadiene is now 1.41114 Å; this has compressed as in the products, it will become a double bond. Similarly, the C=C bonds are now elongated slightly, due to becoming single bonds in the product.

The C=C in ethene for the TS has elongated to 1.38173, as this will be a single bond in the product.

The C atoms involved in the reaction centre for the Diels-Alder mechanism, from butadiene to the ethene carbons are at length 2.11423 and 2.11494 Å.

{| class="wikitable" border="1"
|+ Frontier Orbitals of Reactants
! FMO !! Butadiene !! Ethene
|-
| HOMO || [[File:HOMO Butadiene.jpg|300px]] || [[File:HOMO ethene.jpg|175px]]
|-
| LUMO || [[File:LUMO butadiene.jpg|175px]] || [[File:LUMO ethene.jpg|175px]]
|-
|}

(FMO = Frontier Molecular Orbitals)

{| class="wikitable" border="1"
|+ TS MO's
|-
| [[File:TS MO 16.jpg|175px]] || [[File:TS MO 17.jpg|175px]]
|-
| [[File:TS MO 18.jpg|175px]] || [[File:TS MO 19.jpg|175px]]
|}

==== Cyclohexene ====
[[File:Cyclohexene.jpg|300px]]

==== Bond Distance Variation Over Course of Reaction ====

{| class="wikitable" border="1"
|+ Bond lengths in reactants
! !! Bond lengths Å !!
|-
! Bond Type !! Butadiene !! Ethene
|-
| C-C || 1.46835 || -
|-
| C=C || 1.33531 || 1.32731
|}

{| class="wikitable" border="1"
|+ Bond lengths in TS
! !! Bond lengths Å !!
|-
! Bond Type !! Butadiene fragment !! Ethene fragment
|-
| C-C || 1.41114 || -
|-
| C=C || 1.37978 / 1.37974 || 1.38173
|}

{| class="wikitable" border="1"
|+ 2 C-C lengths in reaction centre
! Reaction centre !! Carbon atom distances Å
|-
| C-C || 2.11423 / 2.11494
|}

{| class="wikitable" border="1"
|+ Bond lengths in Cyclohexene product
! !! Cyclohexene
|-
! Bond type !! Bond lengths Å
|-
| C-C || 1.50085 / 1.50087
|-
| C-C || 1.53714 / 1.53704
|-
| C-C (opposite C=C) || 1.53453
|-
| C=C || 1.33698
|}

In the final product, the C=C is 1.33698 Å, the neighboring C-C on either side to the double bond are 1.50085 and 1.50087 Å. The adjacent C-C to these bonds are 1.53714 and 1.53704 Å. And the C-C directly opposite the C=C is 1.53453 Å.

Typical C-C sp3 length is 1.54 Å and the corresponding sp2 length is 1.34 Å. (ADD REFERENCE)!!! '''ADD VDW RADIII'''

The C-C bonds formed in TS have lengths less than the combined Van der Waals radius of 2 C atoms, which implies a bonding interaction is occuring.

==== The Diels-Alder MO Diagram ====
[[File:DA MO.jpg|400px]]

The MO diagram shows that the HOMO for the diene is closer in energy to the LUMO of the dienophile, hence will allow more efficient/constructive overlap (and lower energy antibonding MO) than the opposite case; which would be the LUMO of the diene with the HOMO of the dienophile.

==== The Symmetry Conditions ====
Let g = gerade (symmetric) and u = ungerade (antisymmetric).

Orbitals of the same symmetry may combine, ie. g-g, u-u. However, orbitals of mis-matched symmetry may not, ie. g-u / u-g.

The orbital overlap integral is non-zero for g-g / u-u, but zero for g-u / u-g.

==== Reference ====
Clayden (MO diagram)
DIELS-ALDER REACTIONS, Mircea D. Gherghiu

== '''A Comparison of Endo- and Exo- Products''' ==
=== The Reaction of Cyclohexadiene and 1,3-Dioxole by PM6 ===
==== Method ====

Both reactants were optimized, and subsequently placed in the endo TS conformation with the 4 C atoms involved in the reaction centre being frozen from eachother at a distance of 2.2 Å. An optimization to a minimum was carried out, followed by an optimization to a TS (Berny). An IRC was done on this TS structure, which ran in both directions, at N=20. The geometry obtained at the start of the reaction profile from the IRC was optimized to a minimum and no imaginary frequencies confirmed this to be the product.

The same procedure was carried out for the exo-conformer.

==== B3LYP frequency pictures for exo and endo ====

A B3LYP/6-31G(d) calculation was run on both TS geometries and the presence of 1 imaginary frequency in both TS structures confirmed them to be the TS. These frequencies were 520.86 and 528.8icm-1 for the endo and exo TS's respectively.

{| class="wikitable" border="1"
|+ B3LYP Vibrations and TS
! Endo !! Exo
|-
| [[File:Endo B3LYP TS.jpg|275px]] || [[File:Exo B3LYP TS.jpg|275px]]
|-
| [[File:Endo B3LYP Vib.jpg|275px]] || [[File:Exo B3LYP Vib.jpg|275px]]
|}

==== The releveant FMOs for Diels-Alder by symmetry ====

From the MO diagram for Diels-Alder, the same orbitals come into play for these reactions.

{| class="wikitable" border="1"
|+ endo-TS MO's
|-
| Bonding Orbitals || [[File:EndoTS MO 29.jpg|175px]] || [[File:EndoTS MO 30.jpg|175px]]
|-
| Antibonding Orbitals ||[[File:EndoTS MO 31.jpg|175px]] || [[File:EndoTS MO 32.jpg|175px]]
|}

{| class="wikitable" border="1"
|+ exo-TS MO's
|-
| Bonding Orbitals || [[File:Exo TS MO 29.jpg|175px]] || [[File:Exo TS MO 30.jpg|175px]]
|-
| Antibonding Orbitals || [[File:Exo TS MO 31.jpg|175px]] || [[File:Exo TS MO 32.jpg|175px]]
|}

{| class="wikitable" border="1"
|+ Endo vs Exo TS's
! !! Endo !! Exo
|-
| TS vibrations || [[File:Endo TS Vibrations.jpg|275px]] || [[File:Exo TS Vibrations.jpg|275px]]
|-
| TS Geometry || [[File:Endo TS Geometry.jpg|275px]] || [[File:Exo TS Geometry.jpg|275px]]
|-
|}

The presence of 1 imaginary negative frequency shows that these are the TS structures for the 2 reactions.

{| class="wikitable" border="1"
|+ Endo and Exo Product Formation from IRC
! !! Endo !! Exo
|-
| IRC || [[File:Endo product.gif|750px|]] || [[File:Exo product.gif|750px]]
|-
| Reaction coordinate || [[File:Endo Reaction Coordinate.jpg|750px]] || [[File:Exo Reaction Coordinate.jpg|750px]]
|}

=== Thermochemistry of Exo- vs Endo- ===

{| class="wikitable" border="1"
|+ Endo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.130081 || 20.64 || -
|-
| TS || 0.137942 || - || -
|-
| Product || 0.244570 || - || 300.59
|}

{| class="wikitable" border="1"
|+ Exo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.136771 || 5.60 || -
|-
| TS || 0.138905 || - || -
|-
| Product || 0.037977 || - || -259.38
|}

==== Secondary Orbital Interactions ====

[[File:Endo TS HOMO 2ndary orbital interaction.jpg|350px]]

[[File:Exo TS HOMO no 2ndary interaction.jpg|150px]]

Primary orbital interactions lead to sigma bond formation. The dienophile, in this case the 1,3 Dioxole, is pointing away from the diene which does not allow for any further orbital interactions; and so only has primary orbital interactions, and forms the exo-product.

In the endo conformation, the dienophile is positioned such that the lobes of the C-O and the back orbitals in the cyclohexadiene can form a favourable bonding interaction, which lowers the energy of the TS, and in turn, is the kinetic product. Such an interaction is a secondary orbital interaction. A point to note is that no such bonds are formed in this case.

== '''Diels Alder and Chelotropic Pathways''' ==
=== o-Xylylene and SO2 optimization to adducts of both reaction types ===
==== Method ====

==== Chelotropic ====

The chelotropic product was drawn and optimized to a minimum. The C-S bonds of this resulting geometry were broken and the coordinates were frozen at approximately 2.2 Å apart. This structure was then optimized to a minimum, and the subsequent geometry reoptimized to a TS (Berny). An IRC was run on this TS with N=200, forward only, to obtain a reaction path.

==== Diels Alder ====

{| class="wikitable" border="1"
|+ Diels-Alder & Chelotropic Reactions
! !! Endo !! Exo !! Chelotropic
|-
| TS || [[File:Endo Xyl TS.jpg|650px]] || [[File:Exo Xyl TS.jpg|650px]] || [[File:Chelotropic TS.jpg|650px]]
|-
| IRC || [[File:Endo Xyl IRC.gif]] || [[File:Exo Xyl IRC.gif]] || [[File:Chelotropic IRC.gif]]
|-
| Reaction Profile || [[File:Endo Xyl Reaction Profile.jpg|650px]] || [[File:Exo Xyl Reaction Coordinate.jpg|650px]] || [[File:Chelotropic Reaction Coordinate.jpg|650px]]
|}

=== Thermochemistry of o-Xylylene and SO2 ===

{| class="wikitable" border="1"
|+ Endo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.130081 || 20.64 || -
|-
| TS || 0.137942 || - || -
|-
| Product || 0.244570 || - || 300.59
|}

{| class="wikitable" border="1"
|+ Exo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.130081 || 20.64 || -
|-
| TS || 0.137942 || - || -
|-
| Product || 0.244570 || - || 300.59
|}

{| class="wikitable" border="1"
|+ Chelotropic
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.130081 || 20.64 || -
|-
| TS || 0.137942 || - || -
|-
| Product || 0.244570 || - || 300.59
|}

Rep:Mod:Mrh214

2016-12-02T00:54:12Z

Mrh214:

== '''Diels Alder Cycloaddition''' ==
=== Butadiene and Ethene optimization to Cyclohexene via PM6 ===
==== Method ====

1) Butadiene and ethene were optimized to a minimum seperately. Once optimized, they were placed in a similar geometry closely resembling that of the transition state (TS) required for the Diels Alder reaction; with the 4 carbon atoms in the reaction centre being frozen approximately 2.2 angstroms from eachother. This geometry was optimized to a minimum. The optimized geometry was then re-optimized to a TS (Berny), and this was confirmed by the presence of 1 negative frequency in the vibrations. An IRC was run on this TS in both directions with N=100. This geometry was manually displaced and optimized further to a minimum and product confirmation was given by all positive frequencies.

==== Butadiene ====
[[File:Butadiene.jpg|300px]]

==== Ethene ====
[[File:Ethene.jpg|300px]]

The C=C bonds in butadiene are 1.33531 Å; the C-C is 1.46835 Å. The C=C in ethene is 1.32731 Å.

==== TS ====
[[File:TS.jpg|300px]]

[[File:TS vibration 1.gif]]

This is the imaginary vibration at -949.3 icm-1, which corresponds to the TS.

[[File:TS vibration 2.gif]]

And this shows the first positive vibration at 144.91 icm-1. The motions are synchronous, therefore implying that the bond formations are also, synchronous.

In the TS the 2 C=C bonds of butadiene are now 1.37978 and 1.37974 Å. The previous C-C in butadiene is now 1.41114 Å; this has compressed as in the products, it will become a double bond. Similarly, the C=C bonds are now elongated slightly, due to becoming single bonds in the product.

The C=C in ethene for the TS has elongated to 1.38173, as this will be a single bond in the product.

The C atoms involved in the reaction centre for the Diels-Alder mechanism, from butadiene to the ethene carbons are at length 2.11423 and 2.11494 Å.

{| class="wikitable" border="1"
|+ Frontier Orbitals of Reactants
! FMO !! Butadiene !! Ethene
|-
| HOMO || [[File:HOMO Butadiene.jpg|300px]] || [[File:HOMO ethene.jpg|175px]]
|-
| LUMO || [[File:LUMO butadiene.jpg|175px]] || [[File:LUMO ethene.jpg|175px]]
|-
|}

(FMO = Frontier Molecular Orbitals)

{| class="wikitable" border="1"
|+ TS MO's
|-
| [[File:TS MO 16.jpg|175px]] || [[File:TS MO 17.jpg|175px]]
|-
| [[File:TS MO 18.jpg|175px]] || [[File:TS MO 19.jpg|175px]]
|}

==== Cyclohexene ====
[[File:Cyclohexene.jpg|300px]]

==== Bond Distance Variation Over Course of Reaction ====

{| class="wikitable" border="1"
|+ Bond lengths in reactants
! !! Bond lengths Å !!
|-
! Bond Type !! Butadiene !! Ethene
|-
| C-C || 1.46835 || -
|-
| C=C || 1.33531 || 1.32731
|}

{| class="wikitable" border="1"
|+ Bond lengths in TS
! !! Bond lengths Å !!
|-
! Bond Type !! Butadiene fragment !! Ethene fragment
|-
| C-C || 1.41114 || -
|-
| C=C || 1.37978 / 1.37974 || 1.38173
|}

{| class="wikitable" border="1"
|+ 2 C-C lengths in reaction centre
! Reaction centre !! Carbon atom distances Å
|-
| C-C || 2.11423 / 2.11494
|}

{| class="wikitable" border="1"
|+ Bond lengths in Cyclohexene product
! !! Cyclohexene
|-
! Bond type !! Bond lengths Å
|-
| C-C || 1.50085 / 1.50087
|-
| C-C || 1.53714 / 1.53704
|-
| C-C (opposite C=C) || 1.53453
|-
| C=C || 1.33698
|}

In the final product, the C=C is 1.33698 Å, the neighboring C-C on either side to the double bond are 1.50085 and 1.50087 Å. The adjacent C-C to these bonds are 1.53714 and 1.53704 Å. And the C-C directly opposite the C=C is 1.53453 Å.

Typical C-C sp3 length is 1.54 Å and the corresponding sp2 length is 1.34 Å. (ADD REFERENCE)!!! '''ADD VDW RADIII'''

The C-C bonds formed in TS have lengths less than the combined Van der Waals radius of 2 C atoms, which implies a bonding interaction is occuring.

==== The Diels-Alder MO Diagram ====
[[File:DA MO.jpg|400px]]

The MO diagram shows that the HOMO for the diene is closer in energy to the LUMO of the dienophile, hence will allow more efficient/constructive overlap (and lower energy antibonding MO) than the opposite case; which would be the LUMO of the diene with the HOMO of the dienophile.

==== The Symmetry Conditions ====
Let g = gerade (symmetric) and u = ungerade (antisymmetric).

Orbitals of the same symmetry may combine, ie. g-g, u-u. However, orbitals of mis-matched symmetry may not, ie. g-u / u-g.

The orbital overlap integral is non-zero for g-g / u-u, but zero for g-u / u-g.

==== Reference ====
Clayden (MO diagram)
DIELS-ALDER REACTIONS, Mircea D. Gherghiu

== '''A Comparison of Endo- and Exo- Products''' ==
=== The Reaction of Cyclohexadiene and 1,3-Dioxole by PM6 ===
==== Method ====

Both reactants were optimized, and subsequently placed in the endo TS conformation with the 4 C atoms involved in the reaction centre being frozen from eachother at a distance of 2.2 Å. An optimization to a minimum was carried out, followed by an optimization to a TS (Berny). An IRC was done on this TS structure, which ran in both directions, at N=20. The geometry obtained at the start of the reaction profile from the IRC was optimized to a minimum and no imaginary frequencies confirmed this to be the product.

The same procedure was carried out for the exo-conformer.

==== B3LYP frequency pictures for exo and endo ====

A B3LYP/6-31G(d) calculation was run on both TS geometries and the presence of 1 imaginary frequency in both TS structures confirmed them to be the TS. These frequencies were 520.86 and 528.8icm-1 for the endo and exo TS's respectively.

{| class="wikitable" border="1"
|+ B3LYP Vibrations and TS
! Endo !! Exo
|-
| [[File:Endo B3LYP TS.jpg|275px]] || [[File:Exo B3LYP TS.jpg|275px]]
|-
| [[File:Endo B3LYP Vib.jpg|275px]] || [[File:Exo B3LYP Vib.jpg|275px]]
|}

==== The releveant FMOs for Diels-Alder by symmetry ====

From the MO diagram for Diels-Alder, the same orbitals come into play for these reactions.

{| class="wikitable" border="1"
|+ endo-TS MO's
|-
| Bonding Orbitals || [[File:EndoTS MO 29.jpg|175px]] || [[File:EndoTS MO 30.jpg|175px]]
|-
| Antibonding Orbitals ||[[File:EndoTS MO 31.jpg|175px]] || [[File:EndoTS MO 32.jpg|175px]]
|}

{| class="wikitable" border="1"
|+ exo-TS MO's
|-
| Bonding Orbitals || [[File:Exo TS MO 29.jpg|175px]] || [[File:Exo TS MO 30.jpg|175px]]
|-
| Antibonding Orbitals || [[File:Exo TS MO 31.jpg|175px]] || [[File:Exo TS MO 32.jpg|175px]]
|}

{| class="wikitable" border="1"
|+ Endo vs Exo TS's
! !! Endo !! Exo
|-
| TS vibrations || [[File:Endo TS Vibrations.jpg|275px]] || [[File:Exo TS Vibrations.jpg|275px]]
|-
| TS Geometry || [[File:Endo TS Geometry.jpg|275px]] || [[File:Exo TS Geometry.jpg|275px]]
|-
|}

The presence of 1 imaginary negative frequency shows that these are the TS structures for the 2 reactions.

{| class="wikitable" border="1"
|+ Endo and Exo Product Formation from IRC
! !! Endo !! Exo
|-
| IRC || [[File:Endo product.gif|750px|]] || [[File:Exo product.gif|750px]]
|-
| Reaction coordinate || [[File:Endo Reaction Coordinate.jpg|750px]] || [[File:Exo Reaction Coordinate.jpg|750px]]
|}

=== Thermochemistry of Exo- vs Endo- ===

{| class="wikitable" border="1"
|+ Endo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.130081 || 20.64 || -
|-
| TS || 0.137942 || - || -
|-
| Product || 0.244570 || - || 300.59
|}

{| class="wikitable" border="1"
|+ Exo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.136771 || 5.60 || -
|-
| TS || 0.138905 || - || -
|-
| Product || 0.037977 || - || -259.38
|}

==== Secondary Orbital Interactions ====

[[File:Endo TS HOMO 2ndary orbital interaction.jpg|350px]]

[[File:Exo TS HOMO no 2ndary interaction.jpg|150px]]

The exo-product has

== '''Diels Alder and Chelotropic Pathways''' ==
=== o-Xylylene and SO2 optimization to adducts of both reaction types ===
==== Method ====

==== Chelotropic ====

The chelotropic product was drawn and optimized to a minimum. The C-S bonds of this resulting geometry were broken and the coordinates were frozen at approximately 2.2 Å apart. This structure was then optimized to a minimum, and the subsequent geometry reoptimized to a TS (Berny). An IRC was run on this TS with N=200, forward only, to obtain a reaction path.

==== Diels Alder ====

{| class="wikitable" border="1"
|+ Diels-Alder & Chelotropic Reactions
! !! Endo !! Exo !! Chelotropic
|-
| TS || [[File:Endo Xyl TS.jpg|650px]] || [[File:Exo Xyl TS.jpg|650px]] || [[File:Chelotropic TS.jpg|650px]]
|-
| IRC || [[File:Endo Xyl IRC.gif]] || [[File:Exo Xyl IRC.gif]] || [[File:Chelotropic IRC.gif]]
|-
| Reaction Profile || [[File:Endo Xyl Reaction Profile.jpg|650px]] || [[File:Exo Xyl Reaction Coordinate.jpg|650px]] || [[File:Chelotropic Reaction Coordinate.jpg|650px]]
|}

=== Thermochemistry of o-Xylylene and SO2 ===

{| class="wikitable" border="1"
|+ Endo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.130081 || 20.64 || -
|-
| TS || 0.137942 || - || -
|-
| Product || 0.244570 || - || 300.59
|}

{| class="wikitable" border="1"
|+ Exo
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.130081 || 20.64 || -
|-
| TS || 0.137942 || - || -
|-
| Product || 0.244570 || - || 300.59
|}

{| class="wikitable" border="1"
|+ Chelotropic
! Optimizations !! Hartrees !! EA (kJmol-1) !! ∆Greaction (kJmol-1)
|-
| Reactants || 0.130081 || 20.64 || -
|-
| TS || 0.137942 || - || -
|-
| Product || 0.244570 || - || 300.59
|}

Rep:Mod:Mrh214

2016-12-02T00:44:27Z

Mrh214:

Rep:Mod:Mrh214

2016-12-02T00:21:55Z

Mrh214:

Rep:Mod:Mrh214

2016-12-01T22:44:35Z

Mrh214:

File:Exo TS HOMO no 2ndary interaction.jpg

2016-12-01T22:38:37Z

Mrh214:

File:Endo TS HOMO 2ndary orbital interaction.jpg

2016-12-01T22:34:54Z

Mrh214:

File:Exo TS MO 32.jpg

2016-12-01T22:30:34Z

Mrh214:

File:Exo TS MO 31.jpg

2016-12-01T22:30:18Z

Mrh214:

File:Exo TS MO 30.jpg

2016-12-01T22:30:06Z

Mrh214:

File:Exo TS MO 29.jpg

2016-12-01T22:28:43Z

Mrh214:

Rep:Mod:Mrh214

2016-12-01T22:22:19Z

Mrh214:

File:TS vibration 2.gif

2016-12-01T22:20:51Z

Mrh214:

Rep:Mod:Mrh214

2016-12-01T21:43:32Z

Mrh214:

Rep:Mod:Mrh214

2016-12-01T21:39:53Z

Mrh214:

File:Endo Xyl Reaction Profile.jpg

2016-12-01T21:38:47Z

Mrh214:

File:Endo Xyl IRC.gif

2016-12-01T21:38:07Z

Mrh214:

File:Endo Xyl TS.jpg

2016-12-01T21:37:56Z

Mrh214:

Rep:Mod:Mrh214

2016-12-01T21:37:37Z

Mrh214:

File:Exo Xyl Reaction Coordinate.jpg

2016-12-01T21:36:33Z

Mrh214:

File:Exo Xyl IRC.gif

2016-12-01T21:36:05Z

Mrh214:

File:Exo Xyl TS.jpg

2016-12-01T21:35:22Z

Mrh214:

File:Chelotropic Reaction Coordinate.jpg

2016-12-01T21:33:48Z

Mrh214:

File:Chelotropic IRC.gif

2016-12-01T21:32:50Z

Mrh214:

File:Chelotropic TS.jpg

2016-12-01T21:31:46Z

Mrh214:

Rep:Mod:Mrh214

2016-12-01T21:00:31Z

Mrh214:

File:Exo B3LYP Vib.jpg

2016-12-01T20:59:53Z

Mrh214:

File:Exo B3LYP TS.jpg

2016-12-01T20:57:55Z

Mrh214: Mrh214 uploaded a new version of File:Exo B3LYP TS.jpg

File:Exo B3LYP TS.jpg

2016-12-01T20:56:28Z

Mrh214:

File:Endo B3LYP Vib.jpg

2016-12-01T20:56:05Z

Mrh214:

File:Endo B3LYP TS.jpg

2016-12-01T20:55:19Z

Mrh214:

Rep:Mod:Mrh214

2016-12-01T20:41:48Z

Mrh214:

File:Endo Reaction Coordinate.jpg

2016-12-01T20:29:03Z

Mrh214:

File:Exo Reaction Coordinate.jpg

2016-12-01T20:28:39Z

Mrh214:

File:Exo product.gif

2016-12-01T20:24:31Z

Mrh214:

File:Endo product.gif

2016-12-01T20:22:22Z

Mrh214: