pm6 opt of ethene

File:BUTADIENE OPT.LOG

2016-12-15T20:51:37Z

Mde14: Mde14 uploaded a new version of File:BUTADIENE OPT.LOG

File:Exercise 3 scheme actual.png

2016-12-15T20:21:55Z

Mde14: ex 3 scheme real - mde14

ex 3 scheme real - mde14

File:Exercise 3 scheme.png

2016-12-15T20:19:48Z

Mde14: ex 3 scheme

ex 3 scheme

File:Xylyl altern rxn.png

2016-12-15T20:05:31Z

Mde14: alternate rxn for xylylene - mde14

alternate rxn for xylylene - mde14

File:Reactiontwo.png

2016-12-15T19:49:52Z

Mde14: endo exo rxm scheme - mde14

endo exo rxm scheme - mde14

File:Reaction - eth but - hex.png

2016-12-15T19:37:34Z

Mde14: rxn scheme 1 - mde14

rxn scheme 1 - mde14

File:Comparitive graph pes.png

2016-12-15T19:28:10Z

Mde14: comparing endo exo chele irc- mde14

comparing endo exo chele irc- mde14

Rep:Mde14tscomp

2016-12-15T18:13:11Z

Mde14:

== Year Three computational lab - Transition Structures ==

Michael Edwards - 00940539

== Introduction ==

Computational methods can be used to measure potential energy surfaces, which are defined as mathematical functions that calculate the energy of molecules as functions of their geometries and degrees of freedom of movement. Through surface calculations it is possible to find energy minima and maxima, which can correspond to the optimised product of a reaction, the optimised geometry of a molecule, or a transition state within a reaction. Energy minima can be determined by a stationary point, which has zero gradient and a positive second derivative of the function, which is a minimum point in standard calculus. Transition states are stationary points with a zero gradient and a negative secondary derivative of the function used, which is a maximum point in calculus. Computations at these transition state structures are shown to yield negative, or imaginary vibrations in a frequency calculation that correspond to the reaction path between the reacting atoms or functional groups. This can be observed by visualising and animating the negative vibration.

The Gaussian computer program can be used to calculate potential energy surfaces to varying degrees of precision dependent on the methods used. In this experiment, a mixture of the semi-empirical PM6 method and the Density Functional Theory B3LYP/6-31GD method were employed to carry out calculations along potential energy surfaces for a number of cycloaddition reactions and alternative proposed reactions. The cycloaddition under investigation are between ethene and butadiene, cyclohexadiene and 1,3-dioxole, and xylylene and sulfur dioxide.

== Exercise One - Cycloaddition of Ethene and Butadiene ==

=== Method ===

The semi-empirical PM6 method was used to optimise the reactant molecules. A 'guess' transition state was employed, with the reacting atomic termini for the reactants frozen for an initial energy optimisation then unfrozen to determine the transition state. An Intrinsic Reaction Co-ordinate calculation was carried out in both forward and reverse directions to illustrate the full reaction.

=== Molecular orbitals of the reactants and the transition state ===

For a standard Diels-Alder reaction, the following molecular orbital diagram illustrates the reacting orbitals in the cycloaddition transition state. The HOMO and LUMO+1 of butadiene, as well as the LUMO of ethene, are antisymmetric, and the HOMO-1 and LUMO of butadiene and the HOMO of ethene are symmetric.

[[File:Butadiene Ethene Cycloaddition123.png|thumb|The MO diagram for the reacting orbitals in the cycloaddition between butadiene and ethene <ref name="MOdiagram" />]]

MOs have been visualised in GaussView for the orbitals under consideration in this MO diagram. The HOMO and LUMO for the reactant molecules, and the four molecular orbitals these produce in the transition state, can be seen here.

{| class="wikitable" border="1"
|+ Molecular Orbitals for the Reactants - the symmetry of these orbitals means the view here is sufficient.
! Butadiene HOMO !! Butadiene LUMO !! Ethene HOMO !! Ethene LUMO
|-
| [[File:Mde14 Buta homo.png|centre|200px]]|| [[File:Mde14 buta lumo.png|centre|200px]]|| [[File:Mde14 ethene homo.png|centre|200px]]|| [[File:Mde14 ethene lumo.png|centre|200px]]
|-
| This orbital is antisymmetric with respect to rotation, or ungerade|| This orbital is symmetric with respect to rotation, or gerade || This orbital is symmetric with respect to rotation, or gerade || This orbital is antisymmetric with respect to rotation, or ungerade
|}

{| class="wikitable" border="1"
|+ Molecular Orbitals for the Transition State
! TS HOMO - 1!! TS HOMO !! TS LUMO !! TS LUMO + 1
|-
| [[File:Mde14TS HOMO-1 - buta homo + ethene lumo.jpg|centre|200px]]|| [[File:Mde14TS HOMO - buta lumo + ethene homo.jpg|centre|200px]]|| [[File:Mde14TS LUMO - buta lumo + ethene homo.jpg|centre|200px]]|| [[File:Mde14TS LUMO+1 - buta homo + ethene lumo.jpg|centre|200px]]
|-
| This bonding MO is the result of interaction between the HOMO of the butadiene and the LUMO of the ethene.|| This bonding MO is the result of interaction between the LUMO of the butadiene and the HOMO of the ethene.|| This antibonding MO is the result of interaction between the LUMO of the butadiene and the HOMO of the ethene, but is seen to have some secondary orbital interactions between the pi systems being formed and destroyed that infer some bonding character within this MO.|| This antibonding MO is the result of interaction between the HOMO of the butadiene and the LUMO of the ethene.
|}

It can be clearly seen that the orbitals predicted to react by symmetry are the ones that react, namely, the HOMO of ethene and the LUMO of butadiene, and the LUMO of ethene and the HOMO of butadiene. It is therefore possible to conclude that the reaction is ‘allowed’ when the symmetry of the reacting orbitals is the same, as per standard molecular orbital theory, and ‘forbidden’ when the orbitals that need to react do not share the same symmetry label (in this case, symmetric or antisymmetric).

Given that an interaction between orbitals is seen to occur when the symmetry labels are the same, it can be stated that the orbital overlap integral is non-zero for symmetric-symmetric and asymmetric-asymmetric interactions, and zero for symmetric-asymmetric interactions.

=== Change in Carbon Bond Lengths within the Reactants and Transition State to form the Product ===

Carbon bond lengths were investigated for the PM6-optimised reactants (namely, ethene and butadiene), the transition state of the Diels-Alder reaction between the two (as determined by PM6 calculation on Gaussian), and the PM6-optimised product, cyclohexene. The changes in bond lengths can be observed in the graph figure. Bond lengths are clearly shown to change throughout the reaction as the cycloaddition reaction between ethene and butadiene occurs. The single bond in the butadiene fragment is seen to shorten as it gains more sp2 character and becomes a double bond, and the opposite is observed with the double bonds. In the ethene fragment, the bond is seen to lengthen as the bond gains more sp3 character and becomes a single bond. The internuclear distance between the fragments is observed to change significantly from the transition state at 2.115 Å, to the product at 1.54 Å.

[[File:Mde14Graph of changing c-c.png|800px|centre|]]

{| class="wikitable" border="1"
|+ Bond lengths (Å , 10-10 m)
! C-C bond!! Reactants (frozen termini)!! Transition State !! Product
|-
| C-C in ethene molecule|| 1.327 || 1.382 || 1.541
|-
| C-C between ethene and butadiene (form during reaction)|| 2.200 || 2.115 || 1.54
|-
| C-C in butadiene double bonds|| 1.335 || 1.378 || 1.500
|-
| C-C in butadiene single bond|| 1.458 || 1.411 || 1.338
|}

When considering typical single and double C-C bonds, which are 1.54 Å and 1.34 Å respectively <ref name="bondlengths" />, it is clear that the transition state has bonds that exhibit a blend of single and double bond characters, due to their intermediate lengths between the two lengths typically observed. The Van der Waals radius of C is 1.70 Å <ref name="vdwcarbon" />, which is longer than the single and double bonds observed in the product (as expected with the overlap of VdW surfaces required for the formation of bonds) showing that the partially formed C-C bonds in the TS are in the early stage of formation. However, since the atoms are much closer than the sum of two Van der Waals radii of carbon (2.11 Å as opposed to the expected 3.4 Å), it is clear that the minimum point of the transition state is in a state of bond formation between the two reactants.

=== IRC and Transition State Vibrational Frequency ===

The formation of the two bonds is seen to be a concerted process from the IRC calculation of the reaction. It is observed from the vibration that corresponds to the reaction path in the transition state (the imaginary vibration at - 948 cm-1) that this process occurs such that the bonds are formed at the same time in a synchronous process. The lowest positive frequency in the product can be seen to support this judgment, since the frequency corresponds to a totally symmetric vibration of the formed bonds.

{| class="wikitable" border="1"
|+ Transition State vibration and IRC
! Imaginary (TS) Vibration!! IRC (forward from TS only)
|-
| [[File:Mde14Gaussian vibration for ts.gif|500px]] || [[File:Gaussian ethene irc.gif|500px]]
|-
| This vibration at -948 cm-1 corresponds to the reaction pathway from the transition state (click) || The IRC supports this (click).
|}

== Exercise Two - Cycloaddition of cyclohexadiene and 1,3-dioxole - Formation of Endo and Exo Products ==

=== Method ===

The semi-empirical PM6 method was used to optimise the reactant molecules, which were reoptimised using the B3LYP-631GD method. A 'guess' transition state was employed, with the reacting atomic termini for the reactants frozen for an initial energy optimisation then unfrozen to determine the transition state at first PM6 and then B3LYP-631GD level. Since two products were possible from the interaction between the orbitals in the cycloaddition, both were considered in this section.

=== Molecular Orbitals in the Transition States for the exo and endo products ===

Employing the MO diagram for the Diels-Alder cycloaddition of ethene and butadiene used in Exercise One, it is possible to infer the MOs for this interaction by symmetry, since the fragments in the interaction are similar to those used previously.

MOs for the Diels-Alder cycloaddition between 1,3-dioxole and cyclohexadiene have been visualised using GaussView. The symmetric nature of these orbitals means that the ‘side-on’ view of the orbitals as provided in the images is sufficient to observe the orbital interactions within the transition states.

{| class="wikitable" border="1"
|+ Molecular Orbitals for the Endo Transition State
! TS HOMO - 1!! TS HOMO !! TS LUMO !! TS LUMO + 1
|-
| [[File:TS HOMO - 1 - oxole lumo and cyclo homo.jpg|centre|200px]]|| [[File:TS HOMO - oxole homo and cyclo lumo.jpg|centre|200px]]|| [[File:TS LUMO - oxole homo and cyclo lumo.jpg|centre|200px]]|| [[File:TS LUMO + 2- oxole lumo and cyclo homo.jpg|centre|200px]]
|-
| This bonding MO is the result of interaction between the HOMO of the cyclohexadiene and the LUMO of the 1,3-dioxole.|| This bonding MO is the result of interaction between the LUMO of the cyclohexadiene and the HOMO of the 1,3-dioxole. There are clear secondary orbital effects arising from the electron density on the O atoms (red).|| This antibonding MO is the result of interaction between the LUMO of the cyclohexadiene and the HOMO of the 1,3-dioxole. Interactions between the forming and deforming π systems can be seen here as in the previous exercise.|| This antibonding MO is the result of interaction between the HOMO of the cyclohexadiene and the LUMO of the 1,3-dioxole.
|}

{| class="wikitable" border="1"
|+ Molecular Orbitals for the Exo Transition State
! TS HOMO - 1!! TS HOMO !! TS LUMO !! TS LUMO + 1
|-
| [[File:Mde14ENDO - TS HOMO-1 - oxole lumo and diene homo.jpg|centre|200px]]|| [[File:ENDO - TS HOMO - oxole homo and diene lumo.jpg|centre|200px]]|| [[File:ENDO - TS LUMO - oxole homo and diene lumo.jpg|centre|200px]]|| [[File:ENDO - TS LUMO+1 - oxole lumo and diene homo.jpg|centre|200px]]
|-
| This bonding MO is the result of interaction between the HOMO of the cyclohexadiene and the LUMO of the 1,3-dioxole.|| This bonding MO is the result of interaction between the LUMO of the cyclohexadiene and the HOMO of the 1,3-dioxole.|| This antibonding MO is the result of interaction between the LUMO of the cyclohexadiene and the HOMO of the 1,3-dioxole. Interactions between the forming and deforming π systems can be seen here as in the previous exercise.|| This antibonding MO is the result of interaction between the HOMO of the cyclohexadiene and the LUMO of the 1,3-dioxole.
|}

Diels-Alder reactions can be classified as either ‘normal’ or ‘inverse’ demand with regards to the electronic interaction occurring. Given the nature of the dienophile within this reaction, namely 1,3-dioxole, it can be inferred from theory that the electron-donating behaviour of the two oxygen atoms into the π system means that this is an inverse-demand Diels-Alder reaction <ref name="DAinv" />, which is confirmed by a quick analysis of the HOMO of both endo and exo transition states, which demonstrate the reaction of the dienophile HOMO with the diene LUMO to form the HOMO of the transition state.

=== Thermochemistry and Reaction Energies - Differences between the exo- and endo- products formed ===

Disclaimer - the data used here is likely subject to large errors due to calculation error.

The calculations for the transition states and products can ideally be used to determine the kinetically and thermodynamically favoured product of the reaction under investigation, by considering the reaction barrier energies and the energy minimum of the formed products from their respective transition states.

An Intrinsic Reaction Co-ordinate calculation was carried out for the formation of the exo and endo products to provide energy profiles for each reaction - these are contained below. The Gibbs free energies are considered in the log files for each of the calculations. The activation energy, reaction barrier, or EA, is taken to be the energy difference between the first IRC point on the left and the transition state IRC, and the change in energy of reaction, or ΔGr, is taken to be the energy difference between the first and last IRC points.

{| class="wikitable" border="1" centre
|+ Intrinsic Reaction Co-ordinate calculations demonstrating reaction energy profile
! Endo!! Exo
|-
| [[File:Graph of endo irc.png|300px]] || [[File:Graph of exo irc.png|300px]]
|-
| Reaction Barrier energy (EA) = 99.77 kJ mol-1 || Reaction Barrier energy (EA) = 110.27 kJ mol-1
|-
| Reaction change in energy (ΔGr) = -152.27 kJ mol-1 || Reaction change in energy (ΔGr) = -141.78 kJ mol-1
|}

The two calculations start at approximately the same energy, and a clear difference can be observed between the first IRC and the transition state IRC of the reactions - this is an energy difference of 10.5 kJ mol-1, arising due to circumstances to be covered later. When considering the overall change in energy, the observed energy difference is once again 10.5 kJ mol-1, and suggests that the endo product is the thermodynamically favoured product in this reaction, whereas the exo product is the kinetically favoured product. Repeats of this calculation yield the same result, but investigation of the wider literature suggests that typical Diels-Alder reactions yield the exo product as the thermodynamic product and the endo product as the kinetic product <ref name="messedup" />, which is against what is observed here and suggests some part of the calculation have not worked correctly. However, since these reactions go to the expected products, in particular through a minimum that can be easily identified to be a suitable transition state, at least some part of the calculations must have been correct.

=== Secondary Orbital Effects and Sterics - differences in exo and endo products ===

Secondary orbital interactions can be observed between the O atoms in the 1,3-dioxole and the π system of the diene in the endo product that reduce the energy of the transition state, making it the more favourable reaction pathway with a lower reaction barrier energy. Comparatively, no such secondary orbital interaction exists in the exo transition state structure, which results, as seen above, in a clear energy difference between the endo and exo transition state. These orbitals can be seen in the table in the MO sub-section of this exercise.

== Exercise Three - Xylylene and SO2 - Diels-Alder vs Cheletropic ==

=== Method ===

The semi-empirical PM6 method was used to optimise the product molecule, after which the symmetry of the lowest vibrational frequency was broken and the structure reoptimised. Bonds between the xylylene and SO2 fragments were broken and the transition state was determined using a PM6 calculation. An IRC for each of the endo, exo and cheletropic reaction.

===IRC and Energy Profiles for the Diels-Alder reactions (endo and exo) and cheletropic reaction between xylylene and SO2 ===

Values for activation and reaction energies were determined from these graphs in the same way as in Exercise 2.

{| class="wikitable" border="1" centre
|+ Intrinsic Reaction Co-ordinate calculations demonstrating reaction energy profile of the reactions - click to activate
! Endo!! Exo (reversed) !! Cheletropic
|-
| [[File:Irc endo gif.gif|400px]] || [[File:Irc exo gif.gif|400px]] || [[File:Irc chele gif.gif|400px]]
|-
| [[File:Endo irc graph.png|400px]] || [[File:Exo irc graph.png|400px]] || [[File:Chele irc graph.png|400px]]
|-
| Reaction Barrier energy (EA) = 19.89 kJ mol-1 || Reaction Barrier energy (EA) = 23.73 kJ mol-1 || Reaction Barrier energy (EA) = 45.22 kJ mol-1
|-
| Reaction change in energy (ΔGr) = -166.79 kJ mol-1 || Reaction change in energy (ΔGr) = -171.64 kJ mol-1 || Reaction change in energy (ΔGr) = -229.21 kJ mol-1
|}

To better illustrate this data, the figure below displays the collated graphs from above. It clearly shows the cheletropic transition state as being of the highest energy, but also with the lowest energy minimum, suggesting that it is a thermodynamically more favoured product than the Diels-Alder reactions, which in this case form the 'kinetic' products. Within the data for Diels-Alder reactions, it can be observed that the endo transition state is lower in energy, and its product is of higher energy, than the exo equivalent, meaning that the endo product is kinetically favoured and the exo product is thermodynamically favoured.

(ADD GRAPH HERE)

== References ==

<references>
<ref name="MOdiagram">Wikimedia Commons, https://commons.wikimedia.org/wiki/File:Butadiene_Ethene_Cycloaddition123.png, accessed 14/12/2016</ref>
<ref name="bondlengths"> Texas A&M University Chemistry Department, http://www.chem.tamu.edu/rgroup/connell/linkfiles/bonds.pdf, accessed 14/12/2016 </ref>
<ref name="vdwcarbon"> PeriodicTable, http://periodictable.com/Properties/A/VanDerWaalsRadius.v.log.html, accessed 14/12/2016 </ref>
<ref name="DAinv"> Organic Chemistry Portal, http://www.organic-chemistry.org/namedreactions/diels-alder-reaction.shtm, accessed 14/12/2016 </ref>
<ref name="messedup"> University of Liverpool, http://www.chemtube3d.com/DAendo_vs_exo,cyclopentadiene_and_maleic_anhydride.html, accessed 15/12/2016 </ref>
</references>

Rep:Mde14tscomp

2016-12-15T18:12:38Z

Mde14:

== Year Three computational lab - Transition Structures ==

Michael Edwards - 00940539

== Introduction ==

Computational methods can be used to measure potential energy surfaces, which are defined as mathematical functions that calculate the energy of molecules as functions of their geometries and degrees of freedom of movement. Through surface calculations it is possible to find energy minima and maxima, which can correspond to the optimised product of a reaction, the optimised geometry of a molecule, or a transition state within a reaction. Energy minima can be determined by a stationary point, which has zero gradient and a positive second derivative of the function, which is a minimum point in standard calculus. Transition states are stationary points with a zero gradient and a negative secondary derivative of the function used, which is a maximum point in calculus. Computations at these transition state structures are shown to yield negative, or imaginary vibrations in a frequency calculation that correspond to the reaction path between the reacting atoms or functional groups. This can be observed by visualising and animating the negative vibration.

The Gaussian computer program can be used to calculate potential energy surfaces to varying degrees of precision dependent on the methods used. In this experiment, a mixture of the semi-empirical PM6 method and the Density Functional Theory B3LYP/6-31GD method were employed to carry out calculations along potential energy surfaces for a number of cycloaddition reactions and alternative proposed reactions. The cycloaddition under investigation are between ethene and butadiene, cyclohexadiene and 1,3-dioxole, and xylylene and sulfur dioxide.

== Exercise One - Cycloaddition of Ethene and Butadiene ==

=== Method ===

The semi-empirical PM6 method was used to optimise the reactant molecules. A 'guess' transition state was employed, with the reacting atomic termini for the reactants frozen for an initial energy optimisation then unfrozen to determine the transition state. An Intrinsic Reaction Co-ordinate calculation was carried out in both forward and reverse directions to illustrate the full reaction.

=== Molecular orbitals of the reactants and the transition state ===

For a standard Diels-Alder reaction, the following molecular orbital diagram illustrates the reacting orbitals in the cycloaddition transition state. The HOMO and LUMO+1 of butadiene, as well as the LUMO of ethene, are antisymmetric, and the HOMO-1 and LUMO of butadiene and the HOMO of ethene are symmetric.

[[File:Butadiene Ethene Cycloaddition123.png|thumb|The MO diagram for the reacting orbitals in the cycloaddition between butadiene and ethene <ref name="MOdiagram" />]]

MOs have been visualised in GaussView for the orbitals under consideration in this MO diagram. The HOMO and LUMO for the reactant molecules, and the four molecular orbitals these produce in the transition state, can be seen here.

{| class="wikitable" border="1"
|+ Molecular Orbitals for the Reactants - the symmetry of these orbitals means the view here is sufficient.
! Butadiene HOMO !! Butadiene LUMO !! Ethene HOMO !! Ethene LUMO
|-
| [[File:Mde14 Buta homo.png|centre|200px]]|| [[File:Mde14 buta lumo.png|centre|200px]]|| [[File:Mde14 ethene homo.png|centre|200px]]|| [[File:Mde14 ethene lumo.png|centre|200px]]
|-
| This orbital is antisymmetric with respect to rotation, or ungerade|| This orbital is symmetric with respect to rotation, or gerade || This orbital is symmetric with respect to rotation, or gerade || This orbital is antisymmetric with respect to rotation, or ungerade
|}

{| class="wikitable" border="1"
|+ Molecular Orbitals for the Transition State
! TS HOMO - 1!! TS HOMO !! TS LUMO !! TS LUMO + 1
|-
| [[File:Mde14TS HOMO-1 - buta homo + ethene lumo.jpg|centre|200px]]|| [[File:Mde14TS HOMO - buta lumo + ethene homo.jpg|centre|200px]]|| [[File:Mde14TS LUMO - buta lumo + ethene homo.jpg|centre|200px]]|| [[File:Mde14TS LUMO+1 - buta homo + ethene lumo.jpg|centre|200px]]
|-
| This bonding MO is the result of interaction between the HOMO of the butadiene and the LUMO of the ethene.|| This bonding MO is the result of interaction between the LUMO of the butadiene and the HOMO of the ethene.|| This antibonding MO is the result of interaction between the LUMO of the butadiene and the HOMO of the ethene, but is seen to have some secondary orbital interactions between the pi systems being formed and destroyed that infer some bonding character within this MO.|| This antibonding MO is the result of interaction between the HOMO of the butadiene and the LUMO of the ethene.
|}

It can be clearly seen that the orbitals predicted to react by symmetry are the ones that react, namely, the HOMO of ethene and the LUMO of butadiene, and the LUMO of ethene and the HOMO of butadiene. It is therefore possible to conclude that the reaction is ‘allowed’ when the symmetry of the reacting orbitals is the same, as per standard molecular orbital theory, and ‘forbidden’ when the orbitals that need to react do not share the same symmetry label (in this case, symmetric or antisymmetric).

Given that an interaction between orbitals is seen to occur when the symmetry labels are the same, it can be stated that the orbital overlap integral is non-zero for symmetric-symmetric and asymmetric-asymmetric interactions, and zero for symmetric-asymmetric interactions.

=== Change in Carbon Bond Lengths within the Reactants and Transition State to form the Product ===

Carbon bond lengths were investigated for the PM6-optimised reactants (namely, ethene and butadiene), the transition state of the Diels-Alder reaction between the two (as determined by PM6 calculation on Gaussian), and the PM6-optimised product, cyclohexene. The changes in bond lengths can be observed in the graph figure. Bond lengths are clearly shown to change throughout the reaction as the cycloaddition reaction between ethene and butadiene occurs. The single bond in the butadiene fragment is seen to shorten as it gains more sp2 character and becomes a double bond, and the opposite is observed with the double bonds. In the ethene fragment, the bond is seen to lengthen as the bond gains more sp3 character and becomes a single bond. The internuclear distance between the fragments is observed to change significantly from the transition state at 2.115 Å, to the product at 1.54 Å.

[[File:Mde14Graph of changing c-c.png|800px|centre|]]

{| class="wikitable" border="1"
|+ Bond lengths (Å , 10-10 m)
! C-C bond!! Reactants (frozen termini)!! Transition State !! Product
|-
| C-C in ethene molecule|| 1.327 || 1.382 || 1.541
|-
| C-C between ethene and butadiene (form during reaction)|| 2.200 || 2.115 || 1.54
|-
| C-C in butadiene double bonds|| 1.335 || 1.378 || 1.500
|-
| C-C in butadiene single bond|| 1.458 || 1.411 || 1.338
|}

When considering typical single and double C-C bonds, which are 1.54 Å and 1.34 Å respectively <ref name="bondlengths" />, it is clear that the transition state has bonds that exhibit a blend of single and double bond characters, due to their intermediate lengths between the two lengths typically observed. The Van der Waals radius of C is 1.70 Å <ref name="vdwcarbon" />, which is longer than the single and double bonds observed in the product (as expected with the overlap of VdW surfaces required for the formation of bonds) showing that the partially formed C-C bonds in the TS are in the early stage of formation. However, since the atoms are much closer than the sum of two Van der Waals radii of carbon (2.11 Å as opposed to the expected 3.4 Å), it is clear that the minimum point of the transition state is in a state of bond formation between the two reactants.

=== IRC and Transition State Vibrational Frequency ===

The formation of the two bonds is seen to be a concerted process from the IRC calculation of the reaction. It is observed from the vibration that corresponds to the reaction path in the transition state (the imaginary vibration at - 948 cm-1) that this process occurs such that the bonds are formed at the same time in a synchronous process. The lowest positive frequency in the product can be seen to support this judgment, since the frequency corresponds to a totally symmetric vibration of the formed bonds.

{| class="wikitable" border="1"
|+ Transition State vibration and IRC
! Imaginary (TS) Vibration!! IRC (forward from TS only)
|-
| [[File:Mde14Gaussian vibration for ts.gif|500px]] || [[File:Gaussian ethene irc.gif|500px]]
|-
| This vibration at -948 cm-1 corresponds to the reaction pathway from the transition state (click) || The IRC supports this (click).
|}

== Exercise Two - Cycloaddition of cyclohexadiene and 1,3-dioxole - Formation of Endo and Exo Products ==

=== Method ===

The semi-empirical PM6 method was used to optimise the reactant molecules, which were reoptimised using the B3LYP-631GD method. A 'guess' transition state was employed, with the reacting atomic termini for the reactants frozen for an initial energy optimisation then unfrozen to determine the transition state at first PM6 and then B3LYP-631GD level. Since two products were possible from the interaction between the orbitals in the cycloaddition, both were considered in this section.

=== Molecular Orbitals in the Transition States for the exo and endo products ===

Employing the MO diagram for the Diels-Alder cycloaddition of ethene and butadiene used in Exercise One, it is possible to infer the MOs for this interaction by symmetry, since the fragments in the interaction are similar to those used previously.

MOs for the Diels-Alder cycloaddition between 1,3-dioxole and cyclohexadiene have been visualised using GaussView. The symmetric nature of these orbitals means that the ‘side-on’ view of the orbitals as provided in the images is sufficient to observe the orbital interactions within the transition states.

{| class="wikitable" border="1"
|+ Molecular Orbitals for the Endo Transition State
! TS HOMO - 1!! TS HOMO !! TS LUMO !! TS LUMO + 1
|-
| [[File:TS HOMO - 1 - oxole lumo and cyclo homo.jpg|centre|200px]]|| [[File:TS HOMO - oxole homo and cyclo lumo.jpg|centre|200px]]|| [[File:TS LUMO - oxole homo and cyclo lumo.jpg|centre|200px]]|| [[File:TS LUMO + 2- oxole lumo and cyclo homo.jpg|centre|200px]]
|-
| This bonding MO is the result of interaction between the HOMO of the cyclohexadiene and the LUMO of the 1,3-dioxole.|| This bonding MO is the result of interaction between the LUMO of the cyclohexadiene and the HOMO of the 1,3-dioxole. There are clear secondary orbital effects arising from the electron density on the O atoms (red).|| This antibonding MO is the result of interaction between the LUMO of the cyclohexadiene and the HOMO of the 1,3-dioxole. Interactions between the forming and deforming π systems can be seen here as in the previous exercise.|| This antibonding MO is the result of interaction between the HOMO of the cyclohexadiene and the LUMO of the 1,3-dioxole.
|}

{| class="wikitable" border="1"
|+ Molecular Orbitals for the Exo Transition State
! TS HOMO - 1!! TS HOMO !! TS LUMO !! TS LUMO + 1
|-
| [[File:Mde14ENDO - TS HOMO-1 - oxole lumo and diene homo.jpg|centre|200px]]|| [[File:ENDO - TS HOMO - oxole homo and diene lumo.jpg|centre|200px]]|| [[File:ENDO - TS LUMO - oxole homo and diene lumo.jpg|centre|200px]]|| [[File:ENDO - TS LUMO+1 - oxole lumo and diene homo.jpg|centre|200px]]
|-
| This bonding MO is the result of interaction between the HOMO of the cyclohexadiene and the LUMO of the 1,3-dioxole.|| This bonding MO is the result of interaction between the LUMO of the cyclohexadiene and the HOMO of the 1,3-dioxole.|| This antibonding MO is the result of interaction between the LUMO of the cyclohexadiene and the HOMO of the 1,3-dioxole. Interactions between the forming and deforming π systems can be seen here as in the previous exercise.|| This antibonding MO is the result of interaction between the HOMO of the cyclohexadiene and the LUMO of the 1,3-dioxole.
|}

Diels-Alder reactions can be classified as either ‘normal’ or ‘inverse’ demand with regards to the electronic interaction occurring. Given the nature of the dienophile within this reaction, namely 1,3-dioxole, it can be inferred from theory that the electron-donating behaviour of the two oxygen atoms into the π system means that this is an inverse-demand Diels-Alder reaction <ref name="DAinv" />, which is confirmed by a quick analysis of the HOMO of both endo and exo transition states, which demonstrate the reaction of the dienophile HOMO with the diene LUMO to form the HOMO of the transition state.

=== Thermochemistry and Reaction Energies - Differences between the exo- and endo- products formed ===

Disclaimer - the data used here is likely subject to large errors due to calculation error.

The calculations for the transition states and products can ideally be used to determine the kinetically and thermodynamically favoured product of the reaction under investigation, by considering the reaction barrier energies and the energy minimum of the formed products from their respective transition states.

An Intrinsic Reaction Co-ordinate calculation was carried out for the formation of the exo and endo products to provide energy profiles for each reaction - these are contained below. The Gibbs free energies are considered in the log files for each of the calculations. The activation energy, reaction barrier, or EA, is taken to be the energy difference between the first IRC point on the left and the transition state IRC, and the change in energy of reaction, or ΔGr, is taken to be the energy difference between the first and last IRC points.

{| class="wikitable" border="1" centre
|+ Intrinsic Reaction Co-ordinate calculations demonstrating reaction energy profile
! Endo!! Exo
|-
| [[File:Graph of endo irc.png|300px]] || [[File:Graph of exo irc.png|300px]]
|-
| Reaction Barrier energy (EA) = 99.77 kJ mol-1 || Reaction Barrier energy (EA) = 110.27 kJ mol-1
|-
| Reaction change in energy (ΔGr) = -152.27 kJ mol-1 || Reaction change in energy (ΔGr) = -141.78 kJ mol-1
|}

The two calculations start at approximately the same energy, and a clear difference can be observed between the first IRC and the transition state IRC of the reactions - this is an energy difference of 10.5 kJ mol-1, arising due to circumstances to be covered later. When considering the overall change in energy, the observed energy difference is once again 10.5 kJ mol-1, and suggests that the endo product is the thermodynamically favoured product in this reaction, whereas the exo product is the kinetically favoured product. Repeats of this calculation yield the same result, but investigation of the wider literature suggests that typical Diels-Alder reactions yield the exo product as the thermodynamic product and the endo product as the kinetic product <ref name="messedup" />, which is against what is observed here and suggests some part of the calculation have not worked correctly. However, since these reactions go to the expected products, in particular through a minimum that can be easily identified to be a suitable transition state, at least some part of the calculations must have been correct.

=== Secondary Orbital Effects and Sterics - differences in exo and endo products ===

Secondary orbital interactions can be observed between the O atoms in the 1,3-dioxole and the π system of the diene in the endo product that reduce the energy of the transition state, making it the more favourable reaction pathway with a lower reaction barrier energy. Comparatively, no such secondary orbital interaction exists in the exo transition state structure, which results, as seen above, in a clear energy difference between the endo and exo transition state. These orbitals can be seen in the table in the MO sub-section of this exercise.

== Exercise Three - Xylylene and SO2 - Diels-Alder vs Cheletropic ==

=== Method ===

The semi-empirical PM6 method was used to optimise the product molecule, after which the symmetry of the lowest vibrational frequency was broken and the structure reoptimised. Bonds between the xylylene and SO2 fragments were broken and the transition state was determined using a PM6 calculation. An IRC for each of the endo, exo and cheletropic reaction.

===IRC and Energy Profiles for the Diels-Alder reactions (endo and exo) and cheletropic reaction between xylylene and SO2 ===

Values for activation and reaction energies were determined from these graphs in the same way as in Exercise 2.

{| class="wikitable" border="1" centre
|+ Intrinsic Reaction Co-ordinate calculations demonstrating reaction energy profile of the reactions - click to activate
! Endo!! Exo (reversed) !! Cheletropic
|-
| [[File:Irc endo gif.gif|400px]] || [[File:Irc exo gif.gif|400px]] || [[File:Irc chele gif.gif|400px]]
|-
| [[File:Endo irc graph.png|400px]] || [[File:Exo irc graph.png|400px]] || [[File:Chele irc graph.png|400px]]
|-
| Reaction Barrier energy (EA) = 19.89 kJ mol-1 || Reaction Barrier energy (EA) = 23.73 kJ mol-1 || Reaction Barrier energy (EA) = 45.22 kJ mol-1
|-
| Reaction change in energy (ΔGr) = -166.79 kJ mol-1 || Reaction change in energy (ΔGr) = -171.64 kJ mol-1 || Reaction change in energy (ΔGr) = -229.21 kJ mol-1
|}

To better illustrate this data, the figure below displays the collated graphs from above. It clearly shows the cheletropic transition state as being of the highest energy, but also with the lowest energy minimum, suggesting that it is a thermodynamically more favoured product than the Diels-Alder reactions, which in this case form the 'kinetic' products. Within the data for Diels-Alder reactions, it can be observed that the endo transition state is lower in energy, and its product is of higher energy, than the exo equivalent, meaning that the endo product is kinetically favoured and the exo product is thermodynamically favoured.

== References ==

<references>
<ref name="MOdiagram">Wikimedia Commons, https://commons.wikimedia.org/wiki/File:Butadiene_Ethene_Cycloaddition123.png, accessed 14/12/2016</ref>
<ref name="bondlengths"> Texas A&M University Chemistry Department, http://www.chem.tamu.edu/rgroup/connell/linkfiles/bonds.pdf, accessed 14/12/2016 </ref>
<ref name="vdwcarbon"> PeriodicTable, http://periodictable.com/Properties/A/VanDerWaalsRadius.v.log.html, accessed 14/12/2016 </ref>
<ref name="DAinv"> Organic Chemistry Portal, http://www.organic-chemistry.org/namedreactions/diels-alder-reaction.shtm, accessed 14/12/2016 </ref>
<ref name="messedup"> University of Liverpool, http://www.chemtube3d.com/DAendo_vs_exo,cyclopentadiene_and_maleic_anhydride.html, accessed 15/12/2016 </ref>
</references>

File:Chele irc graph.png

2016-12-15T17:53:40Z

Mde14: chele irc graph - mde14

chele irc graph - mde14

File:Exo irc graph.png

2016-12-15T17:41:34Z

Mde14: exo irc - mde14

exo irc - mde14

File:Endo irc graph.png

2016-12-15T17:39:19Z

Mde14: Mde14 uploaded a new version of File:Endo irc graph.png

Rep:Mde14tscomp

2016-12-15T17:26:56Z

Mde14:

== Year Three computational lab - Transition Structures ==

Michael Edwards - 00940539

== Introduction ==

Computational methods can be used to measure potential energy surfaces, which are defined as mathematical functions that calculate the energy of molecules as functions of their geometries and degrees of freedom of movement. Through surface calculations it is possible to find energy minima and maxima, which can correspond to the optimised product of a reaction, the optimised geometry of a molecule, or a transition state within a reaction. Energy minima can be determined by a stationary point, which has zero gradient and a positive second derivative of the function, which is a minimum point in standard calculus. Transition states are stationary points with a zero gradient and a negative secondary derivative of the function used, which is a maximum point in calculus. Computations at these transition state structures are shown to yield negative, or imaginary vibrations in a frequency calculation that correspond to the reaction path between the reacting atoms or functional groups. This can be observed by visualising and animating the negative vibration.

The Gaussian computer program can be used to calculate potential energy surfaces to varying degrees of precision dependent on the methods used. In this experiment, a mixture of the semi-empirical PM6 method and the Density Functional Theory B3LYP/6-31GD method were employed to carry out calculations along potential energy surfaces for a number of cycloaddition reactions and alternative proposed reactions. The cycloaddition under investigation are between ethene and butadiene, cyclohexadiene and 1,3-dioxole, and xylylene and sulfur dioxide.

== Exercise One - Cycloaddition of Ethene and Butadiene ==

=== Method ===

The semi-empirical PM6 method was used to optimise the reactant molecules. A 'guess' transition state was employed, with the reacting atomic termini for the reactants frozen for an initial energy optimisation then unfrozen to determine the transition state. An Intrinsic Reaction Co-ordinate calculation was carried out in both forward and reverse directions to illustrate the full reaction.

=== Molecular orbitals of the reactants and the transition state ===

For a standard Diels-Alder reaction, the following molecular orbital diagram illustrates the reacting orbitals in the cycloaddition transition state. The HOMO and LUMO+1 of butadiene, as well as the LUMO of ethene, are antisymmetric, and the HOMO-1 and LUMO of butadiene and the HOMO of ethene are symmetric.

[[File:Butadiene Ethene Cycloaddition123.png|thumb|The MO diagram for the reacting orbitals in the cycloaddition between butadiene and ethene <ref name="MOdiagram" />]]

MOs have been visualised in GaussView for the orbitals under consideration in this MO diagram. The HOMO and LUMO for the reactant molecules, and the four molecular orbitals these produce in the transition state, can be seen here.

{| class="wikitable" border="1"
|+ Molecular Orbitals for the Reactants - the symmetry of these orbitals means the view here is sufficient.
! Butadiene HOMO !! Butadiene LUMO !! Ethene HOMO !! Ethene LUMO
|-
| [[File:Mde14 Buta homo.png|centre|200px]]|| [[File:Mde14 buta lumo.png|centre|200px]]|| [[File:Mde14 ethene homo.png|centre|200px]]|| [[File:Mde14 ethene lumo.png|centre|200px]]
|-
| This orbital is antisymmetric with respect to rotation, or ungerade|| This orbital is symmetric with respect to rotation, or gerade || This orbital is symmetric with respect to rotation, or gerade || This orbital is antisymmetric with respect to rotation, or ungerade
|}

{| class="wikitable" border="1"
|+ Molecular Orbitals for the Transition State
! TS HOMO - 1!! TS HOMO !! TS LUMO !! TS LUMO + 1
|-
| [[File:Mde14TS HOMO-1 - buta homo + ethene lumo.jpg|centre|200px]]|| [[File:Mde14TS HOMO - buta lumo + ethene homo.jpg|centre|200px]]|| [[File:Mde14TS LUMO - buta lumo + ethene homo.jpg|centre|200px]]|| [[File:Mde14TS LUMO+1 - buta homo + ethene lumo.jpg|centre|200px]]
|-
| This bonding MO is the result of interaction between the HOMO of the butadiene and the LUMO of the ethene.|| This bonding MO is the result of interaction between the LUMO of the butadiene and the HOMO of the ethene.|| This antibonding MO is the result of interaction between the LUMO of the butadiene and the HOMO of the ethene, but is seen to have some secondary orbital interactions between the pi systems being formed and destroyed that infer some bonding character within this MO.|| This antibonding MO is the result of interaction between the HOMO of the butadiene and the LUMO of the ethene.
|}

It can be clearly seen that the orbitals predicted to react by symmetry are the ones that react, namely, the HOMO of ethene and the LUMO of butadiene, and the LUMO of ethene and the HOMO of butadiene. It is therefore possible to conclude that the reaction is ‘allowed’ when the symmetry of the reacting orbitals is the same, as per standard molecular orbital theory, and ‘forbidden’ when the orbitals that need to react do not share the same symmetry label (in this case, symmetric or antisymmetric).

Given that an interaction between orbitals is seen to occur when the symmetry labels are the same, it can be stated that the orbital overlap integral is non-zero for symmetric-symmetric and asymmetric-asymmetric interactions, and zero for symmetric-asymmetric interactions.

=== Change in Carbon Bond Lengths within the Reactants and Transition State to form the Product ===

Carbon bond lengths were investigated for the PM6-optimised reactants (namely, ethene and butadiene), the transition state of the Diels-Alder reaction between the two (as determined by PM6 calculation on Gaussian), and the PM6-optimised product, cyclohexene. The changes in bond lengths can be observed in the graph figure. Bond lengths are clearly shown to change throughout the reaction as the cycloaddition reaction between ethene and butadiene occurs. The single bond in the butadiene fragment is seen to shorten as it gains more sp2 character and becomes a double bond, and the opposite is observed with the double bonds. In the ethene fragment, the bond is seen to lengthen as the bond gains more sp3 character and becomes a single bond. The internuclear distance between the fragments is observed to change significantly from the transition state at 2.115 Å, to the product at 1.54 Å.

[[File:Mde14Graph of changing c-c.png|800px|centre|]]

{| class="wikitable" border="1"
|+ Bond lengths (Å , 10-10 m)
! C-C bond!! Reactants (frozen termini)!! Transition State !! Product
|-
| C-C in ethene molecule|| 1.327 || 1.382 || 1.541
|-
| C-C between ethene and butadiene (form during reaction)|| 2.200 || 2.115 || 1.54
|-
| C-C in butadiene double bonds|| 1.335 || 1.378 || 1.500
|-
| C-C in butadiene single bond|| 1.458 || 1.411 || 1.338
|}

When considering typical single and double C-C bonds, which are 1.54 Å and 1.34 Å respectively <ref name="bondlengths" />, it is clear that the transition state has bonds that exhibit a blend of single and double bond characters, due to their intermediate lengths between the two lengths typically observed. The Van der Waals radius of C is 1.70 Å <ref name="vdwcarbon" />, which is longer than the single and double bonds observed in the product (as expected with the overlap of VdW surfaces required for the formation of bonds) showing that the partially formed C-C bonds in the TS are in the early stage of formation. However, since the atoms are much closer than the sum of two Van der Waals radii of carbon (2.11 Å as opposed to the expected 3.4 Å), it is clear that the minimum point of the transition state is in a state of bond formation between the two reactants.

=== IRC and Transition State Vibrational Frequency ===

The formation of the two bonds is seen to be a concerted process from the IRC calculation of the reaction. It is observed from the vibration that corresponds to the reaction path in the transition state (the imaginary vibration at - 948 cm-1) that this process occurs such that the bonds are formed at the same time in a synchronous process. The lowest positive frequency in the product can be seen to support this judgment, since the frequency corresponds to a totally symmetric vibration of the formed bonds.

{| class="wikitable" border="1"
|+ Transition State vibration and IRC
! Imaginary (TS) Vibration!! IRC (forward from TS only)
|-
| [[File:Mde14Gaussian vibration for ts.gif|500px]] || [[File:Gaussian ethene irc.gif|500px]]
|-
| This vibration at -948 cm-1 corresponds to the reaction pathway from the transition state (click) || The IRC supports this (click).
|}

== Exercise Two - Cycloaddition of cyclohexadiene and 1,3-dioxole - Formation of Endo and Exo Products ==

=== Method ===

The semi-empirical PM6 method was used to optimise the reactant molecules, which were reoptimised using the B3LYP-631GD method. A 'guess' transition state was employed, with the reacting atomic termini for the reactants frozen for an initial energy optimisation then unfrozen to determine the transition state at first PM6 and then B3LYP-631GD level. Since two products were possible from the interaction between the orbitals in the cycloaddition, both were considered in this section.

=== Molecular Orbitals in the Transition States for the exo and endo products ===

Employing the MO diagram for the Diels-Alder cycloaddition of ethene and butadiene used in Exercise One, it is possible to infer the MOs for this interaction by symmetry, since the fragments in the interaction are similar to those used previously.

MOs for the Diels-Alder cycloaddition between 1,3-dioxole and cyclohexadiene have been visualised using GaussView. The symmetric nature of these orbitals means that the ‘side-on’ view of the orbitals as provided in the images is sufficient to observe the orbital interactions within the transition states.

{| class="wikitable" border="1"
|+ Molecular Orbitals for the Endo Transition State
! TS HOMO - 1!! TS HOMO !! TS LUMO !! TS LUMO + 1
|-
| [[File:TS HOMO - 1 - oxole lumo and cyclo homo.jpg|centre|200px]]|| [[File:TS HOMO - oxole homo and cyclo lumo.jpg|centre|200px]]|| [[File:TS LUMO - oxole homo and cyclo lumo.jpg|centre|200px]]|| [[File:TS LUMO + 2- oxole lumo and cyclo homo.jpg|centre|200px]]
|-
| This bonding MO is the result of interaction between the HOMO of the cyclohexadiene and the LUMO of the 1,3-dioxole.|| This bonding MO is the result of interaction between the LUMO of the cyclohexadiene and the HOMO of the 1,3-dioxole. There are clear secondary orbital effects arising from the electron density on the O atoms (red).|| This antibonding MO is the result of interaction between the LUMO of the cyclohexadiene and the HOMO of the 1,3-dioxole. Interactions between the forming and deforming π systems can be seen here as in the previous exercise.|| This antibonding MO is the result of interaction between the HOMO of the cyclohexadiene and the LUMO of the 1,3-dioxole.
|}

{| class="wikitable" border="1"
|+ Molecular Orbitals for the Exo Transition State
! TS HOMO - 1!! TS HOMO !! TS LUMO !! TS LUMO + 1
|-
| [[File:Mde14ENDO - TS HOMO-1 - oxole lumo and diene homo.jpg|centre|200px]]|| [[File:ENDO - TS HOMO - oxole homo and diene lumo.jpg|centre|200px]]|| [[File:ENDO - TS LUMO - oxole homo and diene lumo.jpg|centre|200px]]|| [[File:ENDO - TS LUMO+1 - oxole lumo and diene homo.jpg|centre|200px]]
|-
| This bonding MO is the result of interaction between the HOMO of the cyclohexadiene and the LUMO of the 1,3-dioxole.|| This bonding MO is the result of interaction between the LUMO of the cyclohexadiene and the HOMO of the 1,3-dioxole.|| This antibonding MO is the result of interaction between the LUMO of the cyclohexadiene and the HOMO of the 1,3-dioxole. Interactions between the forming and deforming π systems can be seen here as in the previous exercise.|| This antibonding MO is the result of interaction between the HOMO of the cyclohexadiene and the LUMO of the 1,3-dioxole.
|}

Diels-Alder reactions can be classified as either ‘normal’ or ‘inverse’ demand with regards to the electronic interaction occurring. Given the nature of the dienophile within this reaction, namely 1,3-dioxole, it can be inferred from theory that the electron-donating behaviour of the two oxygen atoms into the π system means that this is an inverse-demand Diels-Alder reaction <ref name="DAinv" />, which is confirmed by a quick analysis of the HOMO of both endo and exo transition states, which demonstrate the reaction of the dienophile HOMO with the diene LUMO to form the HOMO of the transition state.

=== Thermochemistry and Reaction Energies - Differences between the exo- and endo- products formed ===

Disclaimer - the data used here is likely subject to large errors due to calculation error.

The calculations for the transition states and products can ideally be used to determine the kinetically and thermodynamically favoured product of the reaction under investigation, by considering the reaction barrier energies and the energy minimum of the formed products from their respective transition states.

An Intrinsic Reaction Co-ordinate calculation was carried out for the formation of the exo and endo products to provide energy profiles for each reaction - these are contained below. The Gibbs free energies are considered in the log files for each of the calculations. The activation energy, reaction barrier, or EA, is taken to be the energy difference between the first IRC point on the left and the transition state IRC, and the change in energy of reaction, or ΔGr, is taken to be the energy difference between the first and last IRC points.

{| class="wikitable" border="1" centre
|+ Intrinsic Reaction Co-ordinate calculations demonstrating reaction energy profile
! Endo!! Exo
|-
| [[File:Graph of endo irc.png|300px]] || [[File:Graph of exo irc.png|300px]]
|-
| Reaction Barrier energy (EA) = 99.77 kJ mol-1 || Reaction Barrier energy (EA) = 110.27 kJ mol-1
|-
| Reaction change in energy (ΔGr) = -152.27 kJ mol-1 || Reaction change in energy (ΔGr) = -141.78 kJ mol-1
|}

The two calculations start at approximately the same energy, and a clear difference can be observed between the first IRC and the transition state IRC of the reactions - this is an energy difference of 10.5 kJ mol-1, arising due to circumstances to be covered later. When considering the overall change in energy, the observed energy difference is once again 10.5 kJ mol-1, and suggests that the endo product is the thermodynamically favoured product in this reaction, whereas the exo product is the kinetically favoured product. Repeats of this calculation yield the same result, but investigation of the wider literature suggests that typical Diels-Alder reactions yield the exo product as the thermodynamic product and the endo product as the kinetic product <ref name="messedup" />, which is against what is observed here and suggests some part of the calculation have not worked correctly. However, since these reactions go to the expected products, in particular through a minimum that can be easily identified to be a suitable transition state, at least some part of the calculations must have been correct.

=== Secondary Orbital Effects and Sterics - differences in exo and endo products ===

Secondary orbital interactions can be observed between the O atoms in the 1,3-dioxole and the π system of the diene in the endo product that reduce the energy of the transition state, making it the more favourable reaction pathway with a lower reaction barrier energy. Comparatively, no such secondary orbital interaction exists in the exo transition state structure, which results, as seen above, in a clear energy difference between the endo and exo transition state. These orbitals can be seen in the table in the MO sub-section of this exercise.

== Exercise Three - Xylylene and SO2 - Diels-Alder vs Cheletropic ==

=== Method ===

The semi-empirical PM6 method was used to optimise the product molecule, after which the symmetry of the lowest vibrational frequency was broken and the structure reoptimised. Bonds between the xylylene and SO2 fragments were broken and the transition state was determined using a PM6 calculation. An IRC for each of the endo, exo and cheletropic reaction.

===IRC and Energy Profiles for the Diels-Alder reactions (endo and exo) and cheletropic reaction between xylylene and SO2 ===

Values for activation and reaction energies were determined from these graphs in the same way as in Exercise 2.

{| class="wikitable" border="1" centre
|+ Intrinsic Reaction Co-ordinate calculations demonstrating reaction energy profile of the reactions
! Endo!! Exo (reversed) !! Cheletropic
|-
| [[File:Irc endo gif.gif|400px]] || [[File:Irc exo gif.gif|400px]] || [[File:Irc chele gif.gif|400px]]
|-
| Reaction Barrier energy (EA) = 99.77 kJ mol-1 || Reaction Barrier energy (EA) = 110.27 kJ mol-1 || Reaction Barrier energy (EA) = 110.27 kJ mol-1
|-
| Reaction change in energy (ΔGr) = -152.27 kJ mol-1 || Reaction change in energy (ΔGr) = -141.78 kJ mol-1
|}

== References ==

<references>
<ref name="MOdiagram">Wikimedia Commons, https://commons.wikimedia.org/wiki/File:Butadiene_Ethene_Cycloaddition123.png, accessed 14/12/2016</ref>
<ref name="bondlengths"> Texas A&M University Chemistry Department, http://www.chem.tamu.edu/rgroup/connell/linkfiles/bonds.pdf, accessed 14/12/2016 </ref>
<ref name="vdwcarbon"> PeriodicTable, http://periodictable.com/Properties/A/VanDerWaalsRadius.v.log.html, accessed 14/12/2016 </ref>
<ref name="DAinv"> Organic Chemistry Portal, http://www.organic-chemistry.org/namedreactions/diels-alder-reaction.shtm, accessed 14/12/2016 </ref>
<ref name="messedup"> University of Liverpool, http://www.chemtube3d.com/DAendo_vs_exo,cyclopentadiene_and_maleic_anhydride.html, accessed 15/12/2016 </ref>
</references>

File:Irc endo gif.gif

2016-12-15T17:25:58Z

Mde14: endo irc gif - mde14

endo irc gif - mde14

File:Irc chele gif.gif

2016-12-15T17:23:57Z

Mde14: chele irc mde14

chele irc mde14

File:Irc exo gif.gif

2016-12-15T17:21:24Z

Mde14: irc of the exo diels alder interaction - mde14

irc of the exo diels alder interaction - mde14

Rep:Mde14tscomp

2016-12-15T17:00:30Z

Mde14: