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Rep:Mod:EO1013TS

2017-12-19T23:36:44Z

Eo1013: /* Analysis of Molecular Orbitals */

==Introduction==
GaussView 5.0.9 is a very powerful program that allows for complex quantum mechanical calculation to be performed on molecules. It was used to investigate several aspects of three Diels-Alder reactions, the orbital interactions (primary and secondary) were moedlled and closely inspected as well as the energies and transition states to better understand the reaction paths of the examples studied.

===Potential Energy Surfaces (PES)===
The concept of PES is fundamental in computational chemistry and has allowed for many breakthroughs. A PES displays the relationship between the energy of a molecule and its geometry.

<math display="block">\text{Equation 1: General Time-dependent Schrödinger equation: } i \hbar \frac{\partial}{\partial t}\Psi(\mathbf{r},t) = \hat H \Psi(\mathbf{r},t)</math>

The energies can be calculated using different computational methods that simplify and solve the Schrödinger equation (''Eqn 1'') using approximations allowing PES to be generated in very little time. A PES conatains a lot of information, namely global and local minima that represent stable confomers/rotamers of the same molecule with the transition state that links them.<ref>The Concept of PES, http://is.muni.cz/el/1431/podzim2015/C9920/um/The_concept_of_PES.pdf, (accessed December 2017)</ref>

===The Transition State (TS) and Minima===
In GaussView 5.0.9 there are various methods (discussed below) to allow for the calculation of energies after optimising a particular geometry to a minimum energy taking into account electron repulsion and several other factors. Methods have also been devised, making use of known atomic separations during transitions to hazard a guess at the TS before performing optimising calculations and running an Intrinsic Reaction Coordinate (IRC) calculation can be performed to plot a reaction profile diagram.

The value of gradient on the PES at the minimum and at the transition structure will both be zero. Minima will have a positive value for the second derivative in every axial direction of the energy potential surface whereas a TS will have a positive value for the second derivative (saddle point) in all axial directions apart from in the reaction coordinate. This means that at a minima, movement in any direction either side of that point will results in a geometry with a higher energy. The same is true for the TS but there is a decrease in energy in one dimension which is known as the reaction pathway. The PES has 3N-6 dimensions, where N is the number of atoms in the molecule of study, corresponding to the degrees of freedom available to the molecule. Running an IRC calculation on the Ts structure allows as to track the geometries along this pathway.<ref>Gaussian – Vibration Analysis in Gaussian, http://gaussian.com/vib, (accessed December 2017)</ref>

The TS is a saddle point and just like a minima or a maxima, its first derivative will be zero. The difference however is apparent when you take the second derivative, which is done using a Hessian matrix in GaussView 5.0.9. The second derivative correlates to the energy and therefore the frequency and force constant of the vibrations in the molecule. As a result, minima always have positive force constants (increases in energy) and the TS, being a saddle point, will have at least one negative force constant (producing an imaginary vibration) which corresponds to the reaction pathway.

===Methods to Locate The TS===
In this investigation, three main methods were used to find the transition state.

'''Method 1:''' This method only works if one has prior knowledge of the transition state. The transition state is guessed using empirically observed bond lengths and a minimisation calculation is performed. If these lengths are wrong, undesired structures could form.

'''Method 2:''' This method also requires prior knowledge of the transition state. A guess of the TS is made and the bonds involved in the reaction are frozen before a minimisation calculation is performed. This structure is then optimised to a TS and is more reliable that '''Method 1'''.

'''Method 3:''' This method does not require prior knowledge of the transition state as you start with the product or reactants (optimised to a minimum). Bonds are then added or removed to closer resemble the TS and similar to '''Method 2''', these are frozen to obtain a minimum. However, It is not very reliable for TS geometries that do not resemble
the minima.

===Computational Methods===
The PM6 and B3LYP methods were used in this lab. PM6 is a semi-empirical method which simplifies the Hartree-Fock method by using empirical data and pre-determined integrals to solve Hamiltonian (the energy operator of the Schrödinger equation) and as a result, runs very quickly as less calculations need to be performed. With all the approximations and generic data used in this method, results are often inaccurate.<ref>Gaussian – Semi-Empirical Methods, http://gaussian.com/semiempirical, (accessed December 2017)</ref>

B3LYP, on the other hand, is a hybrid method that uses elements of Hartree-Fock and Density Funtional Theory (DFT). This method is more expensive than the PM6 as it doesn't use pre-determined integrals: it uses the DFT method to calculate all of the terms of the Hamiltonian apart from the exchange correlation term which is done using a HF method. It gives a very reliable results.<ref>What is B33LYP?, http://www.quora.com/What-is-B3LYP-and-why-is-it-the-most-popular-functional-in-DFT, (accessed December 2017)</ref><ref name=":0">A. Szabo and N. S. Ostlund, ''Modern Quantum Chemistry'', Dover Publications, 1989.</ref>

==Exercise 1: Butadiene + Ethene==
[[File:Reaction_scheme_1_eo1013.png|350px|thumb|center|Figure 1: Reaction Scheme for Butadiene with Ethene]]

This reaction is a [4+2] cycloaddition. Butadiene and ethene react together to form cyclohexene. The diene is more electron-rich than the dienophile. As can be seen from ''Figure 2'', the HOMO of butadiene contributes more to the HOMO-1 of the TS. In addition, the LUMO on ethene contributes more to the LUMO+1 which shows that HOMO of butadiene is lower in energy than the LUMO of ethene. This is an example of a normal electron demand reaction as the closest interaction is between the HOMO of the diene and the LUMO off the dienophile.<ref>J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, 2nd edn., 2012.</ref>

[[File:MO_1_eo1013.jpg|350px|thumb|center|Figure 2: MO Diagram showing orbital interactions in the reaction of Butadiene with Ethene]]

===Analysis of Molecular Orbitals===
A non-zero overlap integral is required in order for an orbital interaction to be favourable. Orbitals involved in this interaction must have the same symmetry as the overlap integral is proportional to the spatial overlap of the orbitals in question. For a non zero overlap, the orbitals must both be symmetric or asymmetric to give overall symmetric function. An anti-symmetric function will be gained when you combine orbitals of different symmetry which will leads overlap integral being zero.<ref>P. W. Atkins and J. De. Paula, ''Atkins' Physical Chemistry'', Oxford University Press, 9th edn., 2006.</ref>

<center>
{| class="wikitable"
|+ Table 1: Jmols for MOs in the dineophile (ethene).
|
<jmol><jmolApplet>
<title>Ethene - HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ETHENE_INITIAL_PM6_eo1013.LOG</uploadedFileContents>
<script>frame 12; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|
<jmol><jmolApplet>
<title>Ethene - LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ETHENE_INITIAL_PM6_eo1013.LOG</uploadedFileContents>
<script>frame 12; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|}
</center>

<center>
{| class="wikitable"
|+ Table 2: Jmols for MOs in the diene (butadiene).
|
<jmol><jmolApplet>
<title>Ethene - HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BUTADIENE_INITIAL_PM6_NEW_eo1013.LOG</uploadedFileContents>
<script>frame 22; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|
<jmol><jmolApplet>
<title>Ethene - LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BUTADIENE_INITIAL_PM6_NEW_eo1013.LOG</uploadedFileContents>
<script>frame 22; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|}
</center>

<center>
{| class="wikitable"
|+ Table 3: Jmols for MOs in the TS on the way to the product (cyclohexene).
|-
|
<jmol><jmolApplet>
<title>TS - HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG</uploadedFileContents>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|
<jmol><jmolApplet>
<title>TS - HOMO-1</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG</uploadedFileContents>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
|
<jmol><jmolApplet>
<title>TS - LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG</uploadedFileContents>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|
<jmol><jmolApplet>
<title>TS - LUMO+1</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG</uploadedFileContents>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|}
</center>

Looking at the HOMO and the LUMO of the TS in ''Table 3'', it is clear that they are formed from the HOMO of ethene and the LUMO of butadiene, both being symmetric orbitals. The opposite interaction from two antisymetic orbitals, the HOMO of butadiene and LUMO of ethene, give the HOMO-1 and the LUMO+1 of the TS. This clearly demonstrates that reactions can only be allowed when orbitals of the same symmetry can interact. Transition states that are of a geometry where orbitals of opposite symmetry are forced to interact will most likely lead to an unsuccessful reaction.

===Analysis of Bond Lengths===
<center>
{| class="wikitable" border="1"
|+ Table 4: Bond lengths (from ''Figure 1'') during the course of the reaction (Å)
! Bonds
! Cyclohexene
! Transition State
! Butadiene and Ethene
|-
| '''C1-C2''' || 1.501 || 1.380 || 1.335
|-
| '''C2-C3''' || 1.338 || 1.441 || 1.468
|-
| '''C3-C4''' || 1.501 || 1.380 || 1.335
|-
| '''C4-C5''' || 1.540 || 2.115 || ----
|-
| '''C5-C6''' || 1.541 || 1.382 || 1.327
|-
| '''C6-C1''' || 1.540 || 2.115 || ----
|}
</center>

A typical carbon to carbon single bond length is 1.54 Å and a double bond is 1.34 Å.<ref>L. Pauling and L. O. Brockway, ''ELECTRON DIFFRACTION INVESTIGATION OF SOME HYDROCARBONS'', California Institute of Technology, 1937.</ref> These are a direct match with the bond lengths predicted by Gaussian. C1-C2 and C3-C4 are a lot shorter due to the pulling effect of the higher electron density in C2-C3. As the carbons change from and sp3 hybridised orbitals to sp2, the bond lengths shorten and vice versa. Both double bonds on butadiene also lengthen as they change from sp2 to sp3 hybridisation. The two new bonds (C4-C5 and C6-C1) that form in the TS have a bond length (2.115 Å) that is smaller than two times the Van der Waal radius of carbon (1.7 Å) showing that the two molecules are starting to interact during the transition state and get shorter once the bond forms into a single C-C bond.<ref>A. Bondi, ''van der Waals Volumes and Radii '', J. Phys. Chem., vol. 68 #3, 1964.</ref>

===The Transition State===
<center>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>350</size>
<uploadedFileContents>BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 7; frank off; vector on; vector scale -4; vector 0.04; color vectors red</script>
<name>CPD_Dimer_TS</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle vibrate</text>
<target>CPD_Dimer_TS</target>
</jmolbutton>
</jmol>
</center>

The vibration above (click toggle vibration) corresponds to the negative frequency in the TS calculations a result of the negative force constant. The bond formation is synchronous as the carbons at both ends of the new bonds are moving at the same time in the TS. This can also seen in the IRC (Figure 3) as the bonds are formed at the same time.

<center>
[[File:IRC.gif|350px|thumb|center|Figure 3: IRC showing the formation of the two new bonds]]
</center>

===Relevant Files===
Product (PM6-Optimised): [[File:PRODUCTS_PM6_eo1016.LOG]]

TS of Reaction (PM6 Optimised): [[File:BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG]]

IRC of Reaction: [[File:BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG]]

==Exercise 2: Reaction of Cyclohexadiene + 1,3-Dioxole==
[[File:Rxn_scheme_eo1013.png|350px|thumb|center|Figure 4: Reaction Scheme for cyclohexadiene with 1,3-dioxole]]
This Diels-Alder reaction ([4+2] cycloaddition) is particularly interesting as there is a possibility of having two products: the endo and exo products. This is due to the fact that the dienophile is substituted and can approach in two different orientations. The exo product is formed when the bulk of the substituent approaches in such a way that it it pointing away from the pi-system of the diene. When it approaches with the bulk of the dienophile facing towards the pi system of the diene, the endo product is formed. This has implications for the energies of the products as will be discussed in the following sections.

[[File:Mo_2_eo1013.PNG|350px|thumb|center|Figure 5: MO diagram for the reaction of cyclohexadiene with 1,3-dioxole]]

The oxygen in either side of the dienophile have an electron donating effect on the p-orbitals of the double bond, causing the dienophile to be "electron rich" and raising the energy of the HOMO and LUMO, compared to ethene, as a result. As a consequence, as can illustrated in ''Figure 5'', the closest interaction is between the LUMO of the diene and the HOMO off the dienophile. Therefore, this is an example of an inverse electron demand reaction.<ref>J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, 2nd edn., 2012.</ref>

===Analysis of Molecular Orbitals===
As mentioned before, the oxygens on the dioxole work to raise the energy of the HOMO and LUMO of the diene compared to ethene. This increases the energy gap and leads to weaker interactions. An example of this is the HOMO-1 which is still lower in energy than the HOMO of the reactants as it only experiences a slight destabilisation. Only orbitals of the same symmetry can interact as seen below in ''Table 5'' and ''Table 6''.

<center>
{| class="wikitable"
|+ Table 5: Jmols for MOs in the TS on the way to the '''endo''' product.
|-
|
<jmol><jmolApplet>
<title>ENDO TS - HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ENDO_TS_B3LYP_NEW.LOG</uploadedFileContents>
<script>frame 50; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|
<jmol><jmolApplet>
<title>ENDO TS - HOMO-1</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ENDO_TS_B3LYP_NEW.LOG</uploadedFileContents>
<script>frame 50; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
|
<jmol><jmolApplet>
<title>ENDO TS - LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ENDO_TS_B3LYP_NEW.LOG</uploadedFileContents>
<script>frame 50; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|
<jmol><jmolApplet>
<title>ENDO TS - LUMO+1</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ENDO_TS_B3LYP_NEW.LOG</uploadedFileContents>
<script>frame 50; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|}
</center>

<center>
{| class="wikitable"
|+ Table 6: Jmols for MOs in the TS on the way to the '''exo''' product.
|-
|
<jmol><jmolApplet>
<title>EXO TS - HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>EXO_TS_B3LYP_NEW.LOG</uploadedFileContents>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|
<jmol><jmolApplet>
<title>EXO TS - HOMO-1</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>EXO_TS_B3LYP_NEW.LOG</uploadedFileContents>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
|
<jmol><jmolApplet>
<title>EXO TS - LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>EXO_TS_B3LYP_NEW.LOG</uploadedFileContents>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|
<jmol><jmolApplet>
<title>EXO TS - LUMO+1</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>EXO_TS_B3LYP_NEW.LOG</uploadedFileContents>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|}
</center>

===Thermochemical Analysis===
<center>
{| class="wikitable" border="1"
|+ Table 7: Thermochemical data for the reaction of cyclohexadiene with 1,3-dioxole
! Product
! Reaction Barrier in kJ mol<sup>-1</sup>
! Reaction Energy in kJ mol<sup>-1</sup>
|-
| Endo || 158.47 || -68.75
|-
| Exo || 166.30 || -65.15
|}
</center>

GaussView 5.0.9 also calculates the free energies of these geometries which can allow for an in-depth analysis of the energetics of the reaction. A summary of this data is presented in ''Table 7''. The reaction barrier is calculated as the difference in energy between the TS and the starting materials. The endo product has a lower reaction barrier compared to the exo product, making it the kinetically-preferred product. This can be attributed to the extra stabilisation present in the endo transition state as a result of the secondary orbital interactions between the oxygens and the pi system on the diene. ''Figure 6'' shows the orbital interaction between the oxygen (red atoms) with the double bond from.

[[File:Oxygen_interaction_eo1013.PNG|350px|thumb|center|Figure 6: MO depicted by GaussView 5.0.9 showing the secondary orbital interactions in the endo TS.]]

The reaction energy is calculated as the free energy difference between the products and the reactants. Comparing the two shows that the endo reaction has a more negative reaction energy compared to the exo reaction, making the endo product the thermodynamically-preferred product. This can be rationalised, as seen in ''Figure 7'', by the location of the CH<sub>2</sub>s on the-5 membered ring. There is some steric clash with the CH<sub>2</sub> fragments in the exo product with he CH<sub>2</sub>s on the bridging carbons which isn't present in the endo product (making it more thermodynamically stable).

[[File:Interaction_eo1013.PNG|350px|thumb|center|Figure 7: A diagram showing the steric clashing of the CH<sub>2</sub> fragments.]]

The endo product is both the kinetic and thermodynamic product. This also agrees with experimental observations stating that in a [4+2] cycloaddition, the endo product is preferred, even if the exo product is more stable, due to favourable secondary orbital interactions in the TS.

===Relevant Files===
1,3-Dioxole (B3LYP-Optimised): [[File:DIOXOLE_B3LYP_eo1013.LOG]]

Cyclohexadiene (B3LYP-Optimised): [[File:CYCLOHEXADIENE_B3LYP_eo1013.LOG]]

Endo Product (B3LYP-Optimised): [[File:ENDO_PRODUCT_PM6_eo1013.LOG]]

Exo Product (B3LYP-Optimised): [[File:EXO_PRODUCT_END_B3LYP_eo1013.LOG]]

IRC of Endo Reaction (PM6 Optimised): [[File:IRC_PM6_ENDO_eo1013.LOG]]

IRC of Exo Reaction (PM6 Optimised): [[File:IRC_EXO_PM6_eo1013.LOG]]

==Exercise 3: O-xylylene + SO<sub>2</sub>==
[[File:Rxn_scheme_3_eo1013.PNG|350px|thumb|center|Figure 8: MO diagram for the reaction of o-xylylene with SO<sub>2</sub>]]

This is another example of another interesting Diels-Alder reaction ([4+2] cycloaddition). As well as having the endo and exo products, this reaction can react to give the chelotropic product where a 5-membered ring is formed with two new bonds both formed to the sulphur. The other caveat to this reaction is that the reaction can occur on the double bonds within the ring to produce three more products: endo, exo and chelotropic. The analysis will be discussed below.

===IRCs of the Exocyclic Reaction===
The IRCs were run showing the geometries along the reaction coordinate. From ''Figure 9'' and ''Figure 10'' is can be seen that the exo and endo reaction proceed with asynchronous bonding, with the oxygen bonding before the sulphur. ''Figure 11'' clearly shows that the chelotropic reaction bonding in a synchronous fashion.

<center>
[[File:Exo_irc_eo1013.gif|x500px|thumb|center|Figure 9: IRC showing the formation of the exo product]]
</center>

<center>
[[File:Endo_irc_eo1013.gif|x500px|thumb|center|Figure 10: IRC showing the formation of the endo product]]
</center>

<center>
[[File:Che_irc_eo1013.gif|x500px|thumb|center|Figure 11: IRC showing the formation of the cheloptopic product]]
</center>

===Thermochemical Analysis===
<center>
{| class="wikitable" border="1"
|+ Table 8: Thermochemical data for the reaction of o-xylylene with SO<sub>2</sub>
! Product
! Reaction Barrier in kJ mol<sup>-1</sup>
! Reaction Energy in kJ mol<sup>-1</sup>
|-
| Endo || 80.12 || -100.66
|-
| Exo || 84.11 || -101.31
|-
| Cheletropic || 102.44 || -157.65
|}
</center>

GaussView 5.0.9 was used to calculate the energetics of the three reactions at the PM6 level. From ''Table 8'' it can be seen that the chelotropic product has the lowest reaction energy and is therefore the thermodynamic product. A consideration of the bond enthalpies involved makes this quite clear, the formation of C-O and S-O is less favorable compared to the formation of S=O and S-C.<ref>PROPERTIES OF ATOMS, RADICALS, AND BONDS, http://labs.chem.ucsb.edu/zakarian/armen/11---bonddissociationenergy.pdf, (accessed December 2017)</ref> It also has the highest energy TS largely due to the the 5-membered ring in the TS which suffers from ring strain compared to 6-membered TS in the endo and exo reaction pathways. Because of this higher energy transition state, the other products will be expected to form in a greater proportion under equilibrium conditions.

[[File:Rxn_profile_3_eo1013.png|450px|thumb|right|Figure 12: Approximate Reaction profile of all three reaction pathways investigated for the reaction of o-xylylene with SO<sub>2</sub>]]

''Figure 12'' illustrates that the endo product has the lowest energy TS and is therefore the kinetic product. These reactions are all very favourable due to the fact that an aromatic ring in formed afterwards. The stabilisation due to aromatisiation is very desired as we can see that ir is large enough to compensate for the high TS energy of the chelotropic reaction. Looking at the IRCs we can see that the aromatic ring forms before the other bonds in the reaction.

===Relevant Files===
Sulphur Dioxide (PM6 Optimised): [[File:SO2_PM6_EO1013.LOG]]

O-xylylene (PM6 Optimised): [[File:XYLYLENE_NEW_PM6_EO1013.LOG]]

Chelotropic TS (PM6 Optimised): [[File:TS_OPTIMISED_FINAL_PM6_che_eo1013.LOG]]

Exo TS (PM6 Optimised): [[File:TS_PM6_FINAL_EXO_eo1013.LOG]]

Endo TS (PM6 Optimised): [[File:TS_PM6_ENDO_FINAL_eo1013.LOG]]

Chelotropic Product (PM6 Optimised): [[File:PRODUCTS_PM6_che_eo1013.LOG]]

Exo Product (PM6 Optimised): [[File:EXO_PRODUCT_PM6_FINAL_eo1013.LOG]]

Endo Product (PM6 Optimised): [[File:PRODUCTS_PM6_ENDO_FINAL_eo1013.LOG]]

===Alternative Reaction Pathway===
<center>
{| class="wikitable" border="1"
|+ Table 9: Thermochemical data for the reaction (alternative pathway) of o-xylylene with SO<sub>2</sub>
! Product
! Reaction Barrier in kJ mol<sup>-1</sup>
! Reaction Energy in kJ mol<sup>-1</sup>
|-
| Endo || 110.34 || 14.62
|-
| Exo || 118.18 || 19.06
|}
</center>

From ''Table 9'', it is clear that the products are less stable than the sum of the energies of the reactants at infinite separation, this is a strong indication that the reaction requires some energy input in order for it to occur (endothermic reaction). The reaction barriers are a lot higher in comparison to those in ''Table 8'' which makes sense as there is the lack of stablisation gained from forming an aromatic ring from this pathway. The IRCs (''Figure 13'' and ''Figure 14'') are shown below.

<center>
[[File:ALT_EXO_IRC_eo1013.gif|x500px|thumb|center|Figure 13: IRC showing the formation of the exo product through the alternative pathway]]
</center>

<center>
[[File:ALT_ENDO_IRC_eo1013.gif|x500px|thumb|center|Figure 14: IRC showing the formation of the endo product through the alternative pathway]]
</center>

===Relevant Files (Alternative Pathway)===

Alternative Exo TS (PM6 Optimised): [[File:TS_EXO_FINAL_PM6_ALT_eo1013.LOG]]

Alternative Endo TS (PM6 Optimised): [[File:TS_ENDO_FINAL_PM6_ALT_eo1013.LOG]]

Alternative Exo Product (PM6 Optimised): [[File:PRODUCT_EXO_PM6_ALT_eo013.LOG]]

Alternative Endo Product (PM6 Optimised): [[File:PRODUCT_ENDO_PM6_ALT_eo1013.LOG]]

==Conclusion==
In conclusion, the results from this lab agree with the established theory around Diels-Alder reactions. Using the PM6 allows for quick calculations that may not be so reliable but aid an understanding of the underlying chemistry. The B3LYP calculations are very reliable but are more expensive in terms of computational cost. GaussView 5.0.9 has proven to be a very useful tool in analysing the thermochemical data of reactions and visualising the MOs to understand favourable orientations for successful reactions.

''Exercise 1'' was useful in understanding the advantages and limitations of the computational methods chosen. Analyzing and comparing the C-C bond lengths reflected how close GaussView 5.0.9 can get to literature values. ''Exercise 2'' required more in-depth analysis of the energies of the optimised geometries and shows how effective computational chemistry can be in predicting the major product of a reaction. ''Exercise 3'' highlighted the importance of utilising our chemical intuition along with the computational methods to investigate alternative pathways to rationalise their feasibility which could prove useful in determining possible side reactions.

All in all, these exercises have shown that the computational approach is a very powerful one indeed and can be used to predict the course, outcomes and shortcomings of a reaction before even entering the lab. This has some very beneficial implications namely in the fact that money can be saved rather than being spent on reagents for a reaction that will not yield desired products. It also proves to be a very useful tool in understanding reaction dynamics/mechanisms.

===References===

Rep:Mod:EO1013TS

2017-12-19T23:36:20Z

Eo1013: /* Analysis of Molecular Orbitals */

==Introduction==
GaussView 5.0.9 is a very powerful program that allows for complex quantum mechanical calculation to be performed on molecules. It was used to investigate several aspects of three Diels-Alder reactions, the orbital interactions (primary and secondary) were moedlled and closely inspected as well as the energies and transition states to better understand the reaction paths of the examples studied.

===Potential Energy Surfaces (PES)===
The concept of PES is fundamental in computational chemistry and has allowed for many breakthroughs. A PES displays the relationship between the energy of a molecule and its geometry.

<math display="block">\text{Equation 1: General Time-dependent Schrödinger equation: } i \hbar \frac{\partial}{\partial t}\Psi(\mathbf{r},t) = \hat H \Psi(\mathbf{r},t)</math>

The energies can be calculated using different computational methods that simplify and solve the Schrödinger equation (''Eqn 1'') using approximations allowing PES to be generated in very little time. A PES conatains a lot of information, namely global and local minima that represent stable confomers/rotamers of the same molecule with the transition state that links them.<ref>The Concept of PES, http://is.muni.cz/el/1431/podzim2015/C9920/um/The_concept_of_PES.pdf, (accessed December 2017)</ref>

===The Transition State (TS) and Minima===
In GaussView 5.0.9 there are various methods (discussed below) to allow for the calculation of energies after optimising a particular geometry to a minimum energy taking into account electron repulsion and several other factors. Methods have also been devised, making use of known atomic separations during transitions to hazard a guess at the TS before performing optimising calculations and running an Intrinsic Reaction Coordinate (IRC) calculation can be performed to plot a reaction profile diagram.

The value of gradient on the PES at the minimum and at the transition structure will both be zero. Minima will have a positive value for the second derivative in every axial direction of the energy potential surface whereas a TS will have a positive value for the second derivative (saddle point) in all axial directions apart from in the reaction coordinate. This means that at a minima, movement in any direction either side of that point will results in a geometry with a higher energy. The same is true for the TS but there is a decrease in energy in one dimension which is known as the reaction pathway. The PES has 3N-6 dimensions, where N is the number of atoms in the molecule of study, corresponding to the degrees of freedom available to the molecule. Running an IRC calculation on the Ts structure allows as to track the geometries along this pathway.<ref>Gaussian – Vibration Analysis in Gaussian, http://gaussian.com/vib, (accessed December 2017)</ref>

The TS is a saddle point and just like a minima or a maxima, its first derivative will be zero. The difference however is apparent when you take the second derivative, which is done using a Hessian matrix in GaussView 5.0.9. The second derivative correlates to the energy and therefore the frequency and force constant of the vibrations in the molecule. As a result, minima always have positive force constants (increases in energy) and the TS, being a saddle point, will have at least one negative force constant (producing an imaginary vibration) which corresponds to the reaction pathway.

===Methods to Locate The TS===
In this investigation, three main methods were used to find the transition state.

'''Method 1:''' This method only works if one has prior knowledge of the transition state. The transition state is guessed using empirically observed bond lengths and a minimisation calculation is performed. If these lengths are wrong, undesired structures could form.

'''Method 2:''' This method also requires prior knowledge of the transition state. A guess of the TS is made and the bonds involved in the reaction are frozen before a minimisation calculation is performed. This structure is then optimised to a TS and is more reliable that '''Method 1'''.

'''Method 3:''' This method does not require prior knowledge of the transition state as you start with the product or reactants (optimised to a minimum). Bonds are then added or removed to closer resemble the TS and similar to '''Method 2''', these are frozen to obtain a minimum. However, It is not very reliable for TS geometries that do not resemble
the minima.

===Computational Methods===
The PM6 and B3LYP methods were used in this lab. PM6 is a semi-empirical method which simplifies the Hartree-Fock method by using empirical data and pre-determined integrals to solve Hamiltonian (the energy operator of the Schrödinger equation) and as a result, runs very quickly as less calculations need to be performed. With all the approximations and generic data used in this method, results are often inaccurate.<ref>Gaussian – Semi-Empirical Methods, http://gaussian.com/semiempirical, (accessed December 2017)</ref>

B3LYP, on the other hand, is a hybrid method that uses elements of Hartree-Fock and Density Funtional Theory (DFT). This method is more expensive than the PM6 as it doesn't use pre-determined integrals: it uses the DFT method to calculate all of the terms of the Hamiltonian apart from the exchange correlation term which is done using a HF method. It gives a very reliable results.<ref>What is B33LYP?, http://www.quora.com/What-is-B3LYP-and-why-is-it-the-most-popular-functional-in-DFT, (accessed December 2017)</ref><ref name=":0">A. Szabo and N. S. Ostlund, ''Modern Quantum Chemistry'', Dover Publications, 1989.</ref>

==Exercise 1: Butadiene + Ethene==
[[File:Reaction_scheme_1_eo1013.png|350px|thumb|center|Figure 1: Reaction Scheme for Butadiene with Ethene]]

This reaction is a [4+2] cycloaddition. Butadiene and ethene react together to form cyclohexene. The diene is more electron-rich than the dienophile. As can be seen from ''Figure 2'', the HOMO of butadiene contributes more to the HOMO-1 of the TS. In addition, the LUMO on ethene contributes more to the LUMO+1 which shows that HOMO of butadiene is lower in energy than the LUMO of ethene. This is an example of a normal electron demand reaction as the closest interaction is between the HOMO of the diene and the LUMO off the dienophile.<ref>J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, 2nd edn., 2012.</ref>

[[File:MO_1_eo1013.jpg|350px|thumb|center|Figure 2: MO Diagram showing orbital interactions in the reaction of Butadiene with Ethene]]

===Analysis of Molecular Orbitals===
A non-zero overlap integral is required in order for an orbital interaction to be favourable. Orbitals involved in this interaction must have the same symmetry as the overlap integral is proportional to the spatial overlap of the orbitals in question. For a non zero overlap, the orbitals must both be symmetric or asymmetric to give overall symmetric function. An anti-symmetric function will be gained when you combine orbitals of different symmetry which will leads overlap integral being zero.<ref>P. W. Atkins and J. De. Paula, ''Atkins' Physical Chemistry'', Oxford University Press, 9th edn., 2006.</ref>

<center>
{| class="wikitable"
|+ Table 1: Jmols for MOs in the dineophile (ethene).
|
<jmol><jmolApplet>
<title>Ethene - HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ETHENE_INITIAL_PM6_eo1013.LOG</uploadedFileContents>
<script>frame 12; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|
<jmol><jmolApplet>
<title>Ethene - LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ETHENE_INITIAL_PM6_eo1013.LOG</uploadedFileContents>
<script>frame 12; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|}
</center>

<center>
{| class="wikitable"
|+ Table 2: Jmols for MOs in the diene (butadiene).
|
<jmol><jmolApplet>
<title>Ethene - HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BUTADIENE_INITIAL_PM6_NEW_eo1013.LOG</uploadedFileContents>
<script>frame 22; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|
<jmol><jmolApplet>
<title>Ethene - LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BUTADIENE_INITIAL_PM6_NEW_eo1013.LOG</uploadedFileContents>
<script>frame 22; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|}
</center>

<center>
{| class="wikitable"
|+ Table 3: Jmols for MOs in the TS on the way to the product (cyclohexene).
|-
|
<jmol><jmolApplet>
<title>TS - HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG</uploadedFileContents>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|
<jmol><jmolApplet>
<title>TS - HOMO-1</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG</uploadedFileContents>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
|
<jmol><jmolApplet>
<title>TS - LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG</uploadedFileContents>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|
<jmol><jmolApplet>
<title>TS - LUMO+1</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG</uploadedFileContents>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|}
</center>

Looking at the HOMO and the LUMO of the TS in ''Table 3'', it is clear that they are formed from the HOMO of ethene and the LUMO of butadiene, both being symmetric orbitals. The opposite interaction from two antisymetic orbitals, the HOMO of butadiene and LUMO of ethene, give the HOMO-1 and the LUMO+1 of the TS. This clearly demonstrates that reactions can only be allowed when orbitals of the same symmetry can interact. Transition states that are of a geometry where orbitals of opposite symmetry are forced to interact will most likely lead to an unsuccessful reaction.

===Analysis of Bond Lengths===
<center>
{| class="wikitable" border="1"
|+ Table 4: Bond lengths (from ''Figure 1'') during the course of the reaction (Å)
! Bonds
! Cyclohexene
! Transition State
! Butadiene and Ethene
|-
| '''C1-C2''' || 1.501 || 1.380 || 1.335
|-
| '''C2-C3''' || 1.338 || 1.441 || 1.468
|-
| '''C3-C4''' || 1.501 || 1.380 || 1.335
|-
| '''C4-C5''' || 1.540 || 2.115 || ----
|-
| '''C5-C6''' || 1.541 || 1.382 || 1.327
|-
| '''C6-C1''' || 1.540 || 2.115 || ----
|}
</center>

A typical carbon to carbon single bond length is 1.54 Å and a double bond is 1.34 Å.<ref>L. Pauling and L. O. Brockway, ''ELECTRON DIFFRACTION INVESTIGATION OF SOME HYDROCARBONS'', California Institute of Technology, 1937.</ref> These are a direct match with the bond lengths predicted by Gaussian. C1-C2 and C3-C4 are a lot shorter due to the pulling effect of the higher electron density in C2-C3. As the carbons change from and sp3 hybridised orbitals to sp2, the bond lengths shorten and vice versa. Both double bonds on butadiene also lengthen as they change from sp2 to sp3 hybridisation. The two new bonds (C4-C5 and C6-C1) that form in the TS have a bond length (2.115 Å) that is smaller than two times the Van der Waal radius of carbon (1.7 Å) showing that the two molecules are starting to interact during the transition state and get shorter once the bond forms into a single C-C bond.<ref>A. Bondi, ''van der Waals Volumes and Radii '', J. Phys. Chem., vol. 68 #3, 1964.</ref>

===The Transition State===
<center>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>350</size>
<uploadedFileContents>BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 7; frank off; vector on; vector scale -4; vector 0.04; color vectors red</script>
<name>CPD_Dimer_TS</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle vibrate</text>
<target>CPD_Dimer_TS</target>
</jmolbutton>
</jmol>
</center>

The vibration above (click toggle vibration) corresponds to the negative frequency in the TS calculations a result of the negative force constant. The bond formation is synchronous as the carbons at both ends of the new bonds are moving at the same time in the TS. This can also seen in the IRC (Figure 3) as the bonds are formed at the same time.

<center>
[[File:IRC.gif|350px|thumb|center|Figure 3: IRC showing the formation of the two new bonds]]
</center>

===Relevant Files===
Product (PM6-Optimised): [[File:PRODUCTS_PM6_eo1016.LOG]]

TS of Reaction (PM6 Optimised): [[File:BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG]]

IRC of Reaction: [[File:BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG]]

==Exercise 2: Reaction of Cyclohexadiene + 1,3-Dioxole==
[[File:Rxn_scheme_eo1013.png|350px|thumb|center|Figure 4: Reaction Scheme for cyclohexadiene with 1,3-dioxole]]
This Diels-Alder reaction ([4+2] cycloaddition) is particularly interesting as there is a possibility of having two products: the endo and exo products. This is due to the fact that the dienophile is substituted and can approach in two different orientations. The exo product is formed when the bulk of the substituent approaches in such a way that it it pointing away from the pi-system of the diene. When it approaches with the bulk of the dienophile facing towards the pi system of the diene, the endo product is formed. This has implications for the energies of the products as will be discussed in the following sections.

[[File:Mo_2_eo1013.PNG|350px|thumb|center|Figure 5: MO diagram for the reaction of cyclohexadiene with 1,3-dioxole]]

The oxygen in either side of the dienophile have an electron donating effect on the p-orbitals of the double bond, causing the dienophile to be "electron rich" and raising the energy of the HOMO and LUMO, compared to ethene, as a result. As a consequence, as can illustrated in ''Figure 5'', the closest interaction is between the LUMO of the diene and the HOMO off the dienophile. Therefore, this is an example of an inverse electron demand reaction.<ref>J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, 2nd edn., 2012.</ref>

===Analysis of Molecular Orbitals===
As mentioned before, the oxygens on the dioxole work to raise the energy of the HOMO and LUMO of the diene compared to ethene. This increases the energy gap and leads to weaker interactions. An example of this is the HOMO-1 which is still lower in energy than the HOMO of the reactants as it only experiences a slight destabilisation. Only orbitals of the same symmetry can interact as seen below in ''Table 5'' and ''Table 6''.

<center>
{| class="wikitable"
|+ Table 6: Jmols for MOs in the TS on the way to the '''exo''' product.
|-
|
<jmol><jmolApplet>
<title>EXO TS - HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>EXO_TS_B3LYP_NEW.LOG</uploadedFileContents>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|
<jmol><jmolApplet>
<title>EXO TS - HOMO-1</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>EXO_TS_B3LYP_NEW.LOG</uploadedFileContents>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
|
<jmol><jmolApplet>
<title>EXO TS - LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>EXO_TS_B3LYP_NEW.LOG</uploadedFileContents>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|
<jmol><jmolApplet>
<title>EXO TS - LUMO+1</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>EXO_TS_B3LYP_NEW.LOG</uploadedFileContents>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|}
</center>

===Thermochemical Analysis===
<center>
{| class="wikitable" border="1"
|+ Table 7: Thermochemical data for the reaction of cyclohexadiene with 1,3-dioxole
! Product
! Reaction Barrier in kJ mol<sup>-1</sup>
! Reaction Energy in kJ mol<sup>-1</sup>
|-
| Endo || 158.47 || -68.75
|-
| Exo || 166.30 || -65.15
|}
</center>

GaussView 5.0.9 also calculates the free energies of these geometries which can allow for an in-depth analysis of the energetics of the reaction. A summary of this data is presented in ''Table 7''. The reaction barrier is calculated as the difference in energy between the TS and the starting materials. The endo product has a lower reaction barrier compared to the exo product, making it the kinetically-preferred product. This can be attributed to the extra stabilisation present in the endo transition state as a result of the secondary orbital interactions between the oxygens and the pi system on the diene. ''Figure 6'' shows the orbital interaction between the oxygen (red atoms) with the double bond from.

[[File:Oxygen_interaction_eo1013.PNG|350px|thumb|center|Figure 6: MO depicted by GaussView 5.0.9 showing the secondary orbital interactions in the endo TS.]]

The reaction energy is calculated as the free energy difference between the products and the reactants. Comparing the two shows that the endo reaction has a more negative reaction energy compared to the exo reaction, making the endo product the thermodynamically-preferred product. This can be rationalised, as seen in ''Figure 7'', by the location of the CH<sub>2</sub>s on the-5 membered ring. There is some steric clash with the CH<sub>2</sub> fragments in the exo product with he CH<sub>2</sub>s on the bridging carbons which isn't present in the endo product (making it more thermodynamically stable).

[[File:Interaction_eo1013.PNG|350px|thumb|center|Figure 7: A diagram showing the steric clashing of the CH<sub>2</sub> fragments.]]

The endo product is both the kinetic and thermodynamic product. This also agrees with experimental observations stating that in a [4+2] cycloaddition, the endo product is preferred, even if the exo product is more stable, due to favourable secondary orbital interactions in the TS.

===Relevant Files===
1,3-Dioxole (B3LYP-Optimised): [[File:DIOXOLE_B3LYP_eo1013.LOG]]

Cyclohexadiene (B3LYP-Optimised): [[File:CYCLOHEXADIENE_B3LYP_eo1013.LOG]]

Endo Product (B3LYP-Optimised): [[File:ENDO_PRODUCT_PM6_eo1013.LOG]]

Exo Product (B3LYP-Optimised): [[File:EXO_PRODUCT_END_B3LYP_eo1013.LOG]]

IRC of Endo Reaction (PM6 Optimised): [[File:IRC_PM6_ENDO_eo1013.LOG]]

IRC of Exo Reaction (PM6 Optimised): [[File:IRC_EXO_PM6_eo1013.LOG]]

==Exercise 3: O-xylylene + SO<sub>2</sub>==
[[File:Rxn_scheme_3_eo1013.PNG|350px|thumb|center|Figure 8: MO diagram for the reaction of o-xylylene with SO<sub>2</sub>]]

This is another example of another interesting Diels-Alder reaction ([4+2] cycloaddition). As well as having the endo and exo products, this reaction can react to give the chelotropic product where a 5-membered ring is formed with two new bonds both formed to the sulphur. The other caveat to this reaction is that the reaction can occur on the double bonds within the ring to produce three more products: endo, exo and chelotropic. The analysis will be discussed below.

===IRCs of the Exocyclic Reaction===
The IRCs were run showing the geometries along the reaction coordinate. From ''Figure 9'' and ''Figure 10'' is can be seen that the exo and endo reaction proceed with asynchronous bonding, with the oxygen bonding before the sulphur. ''Figure 11'' clearly shows that the chelotropic reaction bonding in a synchronous fashion.

<center>
[[File:Exo_irc_eo1013.gif|x500px|thumb|center|Figure 9: IRC showing the formation of the exo product]]
</center>

<center>
[[File:Endo_irc_eo1013.gif|x500px|thumb|center|Figure 10: IRC showing the formation of the endo product]]
</center>

<center>
[[File:Che_irc_eo1013.gif|x500px|thumb|center|Figure 11: IRC showing the formation of the cheloptopic product]]
</center>

===Thermochemical Analysis===
<center>
{| class="wikitable" border="1"
|+ Table 8: Thermochemical data for the reaction of o-xylylene with SO<sub>2</sub>
! Product
! Reaction Barrier in kJ mol<sup>-1</sup>
! Reaction Energy in kJ mol<sup>-1</sup>
|-
| Endo || 80.12 || -100.66
|-
| Exo || 84.11 || -101.31
|-
| Cheletropic || 102.44 || -157.65
|}
</center>

GaussView 5.0.9 was used to calculate the energetics of the three reactions at the PM6 level. From ''Table 8'' it can be seen that the chelotropic product has the lowest reaction energy and is therefore the thermodynamic product. A consideration of the bond enthalpies involved makes this quite clear, the formation of C-O and S-O is less favorable compared to the formation of S=O and S-C.<ref>PROPERTIES OF ATOMS, RADICALS, AND BONDS, http://labs.chem.ucsb.edu/zakarian/armen/11---bonddissociationenergy.pdf, (accessed December 2017)</ref> It also has the highest energy TS largely due to the the 5-membered ring in the TS which suffers from ring strain compared to 6-membered TS in the endo and exo reaction pathways. Because of this higher energy transition state, the other products will be expected to form in a greater proportion under equilibrium conditions.

[[File:Rxn_profile_3_eo1013.png|450px|thumb|right|Figure 12: Approximate Reaction profile of all three reaction pathways investigated for the reaction of o-xylylene with SO<sub>2</sub>]]

''Figure 12'' illustrates that the endo product has the lowest energy TS and is therefore the kinetic product. These reactions are all very favourable due to the fact that an aromatic ring in formed afterwards. The stabilisation due to aromatisiation is very desired as we can see that ir is large enough to compensate for the high TS energy of the chelotropic reaction. Looking at the IRCs we can see that the aromatic ring forms before the other bonds in the reaction.

===Relevant Files===
Sulphur Dioxide (PM6 Optimised): [[File:SO2_PM6_EO1013.LOG]]

O-xylylene (PM6 Optimised): [[File:XYLYLENE_NEW_PM6_EO1013.LOG]]

Chelotropic TS (PM6 Optimised): [[File:TS_OPTIMISED_FINAL_PM6_che_eo1013.LOG]]

Exo TS (PM6 Optimised): [[File:TS_PM6_FINAL_EXO_eo1013.LOG]]

Endo TS (PM6 Optimised): [[File:TS_PM6_ENDO_FINAL_eo1013.LOG]]

Chelotropic Product (PM6 Optimised): [[File:PRODUCTS_PM6_che_eo1013.LOG]]

Exo Product (PM6 Optimised): [[File:EXO_PRODUCT_PM6_FINAL_eo1013.LOG]]

Endo Product (PM6 Optimised): [[File:PRODUCTS_PM6_ENDO_FINAL_eo1013.LOG]]

===Alternative Reaction Pathway===
<center>
{| class="wikitable" border="1"
|+ Table 9: Thermochemical data for the reaction (alternative pathway) of o-xylylene with SO<sub>2</sub>
! Product
! Reaction Barrier in kJ mol<sup>-1</sup>
! Reaction Energy in kJ mol<sup>-1</sup>
|-
| Endo || 110.34 || 14.62
|-
| Exo || 118.18 || 19.06
|}
</center>

From ''Table 9'', it is clear that the products are less stable than the sum of the energies of the reactants at infinite separation, this is a strong indication that the reaction requires some energy input in order for it to occur (endothermic reaction). The reaction barriers are a lot higher in comparison to those in ''Table 8'' which makes sense as there is the lack of stablisation gained from forming an aromatic ring from this pathway. The IRCs (''Figure 13'' and ''Figure 14'') are shown below.

<center>
[[File:ALT_EXO_IRC_eo1013.gif|x500px|thumb|center|Figure 13: IRC showing the formation of the exo product through the alternative pathway]]
</center>

<center>
[[File:ALT_ENDO_IRC_eo1013.gif|x500px|thumb|center|Figure 14: IRC showing the formation of the endo product through the alternative pathway]]
</center>

===Relevant Files (Alternative Pathway)===

Alternative Exo TS (PM6 Optimised): [[File:TS_EXO_FINAL_PM6_ALT_eo1013.LOG]]

Alternative Endo TS (PM6 Optimised): [[File:TS_ENDO_FINAL_PM6_ALT_eo1013.LOG]]

Alternative Exo Product (PM6 Optimised): [[File:PRODUCT_EXO_PM6_ALT_eo013.LOG]]

Alternative Endo Product (PM6 Optimised): [[File:PRODUCT_ENDO_PM6_ALT_eo1013.LOG]]

==Conclusion==
In conclusion, the results from this lab agree with the established theory around Diels-Alder reactions. Using the PM6 allows for quick calculations that may not be so reliable but aid an understanding of the underlying chemistry. The B3LYP calculations are very reliable but are more expensive in terms of computational cost. GaussView 5.0.9 has proven to be a very useful tool in analysing the thermochemical data of reactions and visualising the MOs to understand favourable orientations for successful reactions.

''Exercise 1'' was useful in understanding the advantages and limitations of the computational methods chosen. Analyzing and comparing the C-C bond lengths reflected how close GaussView 5.0.9 can get to literature values. ''Exercise 2'' required more in-depth analysis of the energies of the optimised geometries and shows how effective computational chemistry can be in predicting the major product of a reaction. ''Exercise 3'' highlighted the importance of utilising our chemical intuition along with the computational methods to investigate alternative pathways to rationalise their feasibility which could prove useful in determining possible side reactions.

All in all, these exercises have shown that the computational approach is a very powerful one indeed and can be used to predict the course, outcomes and shortcomings of a reaction before even entering the lab. This has some very beneficial implications namely in the fact that money can be saved rather than being spent on reagents for a reaction that will not yield desired products. It also proves to be a very useful tool in understanding reaction dynamics/mechanisms.

===References===

Rep:Mod:EO1013TS

2017-12-19T23:34:11Z

Eo1013: /* Analysis of Molecular Orbitals */

==Introduction==
GaussView 5.0.9 is a very powerful program that allows for complex quantum mechanical calculation to be performed on molecules. It was used to investigate several aspects of three Diels-Alder reactions, the orbital interactions (primary and secondary) were moedlled and closely inspected as well as the energies and transition states to better understand the reaction paths of the examples studied.

===Potential Energy Surfaces (PES)===
The concept of PES is fundamental in computational chemistry and has allowed for many breakthroughs. A PES displays the relationship between the energy of a molecule and its geometry.

<math display="block">\text{Equation 1: General Time-dependent Schrödinger equation: } i \hbar \frac{\partial}{\partial t}\Psi(\mathbf{r},t) = \hat H \Psi(\mathbf{r},t)</math>

The energies can be calculated using different computational methods that simplify and solve the Schrödinger equation (''Eqn 1'') using approximations allowing PES to be generated in very little time. A PES conatains a lot of information, namely global and local minima that represent stable confomers/rotamers of the same molecule with the transition state that links them.<ref>The Concept of PES, http://is.muni.cz/el/1431/podzim2015/C9920/um/The_concept_of_PES.pdf, (accessed December 2017)</ref>

===The Transition State (TS) and Minima===
In GaussView 5.0.9 there are various methods (discussed below) to allow for the calculation of energies after optimising a particular geometry to a minimum energy taking into account electron repulsion and several other factors. Methods have also been devised, making use of known atomic separations during transitions to hazard a guess at the TS before performing optimising calculations and running an Intrinsic Reaction Coordinate (IRC) calculation can be performed to plot a reaction profile diagram.

The value of gradient on the PES at the minimum and at the transition structure will both be zero. Minima will have a positive value for the second derivative in every axial direction of the energy potential surface whereas a TS will have a positive value for the second derivative (saddle point) in all axial directions apart from in the reaction coordinate. This means that at a minima, movement in any direction either side of that point will results in a geometry with a higher energy. The same is true for the TS but there is a decrease in energy in one dimension which is known as the reaction pathway. The PES has 3N-6 dimensions, where N is the number of atoms in the molecule of study, corresponding to the degrees of freedom available to the molecule. Running an IRC calculation on the Ts structure allows as to track the geometries along this pathway.<ref>Gaussian – Vibration Analysis in Gaussian, http://gaussian.com/vib, (accessed December 2017)</ref>

The TS is a saddle point and just like a minima or a maxima, its first derivative will be zero. The difference however is apparent when you take the second derivative, which is done using a Hessian matrix in GaussView 5.0.9. The second derivative correlates to the energy and therefore the frequency and force constant of the vibrations in the molecule. As a result, minima always have positive force constants (increases in energy) and the TS, being a saddle point, will have at least one negative force constant (producing an imaginary vibration) which corresponds to the reaction pathway.

===Methods to Locate The TS===
In this investigation, three main methods were used to find the transition state.

'''Method 1:''' This method only works if one has prior knowledge of the transition state. The transition state is guessed using empirically observed bond lengths and a minimisation calculation is performed. If these lengths are wrong, undesired structures could form.

'''Method 2:''' This method also requires prior knowledge of the transition state. A guess of the TS is made and the bonds involved in the reaction are frozen before a minimisation calculation is performed. This structure is then optimised to a TS and is more reliable that '''Method 1'''.

'''Method 3:''' This method does not require prior knowledge of the transition state as you start with the product or reactants (optimised to a minimum). Bonds are then added or removed to closer resemble the TS and similar to '''Method 2''', these are frozen to obtain a minimum. However, It is not very reliable for TS geometries that do not resemble
the minima.

===Computational Methods===
The PM6 and B3LYP methods were used in this lab. PM6 is a semi-empirical method which simplifies the Hartree-Fock method by using empirical data and pre-determined integrals to solve Hamiltonian (the energy operator of the Schrödinger equation) and as a result, runs very quickly as less calculations need to be performed. With all the approximations and generic data used in this method, results are often inaccurate.<ref>Gaussian – Semi-Empirical Methods, http://gaussian.com/semiempirical, (accessed December 2017)</ref>

B3LYP, on the other hand, is a hybrid method that uses elements of Hartree-Fock and Density Funtional Theory (DFT). This method is more expensive than the PM6 as it doesn't use pre-determined integrals: it uses the DFT method to calculate all of the terms of the Hamiltonian apart from the exchange correlation term which is done using a HF method. It gives a very reliable results.<ref>What is B33LYP?, http://www.quora.com/What-is-B3LYP-and-why-is-it-the-most-popular-functional-in-DFT, (accessed December 2017)</ref><ref name=":0">A. Szabo and N. S. Ostlund, ''Modern Quantum Chemistry'', Dover Publications, 1989.</ref>

==Exercise 1: Butadiene + Ethene==
[[File:Reaction_scheme_1_eo1013.png|350px|thumb|center|Figure 1: Reaction Scheme for Butadiene with Ethene]]

This reaction is a [4+2] cycloaddition. Butadiene and ethene react together to form cyclohexene. The diene is more electron-rich than the dienophile. As can be seen from ''Figure 2'', the HOMO of butadiene contributes more to the HOMO-1 of the TS. In addition, the LUMO on ethene contributes more to the LUMO+1 which shows that HOMO of butadiene is lower in energy than the LUMO of ethene. This is an example of a normal electron demand reaction as the closest interaction is between the HOMO of the diene and the LUMO off the dienophile.<ref>J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, 2nd edn., 2012.</ref>

[[File:MO_1_eo1013.jpg|350px|thumb|center|Figure 2: MO Diagram showing orbital interactions in the reaction of Butadiene with Ethene]]

===Analysis of Molecular Orbitals===
A non-zero overlap integral is required in order for an orbital interaction to be favourable. Orbitals involved in this interaction must have the same symmetry as the overlap integral is proportional to the spatial overlap of the orbitals in question. For a non zero overlap, the orbitals must both be symmetric or asymmetric to give overall symmetric function. An anti-symmetric function will be gained when you combine orbitals of different symmetry which will leads overlap integral being zero.<ref>P. W. Atkins and J. De. Paula, ''Atkins' Physical Chemistry'', Oxford University Press, 9th edn., 2006.</ref>

<center>
{| class="wikitable"
|+ Table 1: Jmols for MOs in the dineophile (ethene).
|
<jmol><jmolApplet>
<title>Ethene - HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ETHENE_INITIAL_PM6_eo1013.LOG</uploadedFileContents>
<script>frame 12; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|
<jmol><jmolApplet>
<title>Ethene - LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ETHENE_INITIAL_PM6_eo1013.LOG</uploadedFileContents>
<script>frame 12; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|}
</center>

<center>
{| class="wikitable"
|+ Table 2: Jmols for MOs in the diene (butadiene).
|
<jmol><jmolApplet>
<title>Ethene - HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BUTADIENE_INITIAL_PM6_NEW_eo1013.LOG</uploadedFileContents>
<script>frame 22; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|
<jmol><jmolApplet>
<title>Ethene - LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BUTADIENE_INITIAL_PM6_NEW_eo1013.LOG</uploadedFileContents>
<script>frame 22; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|}
</center>

<center>
{| class="wikitable"
|+ Table 3: Jmols for MOs in the TS on the way to the product (cyclohexene).
|-
|
<jmol><jmolApplet>
<title>TS - HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG</uploadedFileContents>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|
<jmol><jmolApplet>
<title>TS - HOMO-1</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG</uploadedFileContents>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
|
<jmol><jmolApplet>
<title>TS - LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG</uploadedFileContents>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|
<jmol><jmolApplet>
<title>TS - LUMO+1</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG</uploadedFileContents>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|}
</center>

<center>
{| class="wikitable"
|+ Table 5: Jmols for MOs in the TS on the way to the '''endo''' product.
|-
|
<jmol><jmolApplet>
<title>ENDO TS - HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ENDO_TS_B3LYP_NEW.LOG</uploadedFileContents>
<script>frame 50; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|
<jmol><jmolApplet>
<title>ENDO TS - HOMO-1</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ENDO_TS_B3LYP_NEW.LOG</uploadedFileContents>
<script>frame 50; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
|
<jmol><jmolApplet>
<title>ENDO TS - LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ENDO_TS_B3LYP_NEW.LOG</uploadedFileContents>
<script>frame 50; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|
<jmol><jmolApplet>
<title>ENDO TS - LUMO+1</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ENDO_TS_B3LYP_NEW.LOG</uploadedFileContents>
<script>frame 50; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|}
</center>

Looking at the HOMO and the LUMO of the TS in ''Table 3'', it is clear that they are formed from the HOMO of ethene and the LUMO of butadiene, both being symmetric orbitals. The opposite interaction from two antisymetic orbitals, the HOMO of butadiene and LUMO of ethene, give the HOMO-1 and the LUMO+1 of the TS. This clearly demonstrates that reactions can only be allowed when orbitals of the same symmetry can interact. Transition states that are of a geometry where orbitals of opposite symmetry are forced to interact will most likely lead to an unsuccessful reaction.

===Analysis of Bond Lengths===
<center>
{| class="wikitable" border="1"
|+ Table 4: Bond lengths (from ''Figure 1'') during the course of the reaction (Å)
! Bonds
! Cyclohexene
! Transition State
! Butadiene and Ethene
|-
| '''C1-C2''' || 1.501 || 1.380 || 1.335
|-
| '''C2-C3''' || 1.338 || 1.441 || 1.468
|-
| '''C3-C4''' || 1.501 || 1.380 || 1.335
|-
| '''C4-C5''' || 1.540 || 2.115 || ----
|-
| '''C5-C6''' || 1.541 || 1.382 || 1.327
|-
| '''C6-C1''' || 1.540 || 2.115 || ----
|}
</center>

A typical carbon to carbon single bond length is 1.54 Å and a double bond is 1.34 Å.<ref>L. Pauling and L. O. Brockway, ''ELECTRON DIFFRACTION INVESTIGATION OF SOME HYDROCARBONS'', California Institute of Technology, 1937.</ref> These are a direct match with the bond lengths predicted by Gaussian. C1-C2 and C3-C4 are a lot shorter due to the pulling effect of the higher electron density in C2-C3. As the carbons change from and sp3 hybridised orbitals to sp2, the bond lengths shorten and vice versa. Both double bonds on butadiene also lengthen as they change from sp2 to sp3 hybridisation. The two new bonds (C4-C5 and C6-C1) that form in the TS have a bond length (2.115 Å) that is smaller than two times the Van der Waal radius of carbon (1.7 Å) showing that the two molecules are starting to interact during the transition state and get shorter once the bond forms into a single C-C bond.<ref>A. Bondi, ''van der Waals Volumes and Radii '', J. Phys. Chem., vol. 68 #3, 1964.</ref>

===The Transition State===
<center>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>350</size>
<uploadedFileContents>BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 7; frank off; vector on; vector scale -4; vector 0.04; color vectors red</script>
<name>CPD_Dimer_TS</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle vibrate</text>
<target>CPD_Dimer_TS</target>
</jmolbutton>
</jmol>
</center>

The vibration above (click toggle vibration) corresponds to the negative frequency in the TS calculations a result of the negative force constant. The bond formation is synchronous as the carbons at both ends of the new bonds are moving at the same time in the TS. This can also seen in the IRC (Figure 3) as the bonds are formed at the same time.

<center>
[[File:IRC.gif|350px|thumb|center|Figure 3: IRC showing the formation of the two new bonds]]
</center>

===Relevant Files===
Product (PM6-Optimised): [[File:PRODUCTS_PM6_eo1016.LOG]]

TS of Reaction (PM6 Optimised): [[File:BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG]]

IRC of Reaction: [[File:BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG]]

==Exercise 2: Reaction of Cyclohexadiene + 1,3-Dioxole==
[[File:Rxn_scheme_eo1013.png|350px|thumb|center|Figure 4: Reaction Scheme for cyclohexadiene with 1,3-dioxole]]
This Diels-Alder reaction ([4+2] cycloaddition) is particularly interesting as there is a possibility of having two products: the endo and exo products. This is due to the fact that the dienophile is substituted and can approach in two different orientations. The exo product is formed when the bulk of the substituent approaches in such a way that it it pointing away from the pi-system of the diene. When it approaches with the bulk of the dienophile facing towards the pi system of the diene, the endo product is formed. This has implications for the energies of the products as will be discussed in the following sections.

[[File:Mo_2_eo1013.PNG|350px|thumb|center|Figure 5: MO diagram for the reaction of cyclohexadiene with 1,3-dioxole]]

The oxygen in either side of the dienophile have an electron donating effect on the p-orbitals of the double bond, causing the dienophile to be "electron rich" and raising the energy of the HOMO and LUMO, compared to ethene, as a result. As a consequence, as can illustrated in ''Figure 5'', the closest interaction is between the LUMO of the diene and the HOMO off the dienophile. Therefore, this is an example of an inverse electron demand reaction.<ref>J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, 2nd edn., 2012.</ref>

===Analysis of Molecular Orbitals===
As mentioned before, the oxygens on the dioxole work to raise the energy of the HOMO and LUMO of the diene compared to ethene. This increases the energy gap and leads to weaker interactions. An example of this is the HOMO-1 which is still lower in energy than the HOMO of the reactants as it only experiences a slight destabilisation. Only orbitals of the same symmetry can interact as seen below in ''Table 5'' and ''Table 6''.

<center>
{| class="wikitable"
|+ Table 6: Jmols for MOs in the TS on the way to the '''exo''' product.
|-
|
<jmol><jmolApplet>
<title>EXO TS - HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>EXO_TS_B3LYP_NEW.LOG</uploadedFileContents>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|
<jmol><jmolApplet>
<title>EXO TS - HOMO-1</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>EXO_TS_B3LYP_NEW.LOG</uploadedFileContents>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
|
<jmol><jmolApplet>
<title>EXO TS - LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>EXO_TS_B3LYP_NEW.LOG</uploadedFileContents>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|
<jmol><jmolApplet>
<title>EXO TS - LUMO+1</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>EXO_TS_B3LYP_NEW.LOG</uploadedFileContents>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|}
</center>

===Thermochemical Analysis===
<center>
{| class="wikitable" border="1"
|+ Table 7: Thermochemical data for the reaction of cyclohexadiene with 1,3-dioxole
! Product
! Reaction Barrier in kJ mol<sup>-1</sup>
! Reaction Energy in kJ mol<sup>-1</sup>
|-
| Endo || 158.47 || -68.75
|-
| Exo || 166.30 || -65.15
|}
</center>

GaussView 5.0.9 also calculates the free energies of these geometries which can allow for an in-depth analysis of the energetics of the reaction. A summary of this data is presented in ''Table 7''. The reaction barrier is calculated as the difference in energy between the TS and the starting materials. The endo product has a lower reaction barrier compared to the exo product, making it the kinetically-preferred product. This can be attributed to the extra stabilisation present in the endo transition state as a result of the secondary orbital interactions between the oxygens and the pi system on the diene. ''Figure 6'' shows the orbital interaction between the oxygen (red atoms) with the double bond from.

[[File:Oxygen_interaction_eo1013.PNG|350px|thumb|center|Figure 6: MO depicted by GaussView 5.0.9 showing the secondary orbital interactions in the endo TS.]]

The reaction energy is calculated as the free energy difference between the products and the reactants. Comparing the two shows that the endo reaction has a more negative reaction energy compared to the exo reaction, making the endo product the thermodynamically-preferred product. This can be rationalised, as seen in ''Figure 7'', by the location of the CH<sub>2</sub>s on the-5 membered ring. There is some steric clash with the CH<sub>2</sub> fragments in the exo product with he CH<sub>2</sub>s on the bridging carbons which isn't present in the endo product (making it more thermodynamically stable).

[[File:Interaction_eo1013.PNG|350px|thumb|center|Figure 7: A diagram showing the steric clashing of the CH<sub>2</sub> fragments.]]

The endo product is both the kinetic and thermodynamic product. This also agrees with experimental observations stating that in a [4+2] cycloaddition, the endo product is preferred, even if the exo product is more stable, due to favourable secondary orbital interactions in the TS.

===Relevant Files===
1,3-Dioxole (B3LYP-Optimised): [[File:DIOXOLE_B3LYP_eo1013.LOG]]

Cyclohexadiene (B3LYP-Optimised): [[File:CYCLOHEXADIENE_B3LYP_eo1013.LOG]]

Endo Product (B3LYP-Optimised): [[File:ENDO_PRODUCT_PM6_eo1013.LOG]]

Exo Product (B3LYP-Optimised): [[File:EXO_PRODUCT_END_B3LYP_eo1013.LOG]]

IRC of Endo Reaction (PM6 Optimised): [[File:IRC_PM6_ENDO_eo1013.LOG]]

IRC of Exo Reaction (PM6 Optimised): [[File:IRC_EXO_PM6_eo1013.LOG]]

==Exercise 3: O-xylylene + SO<sub>2</sub>==
[[File:Rxn_scheme_3_eo1013.PNG|350px|thumb|center|Figure 8: MO diagram for the reaction of o-xylylene with SO<sub>2</sub>]]

This is another example of another interesting Diels-Alder reaction ([4+2] cycloaddition). As well as having the endo and exo products, this reaction can react to give the chelotropic product where a 5-membered ring is formed with two new bonds both formed to the sulphur. The other caveat to this reaction is that the reaction can occur on the double bonds within the ring to produce three more products: endo, exo and chelotropic. The analysis will be discussed below.

===IRCs of the Exocyclic Reaction===
The IRCs were run showing the geometries along the reaction coordinate. From ''Figure 9'' and ''Figure 10'' is can be seen that the exo and endo reaction proceed with asynchronous bonding, with the oxygen bonding before the sulphur. ''Figure 11'' clearly shows that the chelotropic reaction bonding in a synchronous fashion.

<center>
[[File:Exo_irc_eo1013.gif|x500px|thumb|center|Figure 9: IRC showing the formation of the exo product]]
</center>

<center>
[[File:Endo_irc_eo1013.gif|x500px|thumb|center|Figure 10: IRC showing the formation of the endo product]]
</center>

<center>
[[File:Che_irc_eo1013.gif|x500px|thumb|center|Figure 11: IRC showing the formation of the cheloptopic product]]
</center>

===Thermochemical Analysis===
<center>
{| class="wikitable" border="1"
|+ Table 8: Thermochemical data for the reaction of o-xylylene with SO<sub>2</sub>
! Product
! Reaction Barrier in kJ mol<sup>-1</sup>
! Reaction Energy in kJ mol<sup>-1</sup>
|-
| Endo || 80.12 || -100.66
|-
| Exo || 84.11 || -101.31
|-
| Cheletropic || 102.44 || -157.65
|}
</center>

GaussView 5.0.9 was used to calculate the energetics of the three reactions at the PM6 level. From ''Table 8'' it can be seen that the chelotropic product has the lowest reaction energy and is therefore the thermodynamic product. A consideration of the bond enthalpies involved makes this quite clear, the formation of C-O and S-O is less favorable compared to the formation of S=O and S-C.<ref>PROPERTIES OF ATOMS, RADICALS, AND BONDS, http://labs.chem.ucsb.edu/zakarian/armen/11---bonddissociationenergy.pdf, (accessed December 2017)</ref> It also has the highest energy TS largely due to the the 5-membered ring in the TS which suffers from ring strain compared to 6-membered TS in the endo and exo reaction pathways. Because of this higher energy transition state, the other products will be expected to form in a greater proportion under equilibrium conditions.

[[File:Rxn_profile_3_eo1013.png|450px|thumb|right|Figure 12: Approximate Reaction profile of all three reaction pathways investigated for the reaction of o-xylylene with SO<sub>2</sub>]]

''Figure 12'' illustrates that the endo product has the lowest energy TS and is therefore the kinetic product. These reactions are all very favourable due to the fact that an aromatic ring in formed afterwards. The stabilisation due to aromatisiation is very desired as we can see that ir is large enough to compensate for the high TS energy of the chelotropic reaction. Looking at the IRCs we can see that the aromatic ring forms before the other bonds in the reaction.

===Relevant Files===
Sulphur Dioxide (PM6 Optimised): [[File:SO2_PM6_EO1013.LOG]]

O-xylylene (PM6 Optimised): [[File:XYLYLENE_NEW_PM6_EO1013.LOG]]

Chelotropic TS (PM6 Optimised): [[File:TS_OPTIMISED_FINAL_PM6_che_eo1013.LOG]]

Exo TS (PM6 Optimised): [[File:TS_PM6_FINAL_EXO_eo1013.LOG]]

Endo TS (PM6 Optimised): [[File:TS_PM6_ENDO_FINAL_eo1013.LOG]]

Chelotropic Product (PM6 Optimised): [[File:PRODUCTS_PM6_che_eo1013.LOG]]

Exo Product (PM6 Optimised): [[File:EXO_PRODUCT_PM6_FINAL_eo1013.LOG]]

Endo Product (PM6 Optimised): [[File:PRODUCTS_PM6_ENDO_FINAL_eo1013.LOG]]

===Alternative Reaction Pathway===
<center>
{| class="wikitable" border="1"
|+ Table 9: Thermochemical data for the reaction (alternative pathway) of o-xylylene with SO<sub>2</sub>
! Product
! Reaction Barrier in kJ mol<sup>-1</sup>
! Reaction Energy in kJ mol<sup>-1</sup>
|-
| Endo || 110.34 || 14.62
|-
| Exo || 118.18 || 19.06
|}
</center>

From ''Table 9'', it is clear that the products are less stable than the sum of the energies of the reactants at infinite separation, this is a strong indication that the reaction requires some energy input in order for it to occur (endothermic reaction). The reaction barriers are a lot higher in comparison to those in ''Table 8'' which makes sense as there is the lack of stablisation gained from forming an aromatic ring from this pathway. The IRCs (''Figure 13'' and ''Figure 14'') are shown below.

<center>
[[File:ALT_EXO_IRC_eo1013.gif|x500px|thumb|center|Figure 13: IRC showing the formation of the exo product through the alternative pathway]]
</center>

<center>
[[File:ALT_ENDO_IRC_eo1013.gif|x500px|thumb|center|Figure 14: IRC showing the formation of the endo product through the alternative pathway]]
</center>

===Relevant Files (Alternative Pathway)===

Alternative Exo TS (PM6 Optimised): [[File:TS_EXO_FINAL_PM6_ALT_eo1013.LOG]]

Alternative Endo TS (PM6 Optimised): [[File:TS_ENDO_FINAL_PM6_ALT_eo1013.LOG]]

Alternative Exo Product (PM6 Optimised): [[File:PRODUCT_EXO_PM6_ALT_eo013.LOG]]

Alternative Endo Product (PM6 Optimised): [[File:PRODUCT_ENDO_PM6_ALT_eo1013.LOG]]

==Conclusion==
In conclusion, the results from this lab agree with the established theory around Diels-Alder reactions. Using the PM6 allows for quick calculations that may not be so reliable but aid an understanding of the underlying chemistry. The B3LYP calculations are very reliable but are more expensive in terms of computational cost. GaussView 5.0.9 has proven to be a very useful tool in analysing the thermochemical data of reactions and visualising the MOs to understand favourable orientations for successful reactions.

''Exercise 1'' was useful in understanding the advantages and limitations of the computational methods chosen. Analyzing and comparing the C-C bond lengths reflected how close GaussView 5.0.9 can get to literature values. ''Exercise 2'' required more in-depth analysis of the energies of the optimised geometries and shows how effective computational chemistry can be in predicting the major product of a reaction. ''Exercise 3'' highlighted the importance of utilising our chemical intuition along with the computational methods to investigate alternative pathways to rationalise their feasibility which could prove useful in determining possible side reactions.

All in all, these exercises have shown that the computational approach is a very powerful one indeed and can be used to predict the course, outcomes and shortcomings of a reaction before even entering the lab. This has some very beneficial implications namely in the fact that money can be saved rather than being spent on reagents for a reaction that will not yield desired products. It also proves to be a very useful tool in understanding reaction dynamics/mechanisms.

===References===

Rep:Mod:EO1013TS

2017-12-19T23:33:22Z

Eo1013: /* Analysis of Molecular Orbitals */

==Introduction==
GaussView 5.0.9 is a very powerful program that allows for complex quantum mechanical calculation to be performed on molecules. It was used to investigate several aspects of three Diels-Alder reactions, the orbital interactions (primary and secondary) were moedlled and closely inspected as well as the energies and transition states to better understand the reaction paths of the examples studied.

===Potential Energy Surfaces (PES)===
The concept of PES is fundamental in computational chemistry and has allowed for many breakthroughs. A PES displays the relationship between the energy of a molecule and its geometry.

<math display="block">\text{Equation 1: General Time-dependent Schrödinger equation: } i \hbar \frac{\partial}{\partial t}\Psi(\mathbf{r},t) = \hat H \Psi(\mathbf{r},t)</math>

The energies can be calculated using different computational methods that simplify and solve the Schrödinger equation (''Eqn 1'') using approximations allowing PES to be generated in very little time. A PES conatains a lot of information, namely global and local minima that represent stable confomers/rotamers of the same molecule with the transition state that links them.<ref>The Concept of PES, http://is.muni.cz/el/1431/podzim2015/C9920/um/The_concept_of_PES.pdf, (accessed December 2017)</ref>

===The Transition State (TS) and Minima===
In GaussView 5.0.9 there are various methods (discussed below) to allow for the calculation of energies after optimising a particular geometry to a minimum energy taking into account electron repulsion and several other factors. Methods have also been devised, making use of known atomic separations during transitions to hazard a guess at the TS before performing optimising calculations and running an Intrinsic Reaction Coordinate (IRC) calculation can be performed to plot a reaction profile diagram.

The value of gradient on the PES at the minimum and at the transition structure will both be zero. Minima will have a positive value for the second derivative in every axial direction of the energy potential surface whereas a TS will have a positive value for the second derivative (saddle point) in all axial directions apart from in the reaction coordinate. This means that at a minima, movement in any direction either side of that point will results in a geometry with a higher energy. The same is true for the TS but there is a decrease in energy in one dimension which is known as the reaction pathway. The PES has 3N-6 dimensions, where N is the number of atoms in the molecule of study, corresponding to the degrees of freedom available to the molecule. Running an IRC calculation on the Ts structure allows as to track the geometries along this pathway.<ref>Gaussian – Vibration Analysis in Gaussian, http://gaussian.com/vib, (accessed December 2017)</ref>

The TS is a saddle point and just like a minima or a maxima, its first derivative will be zero. The difference however is apparent when you take the second derivative, which is done using a Hessian matrix in GaussView 5.0.9. The second derivative correlates to the energy and therefore the frequency and force constant of the vibrations in the molecule. As a result, minima always have positive force constants (increases in energy) and the TS, being a saddle point, will have at least one negative force constant (producing an imaginary vibration) which corresponds to the reaction pathway.

===Methods to Locate The TS===
In this investigation, three main methods were used to find the transition state.

'''Method 1:''' This method only works if one has prior knowledge of the transition state. The transition state is guessed using empirically observed bond lengths and a minimisation calculation is performed. If these lengths are wrong, undesired structures could form.

'''Method 2:''' This method also requires prior knowledge of the transition state. A guess of the TS is made and the bonds involved in the reaction are frozen before a minimisation calculation is performed. This structure is then optimised to a TS and is more reliable that '''Method 1'''.

'''Method 3:''' This method does not require prior knowledge of the transition state as you start with the product or reactants (optimised to a minimum). Bonds are then added or removed to closer resemble the TS and similar to '''Method 2''', these are frozen to obtain a minimum. However, It is not very reliable for TS geometries that do not resemble
the minima.

===Computational Methods===
The PM6 and B3LYP methods were used in this lab. PM6 is a semi-empirical method which simplifies the Hartree-Fock method by using empirical data and pre-determined integrals to solve Hamiltonian (the energy operator of the Schrödinger equation) and as a result, runs very quickly as less calculations need to be performed. With all the approximations and generic data used in this method, results are often inaccurate.<ref>Gaussian – Semi-Empirical Methods, http://gaussian.com/semiempirical, (accessed December 2017)</ref>

B3LYP, on the other hand, is a hybrid method that uses elements of Hartree-Fock and Density Funtional Theory (DFT). This method is more expensive than the PM6 as it doesn't use pre-determined integrals: it uses the DFT method to calculate all of the terms of the Hamiltonian apart from the exchange correlation term which is done using a HF method. It gives a very reliable results.<ref>What is B33LYP?, http://www.quora.com/What-is-B3LYP-and-why-is-it-the-most-popular-functional-in-DFT, (accessed December 2017)</ref><ref name=":0">A. Szabo and N. S. Ostlund, ''Modern Quantum Chemistry'', Dover Publications, 1989.</ref>

==Exercise 1: Butadiene + Ethene==
[[File:Reaction_scheme_1_eo1013.png|350px|thumb|center|Figure 1: Reaction Scheme for Butadiene with Ethene]]

This reaction is a [4+2] cycloaddition. Butadiene and ethene react together to form cyclohexene. The diene is more electron-rich than the dienophile. As can be seen from ''Figure 2'', the HOMO of butadiene contributes more to the HOMO-1 of the TS. In addition, the LUMO on ethene contributes more to the LUMO+1 which shows that HOMO of butadiene is lower in energy than the LUMO of ethene. This is an example of a normal electron demand reaction as the closest interaction is between the HOMO of the diene and the LUMO off the dienophile.<ref>J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, 2nd edn., 2012.</ref>

[[File:MO_1_eo1013.jpg|350px|thumb|center|Figure 2: MO Diagram showing orbital interactions in the reaction of Butadiene with Ethene]]

===Analysis of Molecular Orbitals===
A non-zero overlap integral is required in order for an orbital interaction to be favourable. Orbitals involved in this interaction must have the same symmetry as the overlap integral is proportional to the spatial overlap of the orbitals in question. For a non zero overlap, the orbitals must both be symmetric or asymmetric to give overall symmetric function. An anti-symmetric function will be gained when you combine orbitals of different symmetry which will leads overlap integral being zero.<ref>P. W. Atkins and J. De. Paula, ''Atkins' Physical Chemistry'', Oxford University Press, 9th edn., 2006.</ref>

<center>
{| class="wikitable"
|+ Table 1: Jmols for MOs in the dineophile (ethene).
|
<jmol><jmolApplet>
<title>Ethene - HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ETHENE_INITIAL_PM6_eo1013.LOG</uploadedFileContents>
<script>frame 12; mo 6; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|
<jmol><jmolApplet>
<title>Ethene - LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ETHENE_INITIAL_PM6_eo1013.LOG</uploadedFileContents>
<script>frame 12; mo 7; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|}
</center>

<center>
{| class="wikitable"
|+ Table 2: Jmols for MOs in the diene (butadiene).
|
<jmol><jmolApplet>
<title>Ethene - HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BUTADIENE_INITIAL_PM6_NEW_eo1013.LOG</uploadedFileContents>
<script>frame 22; mo 11; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|
<jmol><jmolApplet>
<title>Ethene - LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BUTADIENE_INITIAL_PM6_NEW_eo1013.LOG</uploadedFileContents>
<script>frame 22; mo 12; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|}
</center>

<center>
{| class="wikitable"
|+ Table 3: Jmols for MOs in the TS on the way to the product (cyclohexene).
|-
|
<jmol><jmolApplet>
<title>TS - HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG</uploadedFileContents>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|
<jmol><jmolApplet>
<title>TS - HOMO-1</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG</uploadedFileContents>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
|
<jmol><jmolApplet>
<title>TS - LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG</uploadedFileContents>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|
<jmol><jmolApplet>
<title>TS - LUMO+1</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG</uploadedFileContents>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|}
</center>

<center>
{| class="wikitable"
|+ Table 5: Jmols for MOs in the TS on the way to the '''endo''' product.
|-
|
<jmol><jmolApplet>
<title>ENDO TS - HOMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ENDO_TS_B3LYP_NEW.LOG</uploadedFileContents>
<script>frame 50; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|
<jmol><jmolApplet>
<title>ENDO TS - HOMO-1</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ENDO_TS_B3LYP_NEW.LOG</uploadedFileContents>
<script>frame 50; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
|
<jmol><jmolApplet>
<title>ENDO TS - LUMO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ENDO_TS_B3LYP_NEW.LOG</uploadedFileContents>
<script>frame 50; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|
<jmol><jmolApplet>
<title>ENDO TS - LUMO+1</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ENDO_TS_B3LYP_NEW.LOG</uploadedFileContents>
<script>frame 50; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|}
</center>

Looking at the HOMO and the LUMO of the TS in ''Table 3'', it is clear that they are formed from the HOMO of ethene and the LUMO of butadiene, both being symmetric orbitals. The opposite interaction from two antisymetic orbitals, the HOMO of butadiene and LUMO of ethene, give the HOMO-1 and the LUMO+1 of the TS. This clearly demonstrates that reactions can only be allowed when orbitals of the same symmetry can interact. Transition states that are of a geometry where orbitals of opposite symmetry are forced to interact will most likely lead to an unsuccessful reaction.

===Analysis of Bond Lengths===
<center>
{| class="wikitable" border="1"
|+ Table 4: Bond lengths (from ''Figure 1'') during the course of the reaction (Å)
! Bonds
! Cyclohexene
! Transition State
! Butadiene and Ethene
|-
| '''C1-C2''' || 1.501 || 1.380 || 1.335
|-
| '''C2-C3''' || 1.338 || 1.441 || 1.468
|-
| '''C3-C4''' || 1.501 || 1.380 || 1.335
|-
| '''C4-C5''' || 1.540 || 2.115 || ----
|-
| '''C5-C6''' || 1.541 || 1.382 || 1.327
|-
| '''C6-C1''' || 1.540 || 2.115 || ----
|}
</center>

A typical carbon to carbon single bond length is 1.54 Å and a double bond is 1.34 Å.<ref>L. Pauling and L. O. Brockway, ''ELECTRON DIFFRACTION INVESTIGATION OF SOME HYDROCARBONS'', California Institute of Technology, 1937.</ref> These are a direct match with the bond lengths predicted by Gaussian. C1-C2 and C3-C4 are a lot shorter due to the pulling effect of the higher electron density in C2-C3. As the carbons change from and sp3 hybridised orbitals to sp2, the bond lengths shorten and vice versa. Both double bonds on butadiene also lengthen as they change from sp2 to sp3 hybridisation. The two new bonds (C4-C5 and C6-C1) that form in the TS have a bond length (2.115 Å) that is smaller than two times the Van der Waal radius of carbon (1.7 Å) showing that the two molecules are starting to interact during the transition state and get shorter once the bond forms into a single C-C bond.<ref>A. Bondi, ''van der Waals Volumes and Radii '', J. Phys. Chem., vol. 68 #3, 1964.</ref>

===The Transition State===
<center>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>350</size>
<uploadedFileContents>BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 7; frank off; vector on; vector scale -4; vector 0.04; color vectors red</script>
<name>CPD_Dimer_TS</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle vibrate</text>
<target>CPD_Dimer_TS</target>
</jmolbutton>
</jmol>
</center>

The vibration above (click toggle vibration) corresponds to the negative frequency in the TS calculations a result of the negative force constant. The bond formation is synchronous as the carbons at both ends of the new bonds are moving at the same time in the TS. This can also seen in the IRC (Figure 3) as the bonds are formed at the same time.

<center>
[[File:IRC.gif|350px|thumb|center|Figure 3: IRC showing the formation of the two new bonds]]
</center>

===Relevant Files===
Product (PM6-Optimised): [[File:PRODUCTS_PM6_eo1016.LOG]]

TS of Reaction (PM6 Optimised): [[File:BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG]]

IRC of Reaction: [[File:BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG]]

==Exercise 2: Reaction of Cyclohexadiene + 1,3-Dioxole==
[[File:Rxn_scheme_eo1013.png|350px|thumb|center|Figure 4: Reaction Scheme for cyclohexadiene with 1,3-dioxole]]
This Diels-Alder reaction ([4+2] cycloaddition) is particularly interesting as there is a possibility of having two products: the endo and exo products. This is due to the fact that the dienophile is substituted and can approach in two different orientations. The exo product is formed when the bulk of the substituent approaches in such a way that it it pointing away from the pi-system of the diene. When it approaches with the bulk of the dienophile facing towards the pi system of the diene, the endo product is formed. This has implications for the energies of the products as will be discussed in the following sections.

[[File:Mo_2_eo1013.PNG|350px|thumb|center|Figure 5: MO diagram for the reaction of cyclohexadiene with 1,3-dioxole]]

The oxygen in either side of the dienophile have an electron donating effect on the p-orbitals of the double bond, causing the dienophile to be "electron rich" and raising the energy of the HOMO and LUMO, compared to ethene, as a result. As a consequence, as can illustrated in ''Figure 5'', the closest interaction is between the LUMO of the diene and the HOMO off the dienophile. Therefore, this is an example of an inverse electron demand reaction.<ref>J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, 2nd edn., 2012.</ref>

===Analysis of Molecular Orbitals===
As mentioned before, the oxygens on the dioxole work to raise the energy of the HOMO and LUMO of the diene compared to ethene. This increases the energy gap and leads to weaker interactions. An example of this is the HOMO-1 which is still lower in energy than the HOMO of the reactants as it only experiences a slight destabilisation. Only orbitals of the same symmetry can interact as seen below in ''Table 5'' and ''Table 6''.

JMOL BLUB 2 + 3

===Thermochemical Analysis===
<center>
{| class="wikitable" border="1"
|+ Table 7: Thermochemical data for the reaction of cyclohexadiene with 1,3-dioxole
! Product
! Reaction Barrier in kJ mol<sup>-1</sup>
! Reaction Energy in kJ mol<sup>-1</sup>
|-
| Endo || 158.47 || -68.75
|-
| Exo || 166.30 || -65.15
|}
</center>

GaussView 5.0.9 also calculates the free energies of these geometries which can allow for an in-depth analysis of the energetics of the reaction. A summary of this data is presented in ''Table 7''. The reaction barrier is calculated as the difference in energy between the TS and the starting materials. The endo product has a lower reaction barrier compared to the exo product, making it the kinetically-preferred product. This can be attributed to the extra stabilisation present in the endo transition state as a result of the secondary orbital interactions between the oxygens and the pi system on the diene. ''Figure 6'' shows the orbital interaction between the oxygen (red atoms) with the double bond from.

[[File:Oxygen_interaction_eo1013.PNG|350px|thumb|center|Figure 6: MO depicted by GaussView 5.0.9 showing the secondary orbital interactions in the endo TS.]]

The reaction energy is calculated as the free energy difference between the products and the reactants. Comparing the two shows that the endo reaction has a more negative reaction energy compared to the exo reaction, making the endo product the thermodynamically-preferred product. This can be rationalised, as seen in ''Figure 7'', by the location of the CH<sub>2</sub>s on the-5 membered ring. There is some steric clash with the CH<sub>2</sub> fragments in the exo product with he CH<sub>2</sub>s on the bridging carbons which isn't present in the endo product (making it more thermodynamically stable).

[[File:Interaction_eo1013.PNG|350px|thumb|center|Figure 7: A diagram showing the steric clashing of the CH<sub>2</sub> fragments.]]

The endo product is both the kinetic and thermodynamic product. This also agrees with experimental observations stating that in a [4+2] cycloaddition, the endo product is preferred, even if the exo product is more stable, due to favourable secondary orbital interactions in the TS.

===Relevant Files===
1,3-Dioxole (B3LYP-Optimised): [[File:DIOXOLE_B3LYP_eo1013.LOG]]

Cyclohexadiene (B3LYP-Optimised): [[File:CYCLOHEXADIENE_B3LYP_eo1013.LOG]]

Endo Product (B3LYP-Optimised): [[File:ENDO_PRODUCT_PM6_eo1013.LOG]]

Exo Product (B3LYP-Optimised): [[File:EXO_PRODUCT_END_B3LYP_eo1013.LOG]]

IRC of Endo Reaction (PM6 Optimised): [[File:IRC_PM6_ENDO_eo1013.LOG]]

IRC of Exo Reaction (PM6 Optimised): [[File:IRC_EXO_PM6_eo1013.LOG]]

==Exercise 3: O-xylylene + SO<sub>2</sub>==
[[File:Rxn_scheme_3_eo1013.PNG|350px|thumb|center|Figure 8: MO diagram for the reaction of o-xylylene with SO<sub>2</sub>]]

This is another example of another interesting Diels-Alder reaction ([4+2] cycloaddition). As well as having the endo and exo products, this reaction can react to give the chelotropic product where a 5-membered ring is formed with two new bonds both formed to the sulphur. The other caveat to this reaction is that the reaction can occur on the double bonds within the ring to produce three more products: endo, exo and chelotropic. The analysis will be discussed below.

===IRCs of the Exocyclic Reaction===
The IRCs were run showing the geometries along the reaction coordinate. From ''Figure 9'' and ''Figure 10'' is can be seen that the exo and endo reaction proceed with asynchronous bonding, with the oxygen bonding before the sulphur. ''Figure 11'' clearly shows that the chelotropic reaction bonding in a synchronous fashion.

<center>
[[File:Exo_irc_eo1013.gif|x500px|thumb|center|Figure 9: IRC showing the formation of the exo product]]
</center>

<center>
[[File:Endo_irc_eo1013.gif|x500px|thumb|center|Figure 10: IRC showing the formation of the endo product]]
</center>

<center>
[[File:Che_irc_eo1013.gif|x500px|thumb|center|Figure 11: IRC showing the formation of the cheloptopic product]]
</center>

===Thermochemical Analysis===
<center>
{| class="wikitable" border="1"
|+ Table 8: Thermochemical data for the reaction of o-xylylene with SO<sub>2</sub>
! Product
! Reaction Barrier in kJ mol<sup>-1</sup>
! Reaction Energy in kJ mol<sup>-1</sup>
|-
| Endo || 80.12 || -100.66
|-
| Exo || 84.11 || -101.31
|-
| Cheletropic || 102.44 || -157.65
|}
</center>

GaussView 5.0.9 was used to calculate the energetics of the three reactions at the PM6 level. From ''Table 8'' it can be seen that the chelotropic product has the lowest reaction energy and is therefore the thermodynamic product. A consideration of the bond enthalpies involved makes this quite clear, the formation of C-O and S-O is less favorable compared to the formation of S=O and S-C.<ref>PROPERTIES OF ATOMS, RADICALS, AND BONDS, http://labs.chem.ucsb.edu/zakarian/armen/11---bonddissociationenergy.pdf, (accessed December 2017)</ref> It also has the highest energy TS largely due to the the 5-membered ring in the TS which suffers from ring strain compared to 6-membered TS in the endo and exo reaction pathways. Because of this higher energy transition state, the other products will be expected to form in a greater proportion under equilibrium conditions.

[[File:Rxn_profile_3_eo1013.png|450px|thumb|right|Figure 12: Approximate Reaction profile of all three reaction pathways investigated for the reaction of o-xylylene with SO<sub>2</sub>]]

''Figure 12'' illustrates that the endo product has the lowest energy TS and is therefore the kinetic product. These reactions are all very favourable due to the fact that an aromatic ring in formed afterwards. The stabilisation due to aromatisiation is very desired as we can see that ir is large enough to compensate for the high TS energy of the chelotropic reaction. Looking at the IRCs we can see that the aromatic ring forms before the other bonds in the reaction.

===Relevant Files===
Sulphur Dioxide (PM6 Optimised): [[File:SO2_PM6_EO1013.LOG]]

O-xylylene (PM6 Optimised): [[File:XYLYLENE_NEW_PM6_EO1013.LOG]]

Chelotropic TS (PM6 Optimised): [[File:TS_OPTIMISED_FINAL_PM6_che_eo1013.LOG]]

Exo TS (PM6 Optimised): [[File:TS_PM6_FINAL_EXO_eo1013.LOG]]

Endo TS (PM6 Optimised): [[File:TS_PM6_ENDO_FINAL_eo1013.LOG]]

Chelotropic Product (PM6 Optimised): [[File:PRODUCTS_PM6_che_eo1013.LOG]]

Exo Product (PM6 Optimised): [[File:EXO_PRODUCT_PM6_FINAL_eo1013.LOG]]

Endo Product (PM6 Optimised): [[File:PRODUCTS_PM6_ENDO_FINAL_eo1013.LOG]]

===Alternative Reaction Pathway===
<center>
{| class="wikitable" border="1"
|+ Table 9: Thermochemical data for the reaction (alternative pathway) of o-xylylene with SO<sub>2</sub>
! Product
! Reaction Barrier in kJ mol<sup>-1</sup>
! Reaction Energy in kJ mol<sup>-1</sup>
|-
| Endo || 110.34 || 14.62
|-
| Exo || 118.18 || 19.06
|}
</center>

From ''Table 9'', it is clear that the products are less stable than the sum of the energies of the reactants at infinite separation, this is a strong indication that the reaction requires some energy input in order for it to occur (endothermic reaction). The reaction barriers are a lot higher in comparison to those in ''Table 8'' which makes sense as there is the lack of stablisation gained from forming an aromatic ring from this pathway. The IRCs (''Figure 13'' and ''Figure 14'') are shown below.

<center>
[[File:ALT_EXO_IRC_eo1013.gif|x500px|thumb|center|Figure 13: IRC showing the formation of the exo product through the alternative pathway]]
</center>

<center>
[[File:ALT_ENDO_IRC_eo1013.gif|x500px|thumb|center|Figure 14: IRC showing the formation of the endo product through the alternative pathway]]
</center>

===Relevant Files (Alternative Pathway)===

Alternative Exo TS (PM6 Optimised): [[File:TS_EXO_FINAL_PM6_ALT_eo1013.LOG]]

Alternative Endo TS (PM6 Optimised): [[File:TS_ENDO_FINAL_PM6_ALT_eo1013.LOG]]

Alternative Exo Product (PM6 Optimised): [[File:PRODUCT_EXO_PM6_ALT_eo013.LOG]]

Alternative Endo Product (PM6 Optimised): [[File:PRODUCT_ENDO_PM6_ALT_eo1013.LOG]]

==Conclusion==
In conclusion, the results from this lab agree with the established theory around Diels-Alder reactions. Using the PM6 allows for quick calculations that may not be so reliable but aid an understanding of the underlying chemistry. The B3LYP calculations are very reliable but are more expensive in terms of computational cost. GaussView 5.0.9 has proven to be a very useful tool in analysing the thermochemical data of reactions and visualising the MOs to understand favourable orientations for successful reactions.

''Exercise 1'' was useful in understanding the advantages and limitations of the computational methods chosen. Analyzing and comparing the C-C bond lengths reflected how close GaussView 5.0.9 can get to literature values. ''Exercise 2'' required more in-depth analysis of the energies of the optimised geometries and shows how effective computational chemistry can be in predicting the major product of a reaction. ''Exercise 3'' highlighted the importance of utilising our chemical intuition along with the computational methods to investigate alternative pathways to rationalise their feasibility which could prove useful in determining possible side reactions.

All in all, these exercises have shown that the computational approach is a very powerful one indeed and can be used to predict the course, outcomes and shortcomings of a reaction before even entering the lab. This has some very beneficial implications namely in the fact that money can be saved rather than being spent on reagents for a reaction that will not yield desired products. It also proves to be a very useful tool in understanding reaction dynamics/mechanisms.

===References===

Rep:Mod:EO1013TS

2017-12-19T23:32:13Z

Eo1013:

==Introduction==
GaussView 5.0.9 is a very powerful program that allows for complex quantum mechanical calculation to be performed on molecules. It was used to investigate several aspects of three Diels-Alder reactions, the orbital interactions (primary and secondary) were moedlled and closely inspected as well as the energies and transition states to better understand the reaction paths of the examples studied.

===Potential Energy Surfaces (PES)===
The concept of PES is fundamental in computational chemistry and has allowed for many breakthroughs. A PES displays the relationship between the energy of a molecule and its geometry.

<math display="block">\text{Equation 1: General Time-dependent Schrödinger equation: } i \hbar \frac{\partial}{\partial t}\Psi(\mathbf{r},t) = \hat H \Psi(\mathbf{r},t)</math>

The energies can be calculated using different computational methods that simplify and solve the Schrödinger equation (''Eqn 1'') using approximations allowing PES to be generated in very little time. A PES conatains a lot of information, namely global and local minima that represent stable confomers/rotamers of the same molecule with the transition state that links them.<ref>The Concept of PES, http://is.muni.cz/el/1431/podzim2015/C9920/um/The_concept_of_PES.pdf, (accessed December 2017)</ref>

===The Transition State (TS) and Minima===
In GaussView 5.0.9 there are various methods (discussed below) to allow for the calculation of energies after optimising a particular geometry to a minimum energy taking into account electron repulsion and several other factors. Methods have also been devised, making use of known atomic separations during transitions to hazard a guess at the TS before performing optimising calculations and running an Intrinsic Reaction Coordinate (IRC) calculation can be performed to plot a reaction profile diagram.

The value of gradient on the PES at the minimum and at the transition structure will both be zero. Minima will have a positive value for the second derivative in every axial direction of the energy potential surface whereas a TS will have a positive value for the second derivative (saddle point) in all axial directions apart from in the reaction coordinate. This means that at a minima, movement in any direction either side of that point will results in a geometry with a higher energy. The same is true for the TS but there is a decrease in energy in one dimension which is known as the reaction pathway. The PES has 3N-6 dimensions, where N is the number of atoms in the molecule of study, corresponding to the degrees of freedom available to the molecule. Running an IRC calculation on the Ts structure allows as to track the geometries along this pathway.<ref>Gaussian – Vibration Analysis in Gaussian, http://gaussian.com/vib, (accessed December 2017)</ref>

The TS is a saddle point and just like a minima or a maxima, its first derivative will be zero. The difference however is apparent when you take the second derivative, which is done using a Hessian matrix in GaussView 5.0.9. The second derivative correlates to the energy and therefore the frequency and force constant of the vibrations in the molecule. As a result, minima always have positive force constants (increases in energy) and the TS, being a saddle point, will have at least one negative force constant (producing an imaginary vibration) which corresponds to the reaction pathway.

===Methods to Locate The TS===
In this investigation, three main methods were used to find the transition state.

'''Method 1:''' This method only works if one has prior knowledge of the transition state. The transition state is guessed using empirically observed bond lengths and a minimisation calculation is performed. If these lengths are wrong, undesired structures could form.

'''Method 2:''' This method also requires prior knowledge of the transition state. A guess of the TS is made and the bonds involved in the reaction are frozen before a minimisation calculation is performed. This structure is then optimised to a TS and is more reliable that '''Method 1'''.

'''Method 3:''' This method does not require prior knowledge of the transition state as you start with the product or reactants (optimised to a minimum). Bonds are then added or removed to closer resemble the TS and similar to '''Method 2''', these are frozen to obtain a minimum. However, It is not very reliable for TS geometries that do not resemble
the minima.

===Computational Methods===
The PM6 and B3LYP methods were used in this lab. PM6 is a semi-empirical method which simplifies the Hartree-Fock method by using empirical data and pre-determined integrals to solve Hamiltonian (the energy operator of the Schrödinger equation) and as a result, runs very quickly as less calculations need to be performed. With all the approximations and generic data used in this method, results are often inaccurate.<ref>Gaussian – Semi-Empirical Methods, http://gaussian.com/semiempirical, (accessed December 2017)</ref>

B3LYP, on the other hand, is a hybrid method that uses elements of Hartree-Fock and Density Funtional Theory (DFT). This method is more expensive than the PM6 as it doesn't use pre-determined integrals: it uses the DFT method to calculate all of the terms of the Hamiltonian apart from the exchange correlation term which is done using a HF method. It gives a very reliable results.<ref>What is B33LYP?, http://www.quora.com/What-is-B3LYP-and-why-is-it-the-most-popular-functional-in-DFT, (accessed December 2017)</ref><ref name=":0">A. Szabo and N. S. Ostlund, ''Modern Quantum Chemistry'', Dover Publications, 1989.</ref>

==Exercise 1: Butadiene + Ethene==
[[File:Reaction_scheme_1_eo1013.png|350px|thumb|center|Figure 1: Reaction Scheme for Butadiene with Ethene]]

This reaction is a [4+2] cycloaddition. Butadiene and ethene react together to form cyclohexene. The diene is more electron-rich than the dienophile. As can be seen from ''Figure 2'', the HOMO of butadiene contributes more to the HOMO-1 of the TS. In addition, the LUMO on ethene contributes more to the LUMO+1 which shows that HOMO of butadiene is lower in energy than the LUMO of ethene. This is an example of a normal electron demand reaction as the closest interaction is between the HOMO of the diene and the LUMO off the dienophile.<ref>J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, 2nd edn., 2012.</ref>

[[File:MO_1_eo1013.jpg|350px|thumb|center|Figure 2: MO Diagram showing orbital interactions in the reaction of Butadiene with Ethene]]

===Analysis of Molecular Orbitals===
A non-zero overlap integral is required in order for an orbital interaction to be favourable. Orbitals involved in this interaction must have the same symmetry as the overlap integral is proportional to the spatial overlap of the orbitals in question. For a non zero overlap, the orbitals must both be symmetric or asymmetric to give overall symmetric function. An anti-symmetric function will be gained when you combine orbitals of different symmetry which will leads overlap integral being zero.<ref>P. W. Atkins and J. De. Paula, ''Atkins' Physical Chemistry'', Oxford University Press, 9th edn., 2006.</ref>

Jmol BLURB 1

Looking at the HOMO and the LUMO of the TS in ''Table 3'', it is clear that they are formed from the HOMO of ethene and the LUMO of butadiene, both being symmetric orbitals. The opposite interaction from two antisymetic orbitals, the HOMO of butadiene and LUMO of ethene, give the HOMO-1 and the LUMO+1 of the TS. This clearly demonstrates that reactions can only be allowed when orbitals of the same symmetry can interact. Transition states that are of a geometry where orbitals of opposite symmetry are forced to interact will most likely lead to an unsuccessful reaction.

===Analysis of Bond Lengths===
<center>
{| class="wikitable" border="1"
|+ Table 4: Bond lengths (from ''Figure 1'') during the course of the reaction (Å)
! Bonds
! Cyclohexene
! Transition State
! Butadiene and Ethene
|-
| '''C1-C2''' || 1.501 || 1.380 || 1.335
|-
| '''C2-C3''' || 1.338 || 1.441 || 1.468
|-
| '''C3-C4''' || 1.501 || 1.380 || 1.335
|-
| '''C4-C5''' || 1.540 || 2.115 || ----
|-
| '''C5-C6''' || 1.541 || 1.382 || 1.327
|-
| '''C6-C1''' || 1.540 || 2.115 || ----
|}
</center>

A typical carbon to carbon single bond length is 1.54 Å and a double bond is 1.34 Å.<ref>L. Pauling and L. O. Brockway, ''ELECTRON DIFFRACTION INVESTIGATION OF SOME HYDROCARBONS'', California Institute of Technology, 1937.</ref> These are a direct match with the bond lengths predicted by Gaussian. C1-C2 and C3-C4 are a lot shorter due to the pulling effect of the higher electron density in C2-C3. As the carbons change from and sp3 hybridised orbitals to sp2, the bond lengths shorten and vice versa. Both double bonds on butadiene also lengthen as they change from sp2 to sp3 hybridisation. The two new bonds (C4-C5 and C6-C1) that form in the TS have a bond length (2.115 Å) that is smaller than two times the Van der Waal radius of carbon (1.7 Å) showing that the two molecules are starting to interact during the transition state and get shorter once the bond forms into a single C-C bond.<ref>A. Bondi, ''van der Waals Volumes and Radii '', J. Phys. Chem., vol. 68 #3, 1964.</ref>

===The Transition State===
<center>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>350</size>
<uploadedFileContents>BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 7; frank off; vector on; vector scale -4; vector 0.04; color vectors red</script>
<name>CPD_Dimer_TS</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle vibrate</text>
<target>CPD_Dimer_TS</target>
</jmolbutton>
</jmol>
</center>

The vibration above (click toggle vibration) corresponds to the negative frequency in the TS calculations a result of the negative force constant. The bond formation is synchronous as the carbons at both ends of the new bonds are moving at the same time in the TS. This can also seen in the IRC (Figure 3) as the bonds are formed at the same time.

<center>
[[File:IRC.gif|350px|thumb|center|Figure 3: IRC showing the formation of the two new bonds]]
</center>

===Relevant Files===
Product (PM6-Optimised): [[File:PRODUCTS_PM6_eo1016.LOG]]

TS of Reaction (PM6 Optimised): [[File:BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG]]

IRC of Reaction: [[File:BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG]]

==Exercise 2: Reaction of Cyclohexadiene + 1,3-Dioxole==
[[File:Rxn_scheme_eo1013.png|350px|thumb|center|Figure 4: Reaction Scheme for cyclohexadiene with 1,3-dioxole]]
This Diels-Alder reaction ([4+2] cycloaddition) is particularly interesting as there is a possibility of having two products: the endo and exo products. This is due to the fact that the dienophile is substituted and can approach in two different orientations. The exo product is formed when the bulk of the substituent approaches in such a way that it it pointing away from the pi-system of the diene. When it approaches with the bulk of the dienophile facing towards the pi system of the diene, the endo product is formed. This has implications for the energies of the products as will be discussed in the following sections.

[[File:Mo_2_eo1013.PNG|350px|thumb|center|Figure 5: MO diagram for the reaction of cyclohexadiene with 1,3-dioxole]]

The oxygen in either side of the dienophile have an electron donating effect on the p-orbitals of the double bond, causing the dienophile to be "electron rich" and raising the energy of the HOMO and LUMO, compared to ethene, as a result. As a consequence, as can illustrated in ''Figure 5'', the closest interaction is between the LUMO of the diene and the HOMO off the dienophile. Therefore, this is an example of an inverse electron demand reaction.<ref>J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, 2nd edn., 2012.</ref>

===Analysis of Molecular Orbitals===
As mentioned before, the oxygens on the dioxole work to raise the energy of the HOMO and LUMO of the diene compared to ethene. This increases the energy gap and leads to weaker interactions. An example of this is the HOMO-1 which is still lower in energy than the HOMO of the reactants as it only experiences a slight destabilisation. Only orbitals of the same symmetry can interact as seen below in ''Table 5'' and ''Table 6''.

JMOL BLUB 2 + 3

===Thermochemical Analysis===
<center>
{| class="wikitable" border="1"
|+ Table 7: Thermochemical data for the reaction of cyclohexadiene with 1,3-dioxole
! Product
! Reaction Barrier in kJ mol<sup>-1</sup>
! Reaction Energy in kJ mol<sup>-1</sup>
|-
| Endo || 158.47 || -68.75
|-
| Exo || 166.30 || -65.15
|}
</center>

GaussView 5.0.9 also calculates the free energies of these geometries which can allow for an in-depth analysis of the energetics of the reaction. A summary of this data is presented in ''Table 7''. The reaction barrier is calculated as the difference in energy between the TS and the starting materials. The endo product has a lower reaction barrier compared to the exo product, making it the kinetically-preferred product. This can be attributed to the extra stabilisation present in the endo transition state as a result of the secondary orbital interactions between the oxygens and the pi system on the diene. ''Figure 6'' shows the orbital interaction between the oxygen (red atoms) with the double bond from.

[[File:Oxygen_interaction_eo1013.PNG|350px|thumb|center|Figure 6: MO depicted by GaussView 5.0.9 showing the secondary orbital interactions in the endo TS.]]

The reaction energy is calculated as the free energy difference between the products and the reactants. Comparing the two shows that the endo reaction has a more negative reaction energy compared to the exo reaction, making the endo product the thermodynamically-preferred product. This can be rationalised, as seen in ''Figure 7'', by the location of the CH<sub>2</sub>s on the-5 membered ring. There is some steric clash with the CH<sub>2</sub> fragments in the exo product with he CH<sub>2</sub>s on the bridging carbons which isn't present in the endo product (making it more thermodynamically stable).

[[File:Interaction_eo1013.PNG|350px|thumb|center|Figure 7: A diagram showing the steric clashing of the CH<sub>2</sub> fragments.]]

The endo product is both the kinetic and thermodynamic product. This also agrees with experimental observations stating that in a [4+2] cycloaddition, the endo product is preferred, even if the exo product is more stable, due to favourable secondary orbital interactions in the TS.

===Relevant Files===
1,3-Dioxole (B3LYP-Optimised): [[File:DIOXOLE_B3LYP_eo1013.LOG]]

Cyclohexadiene (B3LYP-Optimised): [[File:CYCLOHEXADIENE_B3LYP_eo1013.LOG]]

Endo Product (B3LYP-Optimised): [[File:ENDO_PRODUCT_PM6_eo1013.LOG]]

Exo Product (B3LYP-Optimised): [[File:EXO_PRODUCT_END_B3LYP_eo1013.LOG]]

IRC of Endo Reaction (PM6 Optimised): [[File:IRC_PM6_ENDO_eo1013.LOG]]

IRC of Exo Reaction (PM6 Optimised): [[File:IRC_EXO_PM6_eo1013.LOG]]

==Exercise 3: O-xylylene + SO<sub>2</sub>==
[[File:Rxn_scheme_3_eo1013.PNG|350px|thumb|center|Figure 8: MO diagram for the reaction of o-xylylene with SO<sub>2</sub>]]

This is another example of another interesting Diels-Alder reaction ([4+2] cycloaddition). As well as having the endo and exo products, this reaction can react to give the chelotropic product where a 5-membered ring is formed with two new bonds both formed to the sulphur. The other caveat to this reaction is that the reaction can occur on the double bonds within the ring to produce three more products: endo, exo and chelotropic. The analysis will be discussed below.

===IRCs of the Exocyclic Reaction===
The IRCs were run showing the geometries along the reaction coordinate. From ''Figure 9'' and ''Figure 10'' is can be seen that the exo and endo reaction proceed with asynchronous bonding, with the oxygen bonding before the sulphur. ''Figure 11'' clearly shows that the chelotropic reaction bonding in a synchronous fashion.

<center>
[[File:Exo_irc_eo1013.gif|x500px|thumb|center|Figure 9: IRC showing the formation of the exo product]]
</center>

<center>
[[File:Endo_irc_eo1013.gif|x500px|thumb|center|Figure 10: IRC showing the formation of the endo product]]
</center>

<center>
[[File:Che_irc_eo1013.gif|x500px|thumb|center|Figure 11: IRC showing the formation of the cheloptopic product]]
</center>

===Thermochemical Analysis===
<center>
{| class="wikitable" border="1"
|+ Table 8: Thermochemical data for the reaction of o-xylylene with SO<sub>2</sub>
! Product
! Reaction Barrier in kJ mol<sup>-1</sup>
! Reaction Energy in kJ mol<sup>-1</sup>
|-
| Endo || 80.12 || -100.66
|-
| Exo || 84.11 || -101.31
|-
| Cheletropic || 102.44 || -157.65
|}
</center>

GaussView 5.0.9 was used to calculate the energetics of the three reactions at the PM6 level. From ''Table 8'' it can be seen that the chelotropic product has the lowest reaction energy and is therefore the thermodynamic product. A consideration of the bond enthalpies involved makes this quite clear, the formation of C-O and S-O is less favorable compared to the formation of S=O and S-C.<ref>PROPERTIES OF ATOMS, RADICALS, AND BONDS, http://labs.chem.ucsb.edu/zakarian/armen/11---bonddissociationenergy.pdf, (accessed December 2017)</ref> It also has the highest energy TS largely due to the the 5-membered ring in the TS which suffers from ring strain compared to 6-membered TS in the endo and exo reaction pathways. Because of this higher energy transition state, the other products will be expected to form in a greater proportion under equilibrium conditions.

[[File:Rxn_profile_3_eo1013.png|450px|thumb|right|Figure 12: Approximate Reaction profile of all three reaction pathways investigated for the reaction of o-xylylene with SO<sub>2</sub>]]

''Figure 12'' illustrates that the endo product has the lowest energy TS and is therefore the kinetic product. These reactions are all very favourable due to the fact that an aromatic ring in formed afterwards. The stabilisation due to aromatisiation is very desired as we can see that ir is large enough to compensate for the high TS energy of the chelotropic reaction. Looking at the IRCs we can see that the aromatic ring forms before the other bonds in the reaction.

===Relevant Files===
Sulphur Dioxide (PM6 Optimised): [[File:SO2_PM6_EO1013.LOG]]

O-xylylene (PM6 Optimised): [[File:XYLYLENE_NEW_PM6_EO1013.LOG]]

Chelotropic TS (PM6 Optimised): [[File:TS_OPTIMISED_FINAL_PM6_che_eo1013.LOG]]

Exo TS (PM6 Optimised): [[File:TS_PM6_FINAL_EXO_eo1013.LOG]]

Endo TS (PM6 Optimised): [[File:TS_PM6_ENDO_FINAL_eo1013.LOG]]

Chelotropic Product (PM6 Optimised): [[File:PRODUCTS_PM6_che_eo1013.LOG]]

Exo Product (PM6 Optimised): [[File:EXO_PRODUCT_PM6_FINAL_eo1013.LOG]]

Endo Product (PM6 Optimised): [[File:PRODUCTS_PM6_ENDO_FINAL_eo1013.LOG]]

===Alternative Reaction Pathway===
<center>
{| class="wikitable" border="1"
|+ Table 9: Thermochemical data for the reaction (alternative pathway) of o-xylylene with SO<sub>2</sub>
! Product
! Reaction Barrier in kJ mol<sup>-1</sup>
! Reaction Energy in kJ mol<sup>-1</sup>
|-
| Endo || 110.34 || 14.62
|-
| Exo || 118.18 || 19.06
|}
</center>

From ''Table 9'', it is clear that the products are less stable than the sum of the energies of the reactants at infinite separation, this is a strong indication that the reaction requires some energy input in order for it to occur (endothermic reaction). The reaction barriers are a lot higher in comparison to those in ''Table 8'' which makes sense as there is the lack of stablisation gained from forming an aromatic ring from this pathway. The IRCs (''Figure 13'' and ''Figure 14'') are shown below.

<center>
[[File:ALT_EXO_IRC_eo1013.gif|x500px|thumb|center|Figure 13: IRC showing the formation of the exo product through the alternative pathway]]
</center>

<center>
[[File:ALT_ENDO_IRC_eo1013.gif|x500px|thumb|center|Figure 14: IRC showing the formation of the endo product through the alternative pathway]]
</center>

===Relevant Files (Alternative Pathway)===

Alternative Exo TS (PM6 Optimised): [[File:TS_EXO_FINAL_PM6_ALT_eo1013.LOG]]

Alternative Endo TS (PM6 Optimised): [[File:TS_ENDO_FINAL_PM6_ALT_eo1013.LOG]]

Alternative Exo Product (PM6 Optimised): [[File:PRODUCT_EXO_PM6_ALT_eo013.LOG]]

Alternative Endo Product (PM6 Optimised): [[File:PRODUCT_ENDO_PM6_ALT_eo1013.LOG]]

==Conclusion==
In conclusion, the results from this lab agree with the established theory around Diels-Alder reactions. Using the PM6 allows for quick calculations that may not be so reliable but aid an understanding of the underlying chemistry. The B3LYP calculations are very reliable but are more expensive in terms of computational cost. GaussView 5.0.9 has proven to be a very useful tool in analysing the thermochemical data of reactions and visualising the MOs to understand favourable orientations for successful reactions.

''Exercise 1'' was useful in understanding the advantages and limitations of the computational methods chosen. Analyzing and comparing the C-C bond lengths reflected how close GaussView 5.0.9 can get to literature values. ''Exercise 2'' required more in-depth analysis of the energies of the optimised geometries and shows how effective computational chemistry can be in predicting the major product of a reaction. ''Exercise 3'' highlighted the importance of utilising our chemical intuition along with the computational methods to investigate alternative pathways to rationalise their feasibility which could prove useful in determining possible side reactions.

All in all, these exercises have shown that the computational approach is a very powerful one indeed and can be used to predict the course, outcomes and shortcomings of a reaction before even entering the lab. This has some very beneficial implications namely in the fact that money can be saved rather than being spent on reagents for a reaction that will not yield desired products. It also proves to be a very useful tool in understanding reaction dynamics/mechanisms.

===References===

Rep:Mod:EO1013TS

2017-12-19T23:16:13Z

Eo1013:

==Introduction==
GaussView 5.0.9 is a very powerful program that allows for complex quantum mechanical calculation to be performed on molecules. It was used to investigate several aspects of three Diels-Alder reactions, the orbital interactions (primary and secondary) were moedlled and closely inspected as well as the energies and transition states to better understand the reaction paths of the examples studied.

===Potential Energy Surfaces (PES)===
The concept of PES is fundamental in computational chemistry and has allowed for many breakthroughs. A PES displays the relationship between the energy of a molecule and its geometry.

<math display="block">\text{Equation 1: General Time-dependent Schrödinger equation: } i \hbar \frac{\partial}{\partial t}\Psi(\mathbf{r},t) = \hat H \Psi(\mathbf{r},t)</math>

The energies can be calculated using different computational methods that simplify and solve the Schrödinger equation (''Eqn 1'') using approximations allowing PES to be generated in very little time. A PES conatains a lot of information, namely global and local minima that represent stable confomers/rotamers of the same molecule with the transition state that links them.<ref>The Concept of PES, http://is.muni.cz/el/1431/podzim2015/C9920/um/The_concept_of_PES.pdf, (accessed December 2017)</ref>

===The Transition State (TS) and Minima===
In GaussView 5.0.9 there are various methods (discussed below) to allow for the calculation of energies after optimising a particular geometry to a minimum energy taking into account electron repulsion and several other factors. Methods have also been devised, making use of known atomic separations during transitions to hazard a guess at the TS before performing optimising calculations and running an Intrinsic Reaction Coordinate (IRC) calculation can be performed to plot a reaction profile diagram.

The value of gradient on the PES at the minimum and at the transition structure will both be zero. Minima will have a positive value for the second derivative in every axial direction of the energy potential surface whereas a TS will have a positive value for the second derivative (saddle point) in all axial directions apart from in the reaction coordinate. This means that at a minima, movement in any direction either side of that point will results in a geometry with a higher energy. The same is true for the TS but there is a decrease in energy in one dimension which is known as the reaction pathway. The PES has 3N-6 dimensions, where N is the number of atoms in the molecule of study, corresponding to the degrees of freedom available to the molecule. Running an IRC calculation on the Ts structure allows as to track the geometries along this pathway.<ref>Gaussian – Vibration Analysis in Gaussian, http://gaussian.com/vib, (accessed December 2017)</ref>

The TS is a saddle point and just like a minima or a maxima, its first derivative will be zero. The difference however is apparent when you take the second derivative, which is done using a Hessian matrix in GaussView 5.0.9. The second derivative correlates to the energy and therefore the frequency and force constant of the vibrations in the molecule. As a result, minima always have positive force constants (increases in energy) and the TS, being a saddle point, will have at least one negative force constant (producing an imaginary vibration) which corresponds to the reaction pathway.

===Methods to Locate The TS===
In this investigation, three main methods were used to find the transition state.

'''Method 1:''' This method only works if one has prior knowledge of the transition state. The transition state is guessed using empirically observed bond lengths and a minimisation calculation is performed. If these lengths are wrong, undesired structures could form.

'''Method 2:''' This method also requires prior knowledge of the transition state. A guess of the TS is made and the bonds involved in the reaction are frozen before a minimisation calculation is performed. This structure is then optimised to a TS and is more reliable that '''Method 1'''.

'''Method 3:''' This method does not require prior knowledge of the transition state as you start with the product or reactants (optimised to a minimum). Bonds are then added or removed to closer resemble the TS and similar to '''Method 2''', these are frozen to obtain a minimum. However, It is not very reliable for TS geometries that do not resemble
the minima.

===Computational Methods===
The PM6 and B3LYP methods were used in this lab. PM6 is a semi-empirical method which simplifies the Hartree-Fock method by using empirical data and pre-determined integrals to solve Hamiltonian (the energy operator of the Schrödinger equation) and as a result, runs very quickly as less calculations need to be performed. With all the approximations and generic data used in this method, results are often inaccurate.<ref>Gaussian – Semi-Empirical Methods, http://gaussian.com/semiempirical, (accessed December 2017)</ref>

B3LYP, on the other hand, is a hybrid method that uses elements of Hartree-Fock and Density Funtional Theory (DFT). This method is more expensive than the PM6 as it doesn't use pre-determined integrals: it uses the DFT method to calculate all of the terms of the Hamiltonian apart from the exchange correlation term which is done using a HF method. It gives a very reliable results.<ref>What is B33LYP?, http://www.quora.com/What-is-B3LYP-and-why-is-it-the-most-popular-functional-in-DFT, (accessed December 2017)</ref><ref name=":0">A. Szabo and N. S. Ostlund, ''Modern Quantum Chemistry'', Dover Publications, 1989.</ref>

==Exercise 1: Butadiene + Ethene==
[[File:Reaction_scheme_1_eo1013.png|350px|thumb|center|Figure 1: Reaction Scheme for Butadiene with Ethene]]

This reaction is a [4+2] cycloaddition. Butadiene and ethene react together to form cyclohexene. The diene is more electron-rich than the dienophile. As can be seen from ''Figure 2'', the HOMO of butadiene contributes more to the HOMO-1 of the TS. In addition, the LUMO on ethene contributes more to the LUMO+1 which shows that HOMO of butadiene is lower in energy than the LUMO of ethene. This is an example of a normal electron demand reaction as the closest interaction is between the HOMO of the diene and the LUMO off the dienophile.<ref>J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, 2nd edn., 2012.</ref>

[[File:MO_1_eo1013.jpg|350px|thumb|center|Figure 2: MO Diagram showing orbital interactions in the reaction of Butadiene with Ethene]]

===Analysis of Molecular Orbitals===
A non-zero overlap integral is required in order for an orbital interaction to be favourable. Orbitals involved in this interaction must have the same symmetry as the overlap integral is proportional to the spatial overlap of the orbitals in question. For a non zero overlap, the orbitals must both be symmetric or asymmetric to give overall symmetric function. An anti-symmetric function will be gained when you combine orbitals of different symmetry which will leads overlap integral being zero.(CITE ATKINS AD)

Jmol BLURB 1

Looking at the HOMO and the LUMO of the TS in ''Table 3'', it is clear that they are formed from the HOMO of ethene and the LUMO of butadiene, both being symmetric orbitals. The opposite interaction from two antisymetic orbitals, the HOMO of butadiene and LUMO of ethene, give the HOMO-1 and the LUMO+1 of the TS. This clearly demonstrates that reactions can only be allowed when orbitals of the same symmetry can interact. Transition states that are of a geometry where orbitals of opposite symmetry are forced to interact will most likely lead to an unsuccessful reaction.

===Analysis of Bond Lengths===
<center>
{| class="wikitable" border="1"
|+ Table 4: Bond lengths (from ''Figure 1'') during the course of the reaction (Å)
! Bonds
! Cyclohexene
! Transition State
! Butadiene and Ethene
|-
| '''C1-C2''' || 1.501 || 1.380 || 1.335
|-
| '''C2-C3''' || 1.338 || 1.441 || 1.468
|-
| '''C3-C4''' || 1.501 || 1.380 || 1.335
|-
| '''C4-C5''' || 1.540 || 2.115 || ----
|-
| '''C5-C6''' || 1.541 || 1.382 || 1.327
|-
| '''C6-C1''' || 1.540 || 2.115 || ----
|}
</center>

A typical carbon to carbon single bond length is 1.54 Å and a double bond is 1.34 Å.(CITE) These are a direct match with the bond lengths predicted by Gaussian. C1-C2 and C3-C4 are a lot shorter due to the pulling effect of the higher electron density in C2-C3. As the carbons change from and sp3 hybridised orbitals to sp2, the bond lengths shorten and vice versa. Both double bonds on butadiene also lengthen as they change from sp2 to sp3 hybridisation. The two new bonds (C4-C5 and C6-C1) that form in the TS have a bond length (2.115 Å) that is smaller than two times the Van der Waal radius of carbon (1.7 Å) showing that the two molecules are starting to interact during the transition state and get shorter once the bond forms into a single C-C bond.(VdW reference)

===The Transition State===
<center>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>350</size>
<uploadedFileContents>BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 7; frank off; vector on; vector scale -4; vector 0.04; color vectors red</script>
<name>CPD_Dimer_TS</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle vibrate</text>
<target>CPD_Dimer_TS</target>
</jmolbutton>
</jmol>
</center>

The vibration above (click toggle vibration) corresponds to the negative frequency in the TS calculations a result of the negative force constant. The bond formation is synchronous as the carbons at both ends of the new bonds are moving at the same time in the TS. This can also seen in the IRC (Figure 3) as the bonds are formed at the same time.

<center>
[[File:IRC.gif|350px|thumb|center|Figure 3: IRC showing the formation of the two new bonds]]
</center>

===Relevant Files===
Product (PM6-Optimised): [[File:PRODUCTS_PM6_eo1016.LOG]]

TS of Reaction (PM6 Optimised): [[File:BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG]]

IRC of Reaction: [[File:BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG]]

==Exercise 2: Reaction of Cyclohexadiene + 1,3-Dioxole==
[[File:Rxn_scheme_eo1013.png|350px|thumb|center|Figure 4: Reaction Scheme for cyclohexadiene with 1,3-dioxole]]
This Diels-Alder reaction ([4+2] cycloaddition) is particularly interesting as there is a possibility of having two products: the endo and exo products. This is due to the fact that the dienophile is substituted and can approach in two different orientations. The exo product is formed when the bulk of the substituent approaches in such a way that it it pointing away from the pi-system of the diene. When it approaches with the bulk of the dienophile facing towards the pi system of the diene, the endo product is formed. This has implications for the energies of the products as will be discussed in the following sections.

[[File:Mo_2_eo1013.PNG|350px|thumb|center|Figure 5: MO diagram for the reaction of cyclohexadiene with 1,3-dioxole]]

The oxygen in either side of the dienophile have an electron donating effect on the p-orbitals of the double bond, causing the dienophile to be "electron rich" and raising the energy of the HOMO and LUMO, compared to ethene, as a result. As a consequence, as can illustrated in ''Figure 5'', the closest interaction is between the LUMO of the diene and the HOMO off the dienophile. Therefore, this is an example of an inverse electron demand reaction. (CLAYDEN)

===Analysis of Molecular Orbitals===
As mentioned before, the oxygens on the dioxole work to raise the energy of the HOMO and LUMO of the diene compared to ethene. This increases the energy gap and leads to weaker interactions. An example of this is the HOMO-1 which is still lower in energy than the HOMO of the reactants as it only experiences a slight destabilisation. Only orbitals of the same symmetry can interact as seen below in ''Table 5'' and ''Table 6''.

JMOL BLUB 2 + 3

===Thermochemical Analysis===
<center>
{| class="wikitable" border="1"
|+ Table 7: Thermochemical data for the reaction of cyclohexadiene with 1,3-dioxole
! Product
! Reaction Barrier in kJ mol<sup>-1</sup>
! Reaction Energy in kJ mol<sup>-1</sup>
|-
| Endo || 158.47 || -68.75
|-
| Exo || 166.30 || -65.15
|}
</center>

GaussView 5.0.9 also calculates the free energies of these geometries which can allow for an in-depth analysis of the energetics of the reaction. A summary of this data is presented in ''Table 7''. The reaction barrier is calculated as the difference in energy between the TS and the starting materials. The endo product has a lower reaction barrier compared to the exo product, making it the kinetically-preferred product. This can be attributed to the extra stabilisation present in the endo transition state as a result of the secondary orbital interactions between the oxygens and the pi system on the diene. ''Figure 6'' shows the orbital interaction between the oxygen (red atoms) with the double bond from.

[[File:Oxygen_interaction_eo1013.PNG|350px|thumb|center|Figure 6: MO depicted by GaussView 5.0.9 showing the secondary orbital interactions in the endo TS.]]

The reaction energy is calculated as the free energy difference between the products and the reactants. Comparing the two shows that the endo reaction has a more negative reaction energy compared to the exo reaction, making the endo product the thermodynamically-preferred product. This can be rationalised, as seen in ''Figure 7'', by the location of the CH<sub>2</sub>s on the-5 membered ring. There is some steric clash with the CH<sub>2</sub> fragments in the exo product with he CH<sub>2</sub>s on the bridging carbons which isn't present in the endo product (making it more thermodynamically stable).

[[File:Interaction_eo1013.PNG|350px|thumb|center|Figure 7: A diagram showing the steric clashing of the CH<sub>2</sub> fragments.]]

The endo product is both the kinetic and thermodynamic product. This also agrees with experimental observations stating that in a [4+2] cycloaddition, the endo product is preferred, even if the exo product is more stable, due to favourable secondary orbital interactions in the TS.

===Relevant Files===
1,3-Dioxole (B3LYP-Optimised): [[File:DIOXOLE_B3LYP_eo1013.LOG]]

Cyclohexadiene (B3LYP-Optimised): [[File:CYCLOHEXADIENE_B3LYP_eo1013.LOG]]

Endo Product (B3LYP-Optimised): [[File:ENDO_PRODUCT_PM6_eo1013.LOG]]

Exo Product (B3LYP-Optimised): [[File:EXO_PRODUCT_END_B3LYP_eo1013.LOG]]

IRC of Endo Reaction (PM6 Optimised): [[File:IRC_PM6_ENDO_eo1013.LOG]]

IRC of Exo Reaction (PM6 Optimised): [[File:IRC_EXO_PM6_eo1013.LOG]]

==Exercise 3: O-xylylene + SO<sub>2</sub>==
[[File:Rxn_scheme_3_eo1013.PNG|350px|thumb|center|Figure 8: MO diagram for the reaction of o-xylylene with SO<sub>2</sub>]]

This is another example of another interesting Diels-Alder reaction ([4+2] cycloaddition). As well as having the endo and exo products, this reaction can react to give the chelotropic product where a 5-membered ring is formed with two new bonds both formed to the sulphur. The other caveat to this reaction is that the reaction can occur on the double bonds within the ring to produce three more products: endo, exo and chelotropic. The analysis will be discussed below.

===IRCs of the Exocyclic Reaction===
The IRCs were run showing the geometries along the reaction coordinate. From ''Figure 9'' and ''Figure 10'' is can be seen that the exo and endo reaction proceed with asynchronous bonding, with the oxygen bonding before the sulphur. ''Figure 11'' clearly shows that the chelotropic reaction bonding in a synchronous fashion.

<center>
[[File:Exo_irc_eo1013.gif|x500px|thumb|center|Figure 9: IRC showing the formation of the exo product]]
</center>

<center>
[[File:Endo_irc_eo1013.gif|x500px|thumb|center|Figure 10: IRC showing the formation of the endo product]]
</center>

<center>
[[File:Che_irc_eo1013.gif|x500px|thumb|center|Figure 11: IRC showing the formation of the cheloptopic product]]
</center>

===Thermochemical Analysis===
<center>
{| class="wikitable" border="1"
|+ Table 8: Thermochemical data for the reaction of o-xylylene with SO<sub>2</sub>
! Product
! Reaction Barrier in kJ mol<sup>-1</sup>
! Reaction Energy in kJ mol<sup>-1</sup>
|-
| Endo || 80.12 || -100.66
|-
| Exo || 84.11 || -101.31
|-
| Cheletropic || 102.44 || -157.65
|}
</center>

GaussView 5.0.9 was used to calculate the energetics of the three reactions at the PM6 level. From ''Table 8'' it can be seen that the chelotropic product has the lowest reaction energy and is therefore the thermodynamic product. A consideration of the bond enthalpies involved makes this quite clear, the formation of C-O and S-O is less favorable compared to the formation of S=O and S-C. (bonds REF) It also has the highest energy TS largely due to the the 5-membered ring in the TS which suffers from ring strain compared to 6-membered TS in the endo and exo reaction pathways. Because of this higher energy transition state, the other products will be expected to form in a greater proportion under equilibrium conditions.

[[File:Rxn_profile_3_eo1013.png|450px|thumb|right|Figure 12: Approximate Reaction profile of all three reaction pathways investigated for the reaction of o-xylylene with SO<sub>2</sub>]]

''Figure 12'' illustrates that the endo product has the lowest energy TS and is therefore the kinetic product. These reactions are all very favourable due to the fact that an aromatic ring in formed afterwards. The stabilisation due to aromatisiation is very desired as we can see that ir is large enough to compensate for the high TS energy of the chelotropic reaction. Looking at the IRCs we can see that the aromatic ring forms before the other bonds in the reaction.

===Relevant Files===
Sulphur Dioxide (PM6 Optimised): [[File:SO2_PM6_EO1013.LOG]]

O-xylylene (PM6 Optimised): [[File:XYLYLENE_NEW_PM6_EO1013.LOG]]

Chelotropic TS (PM6 Optimised): [[File:TS_OPTIMISED_FINAL_PM6_che_eo1013.LOG]]

Exo TS (PM6 Optimised): [[File:TS_PM6_FINAL_EXO_eo1013.LOG]]

Endo TS (PM6 Optimised): [[File:TS_PM6_ENDO_FINAL_eo1013.LOG]]

Chelotropic Product (PM6 Optimised): [[File:PRODUCTS_PM6_che_eo1013.LOG]]

Exo Product (PM6 Optimised): [[File:EXO_PRODUCT_PM6_FINAL_eo1013.LOG]]

Endo Product (PM6 Optimised): [[File:PRODUCTS_PM6_ENDO_FINAL_eo1013.LOG]]

===Alternative Reaction Pathway===
<center>
{| class="wikitable" border="1"
|+ Table 9: Thermochemical data for the reaction (alternative pathway) of o-xylylene with SO<sub>2</sub>
! Product
! Reaction Barrier in kJ mol<sup>-1</sup>
! Reaction Energy in kJ mol<sup>-1</sup>
|-
| Endo || 110.34 || 14.62
|-
| Exo || 118.18 || 19.06
|}
</center>

From ''Table 9'', it is clear that the products are less stable than the sum of the energies of the reactants at infinite separation, this is a strong indication that the reaction requires some energy input in order for it to occur (endothermic reaction). The reaction barriers are a lot higher in comparison to those in ''Table 8'' which makes sense as there is the lack of stablisation gained from forming an aromatic ring from this pathway. The IRCs (''Figure 13'' and ''Figure 14'') are shown below.

<center>
[[File:ALT_EXO_IRC_eo1013.gif|x500px|thumb|center|Figure 13: IRC showing the formation of the exo product through the alternative pathway]]
</center>

<center>
[[File:ALT_ENDO_IRC_eo1013.gif|x500px|thumb|center|Figure 14: IRC showing the formation of the endo product through the alternative pathway]]
</center>

===Relevant Files (Alternative Pathway)===

Alternative Exo TS (PM6 Optimised): [[File:TS_EXO_FINAL_PM6_ALT_eo1013.LOG]]

Alternative Endo TS (PM6 Optimised): [[File:TS_ENDO_FINAL_PM6_ALT_eo1013.LOG]]

Alternative Exo Product (PM6 Optimised): [[File:PRODUCT_EXO_PM6_ALT_eo013.LOG]]

Alternative Endo Product (PM6 Optimised): [[File:PRODUCT_ENDO_PM6_ALT_eo1013.LOG]]

==Conclusion==
In conclusion, the results from this lab agree with the established theory around Diels-Alder reactions. Using the PM6 allows for quick calculations that may not be so reliable but aid an understanding of the underlying chemistry. The B3LYP calculations are very reliable but are more expensive in terms of computational cost. GaussView 5.0.9 has proven to be a very useful tool in analysing the thermochemical data of reactions and visualising the MOs to understand favourable orientations for successful reactions.

''Exercise 1'' was useful in understanding the advantages and limitations of the computational methods chosen. Analyzing and comparing the C-C bond lengths reflected how close GaussView 5.0.9 can get to literature values. ''Exercise 2'' required more in-depth analysis of the energies of the optimised geometries and shows how effective computational chemistry can be in predicting the major product of a reaction. ''Exercise 3'' highlighted the importance of utilising our chemical intuition along with the computational methods to investigate alternative pathways to rationalise their feasibility which could prove useful in determining possible side reactions.

All in all, these exercises have shown that the computational approach is a very powerful one indeed and can be used to predict the course, outcomes and shortcomings of a reaction before even entering the lab. This has some very beneficial implications namely in the fact that money can be saved rather than being spent on reagents for a reaction that will not yield desired products. It also proves to be a very useful tool in understanding reaction dynamics/mechanisms.

===References===

Rep:Mod:EO1013TS

2017-12-19T23:14:05Z

Eo1013:

==Introduction==
GaussView 5.0.9 is a very powerful program that allows for complex quantum mechanical calculation to be performed on molecules. It was used to investigate several aspects of three Diels-Alder reactions, the orbital interactions (primary and secondary) were moedlled and closely inspected as well as the energies and transition states to better understand the reaction paths of the examples studied.

===Potential Energy Surfaces (PES)===
The concept of PES is fundamental in computational chemistry and has allowed for many breakthroughs. A PES displays the relationship between the energy of a molecule and its geometry.

<math display="block">\text{Equation 1: General Time-dependent Schrödinger equation: } i \hbar \frac{\partial}{\partial t}\Psi(\mathbf{r},t) = \hat H \Psi(\mathbf{r},t)</math>

The energies can be calculated using different computational methods that simplify and solve the Schrödinger equation (''Eqn 1'') using approximations allowing PES to be generated in very little time. A PES conatains a lot of information, namely global and local minima that represent stable confomers/rotamers of the same molecule with the transition state that links them.<ref>The Concept of PES, http://is.muni.cz/el/1431/podzim2015/C9920/um/The_concept_of_PES.pdf, (accessed December 2017)</ref>

===The Transition State (TS) and Minima===
In GaussView 5.0.9 there are various methods (discussed below) to allow for the calculation of energies after optimising a particular geometry to a minimum energy taking into account electron repulsion and several other factors. Methods have also been devised, making use of known atomic separations during transitions to hazard a guess at the TS before performing optimising calculations and running an Intrinsic Reaction Coordinate (IRC) calculation can be performed to plot a reaction profile diagram.

The value of gradient on the PES at the minimum and at the transition structure will both be zero. Minima will have a positive value for the second derivative in every axial direction of the energy potential surface whereas a TS will have a positive value for the second derivative (saddle point) in all axial directions apart from in the reaction coordinate. This means that at a minima, movement in any direction either side of that point will results in a geometry with a higher energy. The same is true for the TS but there is a decrease in energy in one dimension which is known as the reaction pathway. The PES has 3N-6 dimensions, where N is the number of atoms in the molecule of study, corresponding to the degrees of freedom available to the molecule. Running an IRC calculation on the Ts structure allows as to track the geometries along this pathway.<ref>Gaussian – Vibration Analysis in Gaussian, http://gaussian.com/vib, (accessed December 2017)</ref>

The TS is a saddle point and just like a minima or a maxima, its first derivative will be zero. The difference however is apparent when you take the second derivative, which is done using a Hessian matrix in GaussView 5.0.9. The second derivative correlates to the energy and therefore the frequency and force constant of the vibrations in the molecule. As a result, minima always have positive force constants (increases in energy) and the TS, being a saddle point, will have at least one negative force constant (producing an imaginary vibration) which corresponds to the reaction pathway.

===Methods to Locate The TS===
In this investigation, three main methods were used to find the transition state.

'''Method 1:''' This method only works if one has prior knowledge of the transition state. The transition state is guessed using empirically observed bond lengths and a minimisation calculation is performed. If these lengths are wrong, undesired structures could form.

'''Method 2:''' This method also requires prior knowledge of the transition state. A guess of the TS is made and the bonds involved in the reaction are frozen before a minimisation calculation is performed. This structure is then optimised to a TS and is more reliable that '''Method 1'''.

'''Method 3:''' This method does not require prior knowledge of the transition state as you start with the product or reactants (optimised to a minimum). Bonds are then added or removed to closer resemble the TS and similar to '''Method 2''', these are frozen to obtain a minimum. However, It is not very reliable for TS geometries that do not resemble
the minima.

===Computational Methods===
The PM6 and B3LYP methods were used in this lab. PM6 is a semi-empirical method which simplifies the Hartree-Fock method by using empirical data and pre-determined integrals to solve Hamiltonian (the energy operator of the Schrödinger equation) and as a result, runs very quickly as less calculations need to be performed. With all the approximations and generic data used in this method, results are often inaccurate.<ref>Gaussian – Semi-Empirical Methods, http://gaussian.com/semiempirical, (accessed December 2017)</ref>

B3LYP, on the other hand, is a hybrid method that uses elements of Hartree-Fock and Density Funtional Theory (DFT). This method is more expensive than the PM6 as it doesn't use pre-determined integrals: it uses the DFT method to calculate all of the terms of the Hamiltonian apart from the exchange correlation term which is done using a HF method. It gives a very reliable results.<ref>What is B33LYP?, http://www.quora.com/What-is-B3LYP-and-why-is-it-the-most-popular-functional-in-DFT, (accessed December 2017)</ref><ref name=":0">A. Szabo and N. S. Ostlund, ''Modern Quantum Chemistry'', Dover Publications, 1989.</ref>

==Exercise 1: Butadiene + Ethene==
[[File:Reaction_scheme_1_eo1013.png|350px|thumb|center|Figure 1: Reaction Scheme for Butadiene with Ethene]]

This reaction is a [4+2] cycloaddition. Butadiene and ethene react together to form cyclohexene. The diene is more electron-rich than the dienophile. As can be seen from ''Figure 2'', the HOMO of butadiene contributes more to the HOMO-1 of the TS. In addition, the LUMO on ethene contributes more to the LUMO+1 which shows that HOMO of butadiene is lower in energy than the LUMO of ethene. This is an example of a normal electron demand reaction as the closest interaction is between the HOMO of the diene and the LUMO off the dienophile.<ref name=":0">J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, 2nd edn., 2012.</ref>

[[File:MO_1_eo1013.jpg|350px|thumb|center|Figure 2: MO Diagram showing orbital interactions in the reaction of Butadiene with Ethene]]

===Analysis of Molecular Orbitals===
A non-zero overlap integral is required in order for an orbital interaction to be favourable. Orbitals involved in this interaction must have the same symmetry as the overlap integral is proportional to the spatial overlap of the orbitals in question. For a non zero overlap, the orbitals must both be symmetric or asymmetric to give overall symmetric function. An anti-symmetric function will be gained when you combine orbitals of different symmetry which will leads overlap integral being zero.(CITE ATKINS AD)

Jmol BLURB 1

Looking at the HOMO and the LUMO of the TS in ''Table 3'', it is clear that they are formed from the HOMO of ethene and the LUMO of butadiene, both being symmetric orbitals. The opposite interaction from two antisymetic orbitals, the HOMO of butadiene and LUMO of ethene, give the HOMO-1 and the LUMO+1 of the TS. This clearly demonstrates that reactions can only be allowed when orbitals of the same symmetry can interact. Transition states that are of a geometry where orbitals of opposite symmetry are forced to interact will most likely lead to an unsuccessful reaction.

===Analysis of Bond Lengths===
<center>
{| class="wikitable" border="1"
|+ Table 4: Bond lengths (from ''Figure 1'') during the course of the reaction (Å)
! Bonds
! Cyclohexene
! Transition State
! Butadiene and Ethene
|-
| '''C1-C2''' || 1.501 || 1.380 || 1.335
|-
| '''C2-C3''' || 1.338 || 1.441 || 1.468
|-
| '''C3-C4''' || 1.501 || 1.380 || 1.335
|-
| '''C4-C5''' || 1.540 || 2.115 || ----
|-
| '''C5-C6''' || 1.541 || 1.382 || 1.327
|-
| '''C6-C1''' || 1.540 || 2.115 || ----
|}
</center>

A typical carbon to carbon single bond length is 1.54 Å and a double bond is 1.34 Å.(CITE) These are a direct match with the bond lengths predicted by Gaussian. C1-C2 and C3-C4 are a lot shorter due to the pulling effect of the higher electron density in C2-C3. As the carbons change from and sp3 hybridised orbitals to sp2, the bond lengths shorten and vice versa. Both double bonds on butadiene also lengthen as they change from sp2 to sp3 hybridisation. The two new bonds (C4-C5 and C6-C1) that form in the TS have a bond length (2.115 Å) that is smaller than two times the Van der Waal radius of carbon (1.7 Å) showing that the two molecules are starting to interact during the transition state and get shorter once the bond forms into a single C-C bond.(VdW reference)

===The Transition State===
<center>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>350</size>
<uploadedFileContents>BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 7; frank off; vector on; vector scale -4; vector 0.04; color vectors red</script>
<name>CPD_Dimer_TS</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle vibrate</text>
<target>CPD_Dimer_TS</target>
</jmolbutton>
</jmol>
</center>

The vibration above (click toggle vibration) corresponds to the negative frequency in the TS calculations a result of the negative force constant. The bond formation is synchronous as the carbons at both ends of the new bonds are moving at the same time in the TS. This can also seen in the IRC (Figure 3) as the bonds are formed at the same time.

<center>
[[File:IRC.gif|350px|thumb|center|Figure 3: IRC showing the formation of the two new bonds]]
</center>

===Relevant Files===
Product (PM6-Optimised): [[File:PRODUCTS_PM6_eo1016.LOG]]

TS of Reaction (PM6 Optimised): [[File:BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG]]

IRC of Reaction: [[File:BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG]]

==Exercise 2: Reaction of Cyclohexadiene + 1,3-Dioxole==
[[File:Rxn_scheme_eo1013.png|350px|thumb|center|Figure 4: Reaction Scheme for cyclohexadiene with 1,3-dioxole]]
This Diels-Alder reaction ([4+2] cycloaddition) is particularly interesting as there is a possibility of having two products: the endo and exo products. This is due to the fact that the dienophile is substituted and can approach in two different orientations. The exo product is formed when the bulk of the substituent approaches in such a way that it it pointing away from the pi-system of the diene. When it approaches with the bulk of the dienophile facing towards the pi system of the diene, the endo product is formed. This has implications for the energies of the products as will be discussed in the following sections.

[[File:Mo_2_eo1013.PNG|350px|thumb|center|Figure 5: MO diagram for the reaction of cyclohexadiene with 1,3-dioxole]]

The oxygen in either side of the dienophile have an electron donating effect on the p-orbitals of the double bond, causing the dienophile to be "electron rich" and raising the energy of the HOMO and LUMO, compared to ethene, as a result. As a consequence, as can illustrated in ''Figure 5'', the closest interaction is between the LUMO of the diene and the HOMO off the dienophile. Therefore, this is an example of an inverse electron demand reaction. (CLAYDEN)

===Analysis of Molecular Orbitals===
As mentioned before, the oxygens on the dioxole work to raise the energy of the HOMO and LUMO of the diene compared to ethene. This increases the energy gap and leads to weaker interactions. An example of this is the HOMO-1 which is still lower in energy than the HOMO of the reactants as it only experiences a slight destabilisation. Only orbitals of the same symmetry can interact as seen below in ''Table 5'' and ''Table 6''.

JMOL BLUB 2 + 3

===Thermochemical Analysis===
<center>
{| class="wikitable" border="1"
|+ Table 7: Thermochemical data for the reaction of cyclohexadiene with 1,3-dioxole
! Product
! Reaction Barrier in kJ mol<sup>-1</sup>
! Reaction Energy in kJ mol<sup>-1</sup>
|-
| Endo || 158.47 || -68.75
|-
| Exo || 166.30 || -65.15
|}
</center>

GaussView 5.0.9 also calculates the free energies of these geometries which can allow for an in-depth analysis of the energetics of the reaction. A summary of this data is presented in ''Table 7''. The reaction barrier is calculated as the difference in energy between the TS and the starting materials. The endo product has a lower reaction barrier compared to the exo product, making it the kinetically-preferred product. This can be attributed to the extra stabilisation present in the endo transition state as a result of the secondary orbital interactions between the oxygens and the pi system on the diene. ''Figure 6'' shows the orbital interaction between the oxygen (red atoms) with the double bond from.

[[File:Oxygen_interaction_eo1013.PNG|350px|thumb|center|Figure 6: MO depicted by GaussView 5.0.9 showing the secondary orbital interactions in the endo TS.]]

The reaction energy is calculated as the free energy difference between the products and the reactants. Comparing the two shows that the endo reaction has a more negative reaction energy compared to the exo reaction, making the endo product the thermodynamically-preferred product. This can be rationalised, as seen in ''Figure 7'', by the location of the CH<sub>2</sub>s on the-5 membered ring. There is some steric clash with the CH<sub>2</sub> fragments in the exo product with he CH<sub>2</sub>s on the bridging carbons which isn't present in the endo product (making it more thermodynamically stable).

[[File:Interaction_eo1013.PNG|350px|thumb|center|Figure 7: A diagram showing the steric clashing of the CH<sub>2</sub> fragments.]]

The endo product is both the kinetic and thermodynamic product. This also agrees with experimental observations stating that in a [4+2] cycloaddition, the endo product is preferred, even if the exo product is more stable, due to favourable secondary orbital interactions in the TS.

===Relevant Files===
1,3-Dioxole (B3LYP-Optimised): [[File:DIOXOLE_B3LYP_eo1013.LOG]]

Cyclohexadiene (B3LYP-Optimised): [[File:CYCLOHEXADIENE_B3LYP_eo1013.LOG]]

Endo Product (B3LYP-Optimised): [[File:ENDO_PRODUCT_PM6_eo1013.LOG]]

Exo Product (B3LYP-Optimised): [[File:EXO_PRODUCT_END_B3LYP_eo1013.LOG]]

IRC of Endo Reaction (PM6 Optimised): [[File:IRC_PM6_ENDO_eo1013.LOG]]

IRC of Exo Reaction (PM6 Optimised): [[File:IRC_EXO_PM6_eo1013.LOG]]

==Exercise 3: O-xylylene + SO<sub>2</sub>==
[[File:Rxn_scheme_3_eo1013.PNG|350px|thumb|center|Figure 8: MO diagram for the reaction of o-xylylene with SO<sub>2</sub>]]

This is another example of another interesting Diels-Alder reaction ([4+2] cycloaddition). As well as having the endo and exo products, this reaction can react to give the chelotropic product where a 5-membered ring is formed with two new bonds both formed to the sulphur. The other caveat to this reaction is that the reaction can occur on the double bonds within the ring to produce three more products: endo, exo and chelotropic. The analysis will be discussed below.

===IRCs of the Exocyclic Reaction===
The IRCs were run showing the geometries along the reaction coordinate. From ''Figure 9'' and ''Figure 10'' is can be seen that the exo and endo reaction proceed with asynchronous bonding, with the oxygen bonding before the sulphur. ''Figure 11'' clearly shows that the chelotropic reaction bonding in a synchronous fashion.

<center>
[[File:Exo_irc_eo1013.gif|x500px|thumb|center|Figure 9: IRC showing the formation of the exo product]]
</center>

<center>
[[File:Endo_irc_eo1013.gif|x500px|thumb|center|Figure 10: IRC showing the formation of the endo product]]
</center>

<center>
[[File:Che_irc_eo1013.gif|x500px|thumb|center|Figure 11: IRC showing the formation of the cheloptopic product]]
</center>

===Thermochemical Analysis===
<center>
{| class="wikitable" border="1"
|+ Table 8: Thermochemical data for the reaction of o-xylylene with SO<sub>2</sub>
! Product
! Reaction Barrier in kJ mol<sup>-1</sup>
! Reaction Energy in kJ mol<sup>-1</sup>
|-
| Endo || 80.12 || -100.66
|-
| Exo || 84.11 || -101.31
|-
| Cheletropic || 102.44 || -157.65
|}
</center>

GaussView 5.0.9 was used to calculate the energetics of the three reactions at the PM6 level. From ''Table 8'' it can be seen that the chelotropic product has the lowest reaction energy and is therefore the thermodynamic product. A consideration of the bond enthalpies involved makes this quite clear, the formation of C-O and S-O is less favorable compared to the formation of S=O and S-C. (bonds REF) It also has the highest energy TS largely due to the the 5-membered ring in the TS which suffers from ring strain compared to 6-membered TS in the endo and exo reaction pathways. Because of this higher energy transition state, the other products will be expected to form in a greater proportion under equilibrium conditions.

[[File:Rxn_profile_3_eo1013.png|450px|thumb|right|Figure 12: Approximate Reaction profile of all three reaction pathways investigated for the reaction of o-xylylene with SO<sub>2</sub>]]

''Figure 12'' illustrates that the endo product has the lowest energy TS and is therefore the kinetic product. These reactions are all very favourable due to the fact that an aromatic ring in formed afterwards. The stabilisation due to aromatisiation is very desired as we can see that ir is large enough to compensate for the high TS energy of the chelotropic reaction. Looking at the IRCs we can see that the aromatic ring forms before the other bonds in the reaction.

===Relevant Files===
Sulphur Dioxide (PM6 Optimised): [[File:SO2_PM6_EO1013.LOG]]

O-xylylene (PM6 Optimised): [[File:XYLYLENE_NEW_PM6_EO1013.LOG]]

Chelotropic TS (PM6 Optimised): [[File:TS_OPTIMISED_FINAL_PM6_che_eo1013.LOG]]

Exo TS (PM6 Optimised): [[File:TS_PM6_FINAL_EXO_eo1013.LOG]]

Endo TS (PM6 Optimised): [[File:TS_PM6_ENDO_FINAL_eo1013.LOG]]

Chelotropic Product (PM6 Optimised): [[File:PRODUCTS_PM6_che_eo1013.LOG]]

Exo Product (PM6 Optimised): [[File:EXO_PRODUCT_PM6_FINAL_eo1013.LOG]]

Endo Product (PM6 Optimised): [[File:PRODUCTS_PM6_ENDO_FINAL_eo1013.LOG]]

===Alternative Reaction Pathway===
<center>
{| class="wikitable" border="1"
|+ Table 9: Thermochemical data for the reaction (alternative pathway) of o-xylylene with SO<sub>2</sub>
! Product
! Reaction Barrier in kJ mol<sup>-1</sup>
! Reaction Energy in kJ mol<sup>-1</sup>
|-
| Endo || 110.34 || 14.62
|-
| Exo || 118.18 || 19.06
|}
</center>

From ''Table 9'', it is clear that the products are less stable than the sum of the energies of the reactants at infinite separation, this is a strong indication that the reaction requires some energy input in order for it to occur (endothermic reaction). The reaction barriers are a lot higher in comparison to those in ''Table 8'' which makes sense as there is the lack of stablisation gained from forming an aromatic ring from this pathway. The IRCs (''Figure 13'' and ''Figure 14'') are shown below.

<center>
[[File:ALT_EXO_IRC_eo1013.gif|x500px|thumb|center|Figure 13: IRC showing the formation of the exo product through the alternative pathway]]
</center>

<center>
[[File:ALT_ENDO_IRC_eo1013.gif|x500px|thumb|center|Figure 14: IRC showing the formation of the endo product through the alternative pathway]]
</center>

===Relevant Files (Alternative Pathway)===

Alternative Exo TS (PM6 Optimised): [[File:TS_EXO_FINAL_PM6_ALT_eo1013.LOG]]

Alternative Endo TS (PM6 Optimised): [[File:TS_ENDO_FINAL_PM6_ALT_eo1013.LOG]]

Alternative Exo Product (PM6 Optimised): [[File:PRODUCT_EXO_PM6_ALT_eo013.LOG]]

Alternative Endo Product (PM6 Optimised): [[File:PRODUCT_ENDO_PM6_ALT_eo1013.LOG]]

==Conclusion==
In conclusion, the results from this lab agree with the established theory around Diels-Alder reactions. Using the PM6 allows for quick calculations that may not be so reliable but aid an understanding of the underlying chemistry. The B3LYP calculations are very reliable but are more expensive in terms of computational cost. GaussView 5.0.9 has proven to be a very useful tool in analysing the thermochemical data of reactions and visualising the MOs to understand favourable orientations for successful reactions.

''Exercise 1'' was useful in understanding the advantages and limitations of the computational methods chosen. Analyzing and comparing the C-C bond lengths reflected how close GaussView 5.0.9 can get to literature values. ''Exercise 2'' required more in-depth analysis of the energies of the optimised geometries and shows how effective computational chemistry can be in predicting the major product of a reaction. ''Exercise 3'' highlighted the importance of utilising our chemical intuition along with the computational methods to investigate alternative pathways to rationalise their feasibility which could prove useful in determining possible side reactions.

All in all, these exercises have shown that the computational approach is a very powerful one indeed and can be used to predict the course, outcomes and shortcomings of a reaction before even entering the lab. This has some very beneficial implications namely in the fact that money can be saved rather than being spent on reagents for a reaction that will not yield desired products. It also proves to be a very useful tool in understanding reaction dynamics/mechanisms.

===References===

Rep:Mod:EO1013TS

2017-12-19T23:03:44Z

Eo1013:

==Introduction==
GaussView 5.0.9 is a very powerful program that allows for complex quantum mechanical calculation to be performed on molecules. It was used to investigate several aspects of three Diels-Alder reactions, the orbital interactions (primary and secondary) were moedlled and closely inspected as well as the energies and transition states to better understand the reaction paths of the examples studied.

===Potential Energy Surfaces (PES)===
The concept of PES is fundamental in computational chemistry and has allowed for many breakthroughs. A PES displays the relationship between the energy of a molecule and its geometry.

<math display="block">\text{Equation 1: General Time-dependent Schrödinger equation: } i \hbar \frac{\partial}{\partial t}\Psi(\mathbf{r},t) = \hat H \Psi(\mathbf{r},t)</math>

The energies can be calculated using different computational methods that simplify and solve the Schrödinger equation (''Eqn 1'') using approximations allowing PES to be generated in very little time. A PES conatains a lot of information, namely global and local minima that represent stable confomers/rotamers of the same molecule with the transition state that links them.<ref>The Concept of PES, http://is.muni.cz/el/1431/podzim2015/C9920/um/The_concept_of_PES.pdf, (accessed December 2017)</ref>

===The Transition State (TS) and Minima===
In GaussView 5.0.9 there are various methods (discussed below) to allow for the calculation of energies after optimising a particular geometry to a minimum energy taking into account electron repulsion and several other factors. Methods have also been devised, making use of known atomic separations during transitions to hazard a guess at the TS before performing optimising calculations and running an Intrinsic Reaction Coordinate (IRC) calculation can be performed to plot a reaction profile diagram.

The value of gradient on the PES at the minimum and at the transition structure will both be zero. Minima will have a positive value for the second derivative in every axial direction of the energy potential surface whereas a TS will have a positive value for the second derivative (saddle point) in all axial directions apart from in the reaction coordinate. This means that at a minima, movement in any direction either side of that point will results in a geometry with a higher energy. The same is true for the TS but there is a decrease in energy in one dimension which is known as the reaction pathway. The PES has 3N-6 dimensions, where N is the number of atoms in the molecule of study, corresponding to the degrees of freedom available to the molecule. Running an IRC calculation on the Ts structure allows as to track the geometries along this pathway. (ANA CITATION 1)

The TS is a saddle point and just like a minima or a maxima, its first derivative will be zero. The difference however is apparent when you take the second derivative, which is done using a Hessian matrix in GaussView 5.0.9. The second derivative correlates to the energy and therefore the frequency and force constant of the vibrations in the molecule. As a result, minima always have positive force constants (increases in energy) and the TS, being a saddle point, will have at least one negative force constant (producing an imaginary vibration) which corresponds to the reaction pathway.

===Methods to Locate The TS===
In this investigation, three main methods were used to find the transition state.

'''Method 1:''' This method only works if one has prior knowledge of the transition state. The transition state is guessed using empirically observed bond lengths and a minimisation calculation is performed. If these lengths are wrong, undesired structures could form.

'''Method 2:''' This method also requires prior knowledge of the transition state. A guess of the TS is made and the bonds involved in the reaction are frozen before a minimisation calculation is performed. This structure is then optimised to a TS and is more reliable that '''Method 1'''.

'''Method 3:''' This method does not require prior knowledge of the transition state as you start with the product or reactants (optimised to a minimum). Bonds are then added or removed to closer resemble the TS and similar to '''Method 2''', these are frozen to obtain a minimum. However, It is not very reliable for TS geometries that do not resemble
the minima.

===Computational Methods===
The PM6 and B3LYP methods were used in this lab. PM6 is a semi-empirical method which simplifies the Hartree-Fock method by using empirical data and pre-determined integrals to solve Hamiltonian (the energy operator of the Schrödinger equation) and as a result, runs very quickly as less calculations need to be performed. With all the approximations and generic data used in this method, results are often inaccurate. (pm6 citation!)

B3LYP, on the other hand, is a hybrid method that uses elements of Hartree-Fock and Density Funtional Theory (DFT). This method is more expensive than the PM6 as it doesn't use pre-determined integrals: it uses the DFT method to calculate all of the terms of the Hamiltonian apart from the exchange correlation term which is done using a HF method. It gives a very reliable results. (QUANTUM BIBLE and QUORA).

==Exercise 1: Butadiene + Ethene==
[[File:Reaction_scheme_1_eo1013.png|350px|thumb|center|Figure 1: Reaction Scheme for Butadiene with Ethene]]

This reaction is a [4+2] cycloaddition. Butadiene and ethene react together to form cyclohexene. The diene is more electron-rich than the dienophile. As can be seen from ''Figure 2'', the HOMO of butadiene contributes more to the HOMO-1 of the TS. In addition, the LUMO on ethene contributes more to the LUMO+1 which shows that HOMO of butadiene is lower in energy than the LUMO of ethene. This is an example of a normal electron demand reaction as the closest interaction is between the HOMO of the diene and the LUMO off the dienophile.(CLAYDEN)

[[File:MO_1_eo1013.jpg|350px|thumb|center|Figure 2: MO Diagram showing orbital interactions in the reaction of Butadiene with Ethene]]

===Analysis of Molecular Orbitals===
A non-zero overlap integral is required in order for an orbital interaction to be favourable. Orbitals involved in this interaction must have the same symmetry as the overlap integral is proportional to the spatial overlap of the orbitals in question. For a non zero overlap, the orbitals must both be symmetric or asymmetric to give overall symmetric function. An anti-symmetric function will be gained when you combine orbitals of different symmetry which will leads overlap integral being zero.(CITE ATKINS AD)

Jmol BLURB 1

Looking at the HOMO and the LUMO of the TS in ''Table 3'', it is clear that they are formed from the HOMO of ethene and the LUMO of butadiene, both being symmetric orbitals. The opposite interaction from two antisymetic orbitals, the HOMO of butadiene and LUMO of ethene, give the HOMO-1 and the LUMO+1 of the TS. This clearly demonstrates that reactions can only be allowed when orbitals of the same symmetry can interact. Transition states that are of a geometry where orbitals of opposite symmetry are forced to interact will most likely lead to an unsuccessful reaction.

===Analysis of Bond Lengths===
<center>
{| class="wikitable" border="1"
|+ Table 4: Bond lengths (from ''Figure 1'') during the course of the reaction (Å)
! Bonds
! Cyclohexene
! Transition State
! Butadiene and Ethene
|-
| '''C1-C2''' || 1.501 || 1.380 || 1.335
|-
| '''C2-C3''' || 1.338 || 1.441 || 1.468
|-
| '''C3-C4''' || 1.501 || 1.380 || 1.335
|-
| '''C4-C5''' || 1.540 || 2.115 || ----
|-
| '''C5-C6''' || 1.541 || 1.382 || 1.327
|-
| '''C6-C1''' || 1.540 || 2.115 || ----
|}
</center>

A typical carbon to carbon single bond length is 1.54 Å and a double bond is 1.34 Å.(CITE) These are a direct match with the bond lengths predicted by Gaussian. C1-C2 and C3-C4 are a lot shorter due to the pulling effect of the higher electron density in C2-C3. As the carbons change from and sp3 hybridised orbitals to sp2, the bond lengths shorten and vice versa. Both double bonds on butadiene also lengthen as they change from sp2 to sp3 hybridisation. The two new bonds (C4-C5 and C6-C1) that form in the TS have a bond length (2.115 Å) that is smaller than two times the Van der Waal radius of carbon (1.7 Å) showing that the two molecules are starting to interact during the transition state and get shorter once the bond forms into a single C-C bond.(VdW reference)

===The Transition State===
<center>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>350</size>
<uploadedFileContents>BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 7; frank off; vector on; vector scale -4; vector 0.04; color vectors red</script>
<name>CPD_Dimer_TS</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle vibrate</text>
<target>CPD_Dimer_TS</target>
</jmolbutton>
</jmol>
</center>

The vibration above (click toggle vibration) corresponds to the negative frequency in the TS calculations a result of the negative force constant. The bond formation is synchronous as the carbons at both ends of the new bonds are moving at the same time in the TS. This can also seen in the IRC (Figure 3) as the bonds are formed at the same time.

<center>
[[File:IRC.gif|350px|thumb|center|Figure 3: IRC showing the formation of the two new bonds]]
</center>

===Relevant Files===
Product (PM6-Optimised): [[File:PRODUCTS_PM6_eo1016.LOG]]

TS of Reaction (PM6 Optimised): [[File:BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG]]

IRC of Reaction: [[File:BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG]]

==Exercise 2: Reaction of Cyclohexadiene + 1,3-Dioxole==
[[File:Rxn_scheme_eo1013.png|350px|thumb|center|Figure 4: Reaction Scheme for cyclohexadiene with 1,3-dioxole]]
This Diels-Alder reaction ([4+2] cycloaddition) is particularly interesting as there is a possibility of having two products: the endo and exo products. This is due to the fact that the dienophile is substituted and can approach in two different orientations. The exo product is formed when the bulk of the substituent approaches in such a way that it it pointing away from the pi-system of the diene. When it approaches with the bulk of the dienophile facing towards the pi system of the diene, the endo product is formed. This has implications for the energies of the products as will be discussed in the following sections.

[[File:Mo_2_eo1013.PNG|350px|thumb|center|Figure 5: MO diagram for the reaction of cyclohexadiene with 1,3-dioxole]]

The oxygen in either side of the dienophile have an electron donating effect on the p-orbitals of the double bond, causing the dienophile to be "electron rich" and raising the energy of the HOMO and LUMO, compared to ethene, as a result. As a consequence, as can illustrated in ''Figure 5'', the closest interaction is between the LUMO of the diene and the HOMO off the dienophile. Therefore, this is an example of an inverse electron demand reaction. (CLAYDEN)

===Analysis of Molecular Orbitals===
As mentioned before, the oxygens on the dioxole work to raise the energy of the HOMO and LUMO of the diene compared to ethene. This increases the energy gap and leads to weaker interactions. An example of this is the HOMO-1 which is still lower in energy than the HOMO of the reactants as it only experiences a slight destabilisation. Only orbitals of the same symmetry can interact as seen below in ''Table 5'' and ''Table 6''.

JMOL BLUB 2 + 3

===Thermochemical Analysis===
<center>
{| class="wikitable" border="1"
|+ Table 7: Thermochemical data for the reaction of cyclohexadiene with 1,3-dioxole
! Product
! Reaction Barrier in kJ mol<sup>-1</sup>
! Reaction Energy in kJ mol<sup>-1</sup>
|-
| Endo || 158.47 || -68.75
|-
| Exo || 166.30 || -65.15
|}
</center>

GaussView 5.0.9 also calculates the free energies of these geometries which can allow for an in-depth analysis of the energetics of the reaction. A summary of this data is presented in ''Table 7''. The reaction barrier is calculated as the difference in energy between the TS and the starting materials. The endo product has a lower reaction barrier compared to the exo product, making it the kinetically-preferred product. This can be attributed to the extra stabilisation present in the endo transition state as a result of the secondary orbital interactions between the oxygens and the pi system on the diene. ''Figure 6'' shows the orbital interaction between the oxygen (red atoms) with the double bond from.

[[File:Oxygen_interaction_eo1013.PNG|350px|thumb|center|Figure 6: MO depicted by GaussView 5.0.9 showing the secondary orbital interactions in the endo TS.]]

The reaction energy is calculated as the free energy difference between the products and the reactants. Comparing the two shows that the endo reaction has a more negative reaction energy compared to the exo reaction, making the endo product the thermodynamically-preferred product. This can be rationalised, as seen in ''Figure 7'', by the location of the CH<sub>2</sub>s on the-5 membered ring. There is some steric clash with the CH<sub>2</sub> fragments in the exo product with he CH<sub>2</sub>s on the bridging carbons which isn't present in the endo product (making it more thermodynamically stable).

[[File:Interaction_eo1013.PNG|350px|thumb|center|Figure 7: A diagram showing the steric clashing of the CH<sub>2</sub> fragments.]]

The endo product is both the kinetic and thermodynamic product. This also agrees with experimental observations stating that in a [4+2] cycloaddition, the endo product is preferred, even if the exo product is more stable, due to favourable secondary orbital interactions in the TS.

===Relevant Files===
1,3-Dioxole (B3LYP-Optimised): [[File:DIOXOLE_B3LYP_eo1013.LOG]]

Cyclohexadiene (B3LYP-Optimised): [[File:CYCLOHEXADIENE_B3LYP_eo1013.LOG]]

Endo Product (B3LYP-Optimised): [[File:ENDO_PRODUCT_PM6_eo1013.LOG]]

Exo Product (B3LYP-Optimised): [[File:EXO_PRODUCT_END_B3LYP_eo1013.LOG]]

IRC of Endo Reaction (PM6 Optimised): [[File:IRC_PM6_ENDO_eo1013.LOG]]

IRC of Exo Reaction (PM6 Optimised): [[File:IRC_EXO_PM6_eo1013.LOG]]

==Exercise 3: O-xylylene + SO<sub>2</sub>==
[[File:Rxn_scheme_3_eo1013.PNG|350px|thumb|center|Figure 8: MO diagram for the reaction of o-xylylene with SO<sub>2</sub>]]

This is another example of another interesting Diels-Alder reaction ([4+2] cycloaddition). As well as having the endo and exo products, this reaction can react to give the chelotropic product where a 5-membered ring is formed with two new bonds both formed to the sulphur. The other caveat to this reaction is that the reaction can occur on the double bonds within the ring to produce three more products: endo, exo and chelotropic. The analysis will be discussed below.

===IRCs of the Exocyclic Reaction===
The IRCs were run showing the geometries along the reaction coordinate. From ''Figure 9'' and ''Figure 10'' is can be seen that the exo and endo reaction proceed with asynchronous bonding, with the oxygen bonding before the sulphur. ''Figure 11'' clearly shows that the chelotropic reaction bonding in a synchronous fashion.

<center>
[[File:Exo_irc_eo1013.gif|x500px|thumb|center|Figure 9: IRC showing the formation of the exo product]]
</center>

<center>
[[File:Endo_irc_eo1013.gif|x500px|thumb|center|Figure 10: IRC showing the formation of the endo product]]
</center>

<center>
[[File:Che_irc_eo1013.gif|x500px|thumb|center|Figure 11: IRC showing the formation of the cheloptopic product]]
</center>

===Thermochemical Analysis===
<center>
{| class="wikitable" border="1"
|+ Table 8: Thermochemical data for the reaction of o-xylylene with SO<sub>2</sub>
! Product
! Reaction Barrier in kJ mol<sup>-1</sup>
! Reaction Energy in kJ mol<sup>-1</sup>
|-
| Endo || 80.12 || -100.66
|-
| Exo || 84.11 || -101.31
|-
| Cheletropic || 102.44 || -157.65
|}
</center>

GaussView 5.0.9 was used to calculate the energetics of the three reactions at the PM6 level. From ''Table 8'' it can be seen that the chelotropic product has the lowest reaction energy and is therefore the thermodynamic product. A consideration of the bond enthalpies involved makes this quite clear, the formation of C-O and S-O is less favorable compared to the formation of S=O and S-C. (bonds REF) It also has the highest energy TS largely due to the the 5-membered ring in the TS which suffers from ring strain compared to 6-membered TS in the endo and exo reaction pathways. Because of this higher energy transition state, the other products will be expected to form in a greater proportion under equilibrium conditions.

[[File:Rxn_profile_3_eo1013.png|450px|thumb|right|Figure 12: Approximate Reaction profile of all three reaction pathways investigated for the reaction of o-xylylene with SO<sub>2</sub>]]

''Figure 12'' illustrates that the endo product has the lowest energy TS and is therefore the kinetic product. These reactions are all very favourable due to the fact that an aromatic ring in formed afterwards. The stabilisation due to aromatisiation is very desired as we can see that ir is large enough to compensate for the high TS energy of the chelotropic reaction. Looking at the IRCs we can see that the aromatic ring forms before the other bonds in the reaction.

===Relevant Files===
Sulphur Dioxide (PM6 Optimised): [[File:SO2_PM6_EO1013.LOG]]

O-xylylene (PM6 Optimised): [[File:XYLYLENE_NEW_PM6_EO1013.LOG]]

Chelotropic TS (PM6 Optimised): [[File:TS_OPTIMISED_FINAL_PM6_che_eo1013.LOG]]

Exo TS (PM6 Optimised): [[File:TS_PM6_FINAL_EXO_eo1013.LOG]]

Endo TS (PM6 Optimised): [[File:TS_PM6_ENDO_FINAL_eo1013.LOG]]

Chelotropic Product (PM6 Optimised): [[File:PRODUCTS_PM6_che_eo1013.LOG]]

Exo Product (PM6 Optimised): [[File:EXO_PRODUCT_PM6_FINAL_eo1013.LOG]]

Endo Product (PM6 Optimised): [[File:PRODUCTS_PM6_ENDO_FINAL_eo1013.LOG]]

===Alternative Reaction Pathway===
<center>
{| class="wikitable" border="1"
|+ Table 9: Thermochemical data for the reaction (alternative pathway) of o-xylylene with SO<sub>2</sub>
! Product
! Reaction Barrier in kJ mol<sup>-1</sup>
! Reaction Energy in kJ mol<sup>-1</sup>
|-
| Endo || 110.34 || 14.62
|-
| Exo || 118.18 || 19.06
|}
</center>

From ''Table 9'', it is clear that the products are less stable than the sum of the energies of the reactants at infinite separation, this is a strong indication that the reaction requires some energy input in order for it to occur (endothermic reaction). The reaction barriers are a lot higher in comparison to those in ''Table 8'' which makes sense as there is the lack of stablisation gained from forming an aromatic ring from this pathway. The IRCs (''Figure 13'' and ''Figure 14'') are shown below.

<center>
[[File:ALT_EXO_IRC_eo1013.gif|x500px|thumb|center|Figure 13: IRC showing the formation of the exo product through the alternative pathway]]
</center>

<center>
[[File:ALT_ENDO_IRC_eo1013.gif|x500px|thumb|center|Figure 14: IRC showing the formation of the endo product through the alternative pathway]]
</center>

===Relevant Files (Alternative Pathway)===

Alternative Exo TS (PM6 Optimised): [[File:TS_EXO_FINAL_PM6_ALT_eo1013.LOG]]

Alternative Endo TS (PM6 Optimised): [[File:TS_ENDO_FINAL_PM6_ALT_eo1013.LOG]]

Alternative Exo Product (PM6 Optimised): [[File:PRODUCT_EXO_PM6_ALT_eo013.LOG]]

Alternative Endo Product (PM6 Optimised): [[File:PRODUCT_ENDO_PM6_ALT_eo1013.LOG]]

==Conclusion==
In conclusion, the results from this lab agree with the established theory around Diels-Alder reactions. Using the PM6 allows for quick calculations that may not be so reliable but aid an understanding of the underlying chemistry. The B3LYP calculations are very reliable but are more expensive in terms of computational cost. GaussView 5.0.9 has proven to be a very useful tool in analysing the thermochemical data of reactions and visualising the MOs to understand favourable orientations for successful reactions.

''Exercise 1'' was useful in understanding the advantages and limitations of the computational methods chosen. Analyzing and comparing the C-C bond lengths reflected how close GaussView 5.0.9 can get to literature values. ''Exercise 2'' required more in-depth analysis of the energies of the optimised geometries and shows how effective computational chemistry can be in predicting the major product of a reaction. ''Exercise 3'' highlighted the importance of utilising our chemical intuition along with the computational methods to investigate alternative pathways to rationalise their feasibility which could prove useful in determining possible side reactions.

All in all, these exercises have shown that the computational approach is a very powerful one indeed and can be used to predict the course, outcomes and shortcomings of a reaction before even entering the lab. This has some very beneficial implications namely in the fact that money can be saved rather than being spent on reagents for a reaction that will not yield desired products. It also proves to be a very useful tool in understanding reaction dynamics/mechanisms.

===References===

Rep:Mod:EO1013TS

2017-12-19T22:58:28Z

Eo1013:

==Introduction==
GaussView 5.0.9 is a very powerful program that allows for complex quantum mechanical calculation to be performed on molecules. It was used to investigate several aspects of three Diels-Alder reactions, the orbital interactions (primary and secondary) were moedlled and closely inspected as well as the energies and transition states to better understand the reaction paths of the examples studied.

===Potential Energy Surfaces (PES)===
The concept of PES is fundamental in computational chemistry and has allowed for many breakthroughs. A PES displays the relationship between the energy of a molecule and its geometry.

<math display="block">\text{Equation 1: General Time-dependent Schrödinger equation: } i \hbar \frac{\partial}{\partial t}\Psi(\mathbf{r},t) = \hat H \Psi(\mathbf{r},t)</math>

The energies can be calculated using different computational methods that simplify and solve the Schrödinger equation (''Eqn 1'') using approximations allowing PES to be generated in very little time. A PES conatains a lot of information, namely global and local minima that represent stable confomers/rotamers of the same molecule with the transition state that links them.<ref>The Concept of PES, hhttps://is.muni.cz/el/1431/podzim2015/C9920/um/The_concept_of_PES.pdf, (accessed December 2017)</ref>

===The Transition State (TS) and Minima===
In GaussView 5.0.9 there are various methods (discussed below) to allow for the calculation of energies after optimising a particular geometry to a minimum energy taking into account electron repulsion and several other factors. Methods have also been devised, making use of known atomic separations during transitions to hazard a guess at the TS before performing optimising calculations and running an Intrinsic Reaction Coordinate (IRC) calculation can be performed to plot a reaction profile diagram.

sencond year screencap

The value of gradient on the PES at the minimum and at the transition structure will both be zero. Minima will have a positive value for the second derivative in every axial direction of the energy potential surface whereas a TS will have a positive value for the second derivative (saddle point) in all axial directions apart from in the reaction coordinate. This means that at a minima, movement in any direction either side of that point will results in a geometry with a higher energy. The same is true for the TS but there is a decrease in energy in one dimension which is known as the reaction pathway (Figure 1). The PES has 3N-6 dimensions, where N is the number of atoms in the molecule of study, corresponding to the degrees of freedom available to the molecule. Running an IRC calculation on the Ts structure allows as to track the geometries along this pathway. (ANA CITATION 1)

The TS is a saddle point and just like a minima or a maxima, its first derivative will be zero. The difference however is apparent when you take the second derivative, which is done using a Hessian matrix in GaussView 5.0.9. The second derivative correlates to the energy and therefore the frequency and force constant of the vibrations in the molecule. As a result, minima always have positive force constants (increases in energy) and the TS, being a saddle point, will have at least one negative force constant (producing an imaginary vibration) which corresponds to the reaction pathway.

===Methods to Locate The TS===
In this investigation, three main methods were used to find the transition state.

'''Method 1:''' This method only works if one has prior knowledge of the transition state. The transition state is guessed using empirically observed bond lengths and a minimisation calculation is performed. If these lengths are wrong, undesired structures could form.

'''Method 2:''' This method also requires prior knowledge of the transition state. A guess of the TS is made and the bonds involved in the reaction are frozen before a minimisation calculation is performed. This structure is then optimised to a TS and is more reliable that '''Method 1'''.

'''Method 3:''' This method does not require prior knowledge of the transition state as you start with the product or reactants (optimised to a minimum). Bonds are then added or removed to closer resemble the TS and similar to '''Method 2''', these are frozen to obtain a minimum. However, It is not very reliable for TS geometries that do not resemble
the minima.

===Computational Methods===
The PM6 and B3LYP methods were used in this lab. PM6 is a semi-empirical method which simplifies the Hartree-Fock method by using empirical data and pre-determined integrals to solve Hamiltonian (the energy operator of the Schrödinger equation) and as a result, runs very quickly as less calculations need to be performed. With all the approximations and generic data used in this method, results are often inaccurate. (pm6 citation!)

B3LYP, on the other hand, is a hybrid method that uses elements of Hartree-Fock and Density Funtional Theory (DFT). This method is more expensive than the PM6 as it doesn't use pre-determined integrals: it uses the DFT method to calculate all of the terms of the Hamiltonian apart from the exchange correlation term which is done using a HF method. It gives a very reliable results. (QUANTUM BIBLE and QUORA).

==Exercise 1: Butadiene + Ethene==
[[File:Reaction_scheme_1_eo1013.png|350px|thumb|center|Figure 1: Reaction Scheme for Butadiene with Ethene]]

This reaction is a [4+2] cycloaddition. Butadiene and ethene react together to form cyclohexene. The diene is more electron-rich than the dienophile. As can be seen from ''Figure 2'', the HOMO of butadiene contributes more to the HOMO-1 of the TS. In addition, the LUMO on ethene contributes more to the LUMO+1 which shows that HOMO of butadiene is lower in energy than the LUMO of ethene. This is an example of a normal electron demand reaction as the closest interaction is between the HOMO of the diene and the LUMO off the dienophile.(CLAYDEN)

[[File:MO_1_eo1013.jpg|350px|thumb|center|Figure 2: MO Diagram showing orbital interactions in the reaction of Butadiene with Ethene]]

===Analysis of Molecular Orbitals===
A non-zero overlap integral is required in order for an orbital interaction to be favourable. Orbitals involved in this interaction must have the same symmetry as the overlap integral is proportional to the spatial overlap of the orbitals in question. For a non zero overlap, the orbitals must both be symmetric or asymmetric to give overall symmetric function. An anti-symmetric function will be gained when you combine orbitals of different symmetry which will leads overlap integral being zero.(CITE ATKINS AD)

Jmol BLURB 1

Looking at the HOMO and the LUMO of the TS in ''Table 3'', it is clear that they are formed from the HOMO of ethene and the LUMO of butadiene, both being symmetric orbitals. The opposite interaction from two antisymetic orbitals, the HOMO of butadiene and LUMO of ethene, give the HOMO-1 and the LUMO+1 of the TS. This clearly demonstrates that reactions can only be allowed when orbitals of the same symmetry can interact. Transition states that are of a geometry where orbitals of opposite symmetry are forced to interact will most likely lead to an unsuccessful reaction.

===Analysis of Bond Lengths===
<center>
{| class="wikitable" border="1"
|+ Table 4: Bond lengths (from ''Figure 1'') during the course of the reaction (Å)
! Bonds
! Cyclohexene
! Transition State
! Butadiene and Ethene
|-
| '''C1-C2''' || 1.501 || 1.380 || 1.335
|-
| '''C2-C3''' || 1.338 || 1.441 || 1.468
|-
| '''C3-C4''' || 1.501 || 1.380 || 1.335
|-
| '''C4-C5''' || 1.540 || 2.115 || ----
|-
| '''C5-C6''' || 1.541 || 1.382 || 1.327
|-
| '''C6-C1''' || 1.540 || 2.115 || ----
|}
</center>

A typical carbon to carbon single bond length is 1.54 Å and a double bond is 1.34 Å.(CITE) These are a direct match with the bond lengths predicted by Gaussian. C1-C2 and C3-C4 are a lot shorter due to the pulling effect of the higher electron density in C2-C3. As the carbons change from and sp3 hybridised orbitals to sp2, the bond lengths shorten and vice versa. Both double bonds on butadiene also lengthen as they change from sp2 to sp3 hybridisation. The two new bonds (C4-C5 and C6-C1) that form in the TS have a bond length (2.115 Å) that is smaller than two times the Van der Waal radius of carbon (1.7 Å) showing that the two molecules are starting to interact during the transition state and get shorter once the bond forms into a single C-C bond.(VdW reference)

===The Transition State===
<center>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>350</size>
<uploadedFileContents>BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 7; frank off; vector on; vector scale -4; vector 0.04; color vectors red</script>
<name>CPD_Dimer_TS</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle vibrate</text>
<target>CPD_Dimer_TS</target>
</jmolbutton>
</jmol>
</center>

The vibration above (click toggle vibration) corresponds to the negative frequency in the TS calculations a result of the negative force constant. The bond formation is synchronous as the carbons at both ends of the new bonds are moving at the same time in the TS. This can also seen in the IRC (Figure 3) as the bonds are formed at the same time.

<center>
[[File:IRC.gif|350px|thumb|center|Figure 3: IRC showing the formation of the two new bonds]]
</center>

===Relevant Files===
Product (PM6-Optimised): [[File:PRODUCTS_PM6_eo1016.LOG]]

TS of Reaction (PM6 Optimised): [[File:BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG]]

IRC of Reaction: [[File:BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG]]

==Exercise 2: Reaction of Cyclohexadiene + 1,3-Dioxole==
[[File:Rxn_scheme_eo1013.png|350px|thumb|center|Figure 4: Reaction Scheme for cyclohexadiene with 1,3-dioxole]]
This Diels-Alder reaction ([4+2] cycloaddition) is particularly interesting as there is a possibility of having two products: the endo and exo products. This is due to the fact that the dienophile is substituted and can approach in two different orientations. The exo product is formed when the bulk of the substituent approaches in such a way that it it pointing away from the pi-system of the diene. When it approaches with the bulk of the dienophile facing towards the pi system of the diene, the endo product is formed. This has implications for the energies of the products as will be discussed in the following sections.

[[File:Mo_2_eo1013.PNG|350px|thumb|center|Figure 5: MO diagram for the reaction of cyclohexadiene with 1,3-dioxole]]

The oxygen in either side of the dienophile have an electron donating effect on the p-orbitals of the double bond, causing the dienophile to be "electron rich" and raising the energy of the HOMO and LUMO, compared to ethene, as a result. As a consequence, as can illustrated in ''Figure 5'', the closest interaction is between the LUMO of the diene and the HOMO off the dienophile. Therefore, this is an example of an inverse electron demand reaction. (CLAYDEN)

===Analysis of Molecular Orbitals===
As mentioned before, the oxygens on the dioxole work to raise the energy of the HOMO and LUMO of the diene compared to ethene. This increases the energy gap and leads to weaker interactions. An example of this is the HOMO-1 which is still lower in energy than the HOMO of the reactants as it only experiences a slight destabilisation. Only orbitals of the same symmetry can interact as seen below in ''Table 5'' and ''Table 6''.

JMOL BLUB 2 + 3

===Thermochemical Analysis===
<center>
{| class="wikitable" border="1"
|+ Table 7: Thermochemical data for the reaction of cyclohexadiene with 1,3-dioxole
! Product
! Reaction Barrier in kJ mol<sup>-1</sup>
! Reaction Energy in kJ mol<sup>-1</sup>
|-
| Endo || 158.47 || -68.75
|-
| Exo || 166.30 || -65.15
|}
</center>

GaussView 5.0.9 also calculates the free energies of these geometries which can allow for an in-depth analysis of the energetics of the reaction. A summary of this data is presented in ''Table 7''. The reaction barrier is calculated as the difference in energy between the TS and the starting materials. The endo product has a lower reaction barrier compared to the exo product, making it the kinetically-preferred product. This can be attributed to the extra stabilisation present in the endo transition state as a result of the secondary orbital interactions between the oxygens and the pi system on the diene. ''Figure 6'' shows the orbital interaction between the oxygen (red atoms) with the double bond from.

[[File:Oxygen_interaction_eo1013.PNG|350px|thumb|center|Figure 6: MO depicted by GaussView 5.0.9 showing the secondary orbital interactions in the endo TS.]]

The reaction energy is calculated as the free energy difference between the products and the reactants. Comparing the two shows that the endo reaction has a more negative reaction energy compared to the exo reaction, making the endo product the thermodynamically-preferred product. This can be rationalised, as seen in ''Figure 7'', by the location of the CH<sub>2</sub>s on the-5 membered ring. There is some steric clash with the CH<sub>2</sub> fragments in the exo product with he CH<sub>2</sub>s on the bridging carbons which isn't present in the endo product (making it more thermodynamically stable).

[[File:Interaction_eo1013.PNG|350px|thumb|center|Figure 7: A diagram showing the steric clashing of the CH<sub>2</sub> fragments.]]

The endo product is both the kinetic and thermodynamic product. This also agrees with experimental observations stating that in a [4+2] cycloaddition, the endo product is preferred, even if the exo product is more stable, due to favourable secondary orbital interactions in the TS.

===Relevant Files===
1,3-Dioxole (B3LYP-Optimised): [[File:DIOXOLE_B3LYP_eo1013.LOG]]

Cyclohexadiene (B3LYP-Optimised): [[File:CYCLOHEXADIENE_B3LYP_eo1013.LOG]]

Endo Product (B3LYP-Optimised): [[File:ENDO_PRODUCT_PM6_eo1013.LOG]]

Exo Product (B3LYP-Optimised): [[File:EXO_PRODUCT_END_B3LYP_eo1013.LOG]]

IRC of Endo Reaction (PM6 Optimised): [[File:IRC_PM6_ENDO_eo1013.LOG]]

IRC of Exo Reaction (PM6 Optimised): [[File:IRC_EXO_PM6_eo1013.LOG]]

==Exercise 3: O-xylylene + SO<sub>2</sub>==
[[File:Rxn_scheme_3_eo1013.PNG|350px|thumb|center|Figure 8: MO diagram for the reaction of o-xylylene with SO<sub>2</sub>]]

This is another example of another interesting Diels-Alder reaction ([4+2] cycloaddition). As well as having the endo and exo products, this reaction can react to give the chelotropic product where a 5-membered ring is formed with two new bonds both formed to the sulphur. The other caveat to this reaction is that the reaction can occur on the double bonds within the ring to produce three more products: endo, exo and chelotropic. The analysis will be discussed below.

===IRCs of the Exocyclic Reaction===
The IRCs were run showing the geometries along the reaction coordinate. From ''Figure 9'' and ''Figure 10'' is can be seen that the exo and endo reaction proceed with asynchronous bonding, with the oxygen bonding before the sulphur. ''Figure 11'' clearly shows that the chelotropic reaction bonding in a synchronous fashion.

<center>
[[File:Exo_irc_eo1013.gif|x500px|thumb|center|Figure 9: IRC showing the formation of the exo product]]
</center>

<center>
[[File:Endo_irc_eo1013.gif|x500px|thumb|center|Figure 10: IRC showing the formation of the endo product]]
</center>

<center>
[[File:Che_irc_eo1013.gif|x500px|thumb|center|Figure 11: IRC showing the formation of the cheloptopic product]]
</center>

===Thermochemical Analysis===
<center>
{| class="wikitable" border="1"
|+ Table 8: Thermochemical data for the reaction of o-xylylene with SO<sub>2</sub>
! Product
! Reaction Barrier in kJ mol<sup>-1</sup>
! Reaction Energy in kJ mol<sup>-1</sup>
|-
| Endo || 80.12 || -100.66
|-
| Exo || 84.11 || -101.31
|-
| Cheletropic || 102.44 || -157.65
|}
</center>

GaussView 5.0.9 was used to calculate the energetics of the three reactions at the PM6 level. From ''Table 8'' it can be seen that the chelotropic product has the lowest reaction energy and is therefore the thermodynamic product. A consideration of the bond enthalpies involved makes this quite clear, the formation of C-O and S-O is less favorable compared to the formation of S=O and S-C. (bonds REF) It also has the highest energy TS largely due to the the 5-membered ring in the TS which suffers from ring strain compared to 6-membered TS in the endo and exo reaction pathways. Because of this higher energy transition state, the other products will be expected to form in a greater proportion under equilibrium conditions.

[[File:Rxn_profile_3_eo1013.png|450px|thumb|right|Figure 12: Approximate Reaction profile of all three reaction pathways investigated for the reaction of o-xylylene with SO<sub>2</sub>]]

''Figure 12'' illustrates that the endo product has the lowest energy TS and is therefore the kinetic product. These reactions are all very favourable due to the fact that an aromatic ring in formed afterwards. The stabilisation due to aromatisiation is very desired as we can see that ir is large enough to compensate for the high TS energy of the chelotropic reaction. Looking at the IRCs we can see that the aromatic ring forms before the other bonds in the reaction.

===Relevant Files===
Sulphur Dioxide (PM6 Optimised): [[File:SO2_PM6_EO1013.LOG]]

O-xylylene (PM6 Optimised): [[File:XYLYLENE_NEW_PM6_EO1013.LOG]]

Chelotropic TS (PM6 Optimised): [[File:TS_OPTIMISED_FINAL_PM6_che_eo1013.LOG]]

Exo TS (PM6 Optimised): [[File:TS_PM6_FINAL_EXO_eo1013.LOG]]

Endo TS (PM6 Optimised): [[File:TS_PM6_ENDO_FINAL_eo1013.LOG]]

Chelotropic Product (PM6 Optimised): [[File:PRODUCTS_PM6_che_eo1013.LOG]]

Exo Product (PM6 Optimised): [[File:EXO_PRODUCT_PM6_FINAL_eo1013.LOG]]

Endo Product (PM6 Optimised): [[File:PRODUCTS_PM6_ENDO_FINAL_eo1013.LOG]]

===Alternative Reaction Pathway===
<center>
{| class="wikitable" border="1"
|+ Table 9: Thermochemical data for the reaction (alternative pathway) of o-xylylene with SO<sub>2</sub>
! Product
! Reaction Barrier in kJ mol<sup>-1</sup>
! Reaction Energy in kJ mol<sup>-1</sup>
|-
| Endo || 110.34 || 14.62
|-
| Exo || 118.18 || 19.06
|}
</center>

From ''Table 9'', it is clear that the products are less stable than the sum of the energies of the reactants at infinite separation, this is a strong indication that the reaction requires some energy input in order for it to occur (endothermic reaction). The reaction barriers are a lot higher in comparison to those in ''Table 8'' which makes sense as there is the lack of stablisation gained from forming an aromatic ring from this pathway. The IRCs (''Figure 13'' and ''Figure 14'') are shown below.

<center>
[[File:ALT_EXO_IRC_eo1013.gif|x500px|thumb|center|Figure 13: IRC showing the formation of the exo product through the alternative pathway]]
</center>

<center>
[[File:ALT_ENDO_IRC_eo1013.gif|x500px|thumb|center|Figure 14: IRC showing the formation of the endo product through the alternative pathway]]
</center>

===Relevant Files (Alternative Pathway)===

Alternative Exo TS (PM6 Optimised): [[File:TS_EXO_FINAL_PM6_ALT_eo1013.LOG]]

Alternative Endo TS (PM6 Optimised): [[File:TS_ENDO_FINAL_PM6_ALT_eo1013.LOG]]

Alternative Exo Product (PM6 Optimised): [[File:PRODUCT_EXO_PM6_ALT_eo013.LOG]]

Alternative Endo Product (PM6 Optimised): [[File:PRODUCT_ENDO_PM6_ALT_eo1013.LOG]]

==Conclusion==
In conclusion, the results from this lab agree with the established theory around Diels-Alder reactions. Using the PM6 allows for quick calculations that may not be so reliable but aid an understanding of the underlying chemistry. The B3LYP calculations are very reliable but are more expensive in terms of computational cost. GaussView 5.0.9 has proven to be a very useful tool in analysing the thermochemical data of reactions and visualising the MOs to understand favourable orientations for successful reactions.

''Exercise 1'' was useful in understanding the advantages and limitations of the computational methods chosen. Analyzing and comparing the C-C bond lengths reflected how close GaussView 5.0.9 can get to literature values. ''Exercise 2'' required more in-depth analysis of the energies of the optimised geometries and shows how effective computational chemistry can be in predicting the major product of a reaction. ''Exercise 3'' highlighted the importance of utilising our chemical intuition along with the computational methods to investigate alternative pathways to rationalise their feasibility which could prove useful in determining possible side reactions.

All in all, these exercises have shown that the computational approach is a very powerful one indeed and can be used to predict the course, outcomes and shortcomings of a reaction before even entering the lab. This has some very beneficial implications namely in the fact that money can be saved rather than being spent on reagents for a reaction that will not yield desired products. It also proves to be a very useful tool in understanding reaction dynamics/mechanisms.

Rep:Mod:EO1013TS

2017-12-19T22:54:14Z

Eo1013:

==Introduction==
GaussView 5.0.9 is a very powerful program that allows for complex quantum mechanical calculation to be performed on molecules. It was used to investigate several aspects of three Diels-Alder reactions, the orbital interactions (primary and secondary) were moedlled and closely inspected as well as the energies and transition states to better understand the reaction paths of the examples studied.

===Potential Energy Surfaces (PES)===
The concept of PES is fundamental in computational chemistry and has allowed for many breakthroughs. A PES displays the relationship between the energy of a molecule and its geometry.

<math display="block">\text{Equation 1: General Time-dependent Schrödinger equation: } i \hbar \frac{\partial}{\partial t}\Psi(\mathbf{r},t) = \hat H \Psi(\mathbf{r},t)</math>

The energies can be calculated using different computational methods that simplify and solve the Schrödinger equation (''Eqn 1'') using approximations allowing PES to be generated in very little time. A PES conatains a lot of information, namely global and local minima that represent stable confomers/rotamers of the same molecule with the transition state that links them.
(reference=hhttps://is.muni.cz/el/1431/podzim2015/C9920/um/The_concept_of_PES.pdf

===The Transition State (TS) and Minima===
In GaussView 5.0.9 there are various methods (discussed below) to allow for the calculation of energies after optimising a particular geometry to a minimum energy taking into account electron repulsion and several other factors. Methods have also been devised, making use of known atomic separations during transitions to hazard a guess at the TS before performing optimising calculations and running an Intrinsic Reaction Coordinate (IRC) calculation can be performed to plot a reaction profile diagram.

sencond year screencap

The value of gradient on the PES at the minimum and at the transition structure will both be zero. Minima will have a positive value for the second derivative in every axial direction of the energy potential surface whereas a TS will have a positive value for the second derivative (saddle point) in all axial directions apart from in the reaction coordinate. This means that at a minima, movement in any direction either side of that point will results in a geometry with a higher energy. The same is true for the TS but there is a decrease in energy in one dimension which is known as the reaction pathway (Figure 1). The PES has 3N-6 dimensions, where N is the number of atoms in the molecule of study, corresponding to the degrees of freedom available to the molecule. Running an IRC calculation on the Ts structure allows as to track the geometries along this pathway. (ANA CITATION 1)

The TS is a saddle point and just like a minima or a maxima, its first derivative will be zero. The difference however is apparent when you take the second derivative, which is done using a Hessian matrix in GaussView 5.0.9. The second derivative correlates to the energy and therefore the frequency and force constant of the vibrations in the molecule. As a result, minima always have positive force constants (increases in energy) and the TS, being a saddle point, will have at least one negative force constant (producing an imaginary vibration) which corresponds to the reaction pathway.

===Methods to Locate The TS===
In this investigation, three main methods were used to find the transition state.

'''Method 1:''' This method only works if one has prior knowledge of the transition state. The transition state is guessed using empirically observed bond lengths and a minimisation calculation is performed. If these lengths are wrong, undesired structures could form.

'''Method 2:''' This method also requires prior knowledge of the transition state. A guess of the TS is made and the bonds involved in the reaction are frozen before a minimisation calculation is performed. This structure is then optimised to a TS and is more reliable that '''Method 1'''.

'''Method 3:''' This method does not require prior knowledge of the transition state as you start with the product or reactants (optimised to a minimum). Bonds are then added or removed to closer resemble the TS and similar to '''Method 2''', these are frozen to obtain a minimum. However, It is not very reliable for TS geometries that do not resemble
the minima.

===Computational Methods===
The PM6 and B3LYP methods were used in this lab. PM6 is a semi-empirical method which simplifies the Hartree-Fock method by using empirical data and pre-determined integrals to solve Hamiltonian (the energy operator of the Schrödinger equation) and as a result, runs very quickly as less calculations need to be performed. With all the approximations and generic data used in this method, results are often inaccurate. (pm6 citation!)

B3LYP, on the other hand, is a hybrid method that uses elements of Hartree-Fock and Density Funtional Theory (DFT). This method is more expensive than the PM6 as it doesn't use pre-determined integrals: it uses the DFT method to calculate all of the terms of the Hamiltonian apart from the exchange correlation term which is done using a HF method. It gives a very reliable results. (QUANTUM BIBLE and QUORA).

==Exercise 1: Butadiene + Ethene==
[[File:Reaction_scheme_1_eo1013.png|350px|thumb|center|Figure 1: Reaction Scheme for Butadiene with Ethene]]

This reaction is a [4+2] cycloaddition. Butadiene and ethene react together to form cyclohexene. The diene is more electron-rich than the dienophile. As can be seen from ''Figure 2'', the HOMO of butadiene contributes more to the HOMO-1 of the TS. In addition, the LUMO on ethene contributes more to the LUMO+1 which shows that HOMO of butadiene is lower in energy than the LUMO of ethene. This is an example of a normal electron demand reaction as the closest interaction is between the HOMO of the diene and the LUMO off the dienophile.(CLAYDEN)

[[File:MO_1_eo1013.jpg|350px|thumb|center|Figure 2: MO Diagram showing orbital interactions in the reaction of Butadiene with Ethene]]

===Analysis of Molecular Orbitals===
A non-zero overlap integral is required in order for an orbital interaction to be favourable. Orbitals involved in this interaction must have the same symmetry as the overlap integral is proportional to the spatial overlap of the orbitals in question. For a non zero overlap, the orbitals must both be symmetric or asymmetric to give overall symmetric function. An anti-symmetric function will be gained when you combine orbitals of different symmetry which will leads overlap integral being zero.(CITE ATKINS AD)

Jmol BLURB 1

Looking at the HOMO and the LUMO of the TS in ''Table 3'', it is clear that they are formed from the HOMO of ethene and the LUMO of butadiene, both being symmetric orbitals. The opposite interaction from two antisymetic orbitals, the HOMO of butadiene and LUMO of ethene, give the HOMO-1 and the LUMO+1 of the TS. This clearly demonstrates that reactions can only be allowed when orbitals of the same symmetry can interact. Transition states that are of a geometry where orbitals of opposite symmetry are forced to interact will most likely lead to an unsuccessful reaction.

===Analysis of Bond Lengths===
<center>
{| class="wikitable" border="1"
|+ Table 4: Bond lengths (from ''Figure 1'') during the course of the reaction (Å)
! Bonds
! Cyclohexene
! Transition State
! Butadiene and Ethene
|-
| '''C1-C2''' || 1.501 || 1.380 || 1.335
|-
| '''C2-C3''' || 1.338 || 1.441 || 1.468
|-
| '''C3-C4''' || 1.501 || 1.380 || 1.335
|-
| '''C4-C5''' || 1.540 || 2.115 || ----
|-
| '''C5-C6''' || 1.541 || 1.382 || 1.327
|-
| '''C6-C1''' || 1.540 || 2.115 || ----
|}
</center>

A typical carbon to carbon single bond length is 1.54 Å and a double bond is 1.34 Å.(CITE) These are a direct match with the bond lengths predicted by Gaussian. C1-C2 and C3-C4 are a lot shorter due to the pulling effect of the higher electron density in C2-C3. As the carbons change from and sp3 hybridised orbitals to sp2, the bond lengths shorten and vice versa. Both double bonds on butadiene also lengthen as they change from sp2 to sp3 hybridisation. The two new bonds (C4-C5 and C6-C1) that form in the TS have a bond length (2.115 Å) that is smaller than two times the Van der Waal radius of carbon (1.7 Å) showing that the two molecules are starting to interact during the transition state and get shorter once the bond forms into a single C-C bond.(VdW reference)

===The Transition State===
<center>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>350</size>
<uploadedFileContents>BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 7; frank off; vector on; vector scale -4; vector 0.04; color vectors red</script>
<name>CPD_Dimer_TS</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle vibrate</text>
<target>CPD_Dimer_TS</target>
</jmolbutton>
</jmol>
</center>

The vibration above (click toggle vibration) corresponds to the negative frequency in the TS calculations a result of the negative force constant. The bond formation is synchronous as the carbons at both ends of the new bonds are moving at the same time in the TS. This can also seen in the IRC (Figure 3) as the bonds are formed at the same time.

<center>
[[File:IRC.gif|350px|thumb|center|Figure 3: IRC showing the formation of the two new bonds]]
</center>

===Relevant Files===
Product (PM6-Optimised): [[File:PRODUCTS_PM6_eo1016.LOG]]

TS of Reaction (PM6 Optimised): [[File:BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG]]

IRC of Reaction: [[File:BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG]]

==Exercise 2: Reaction of Cyclohexadiene + 1,3-Dioxole==
[[File:Rxn_scheme_eo1013.png|350px|thumb|center|Figure 4: Reaction Scheme for cyclohexadiene with 1,3-dioxole]]
This Diels-Alder reaction ([4+2] cycloaddition) is particularly interesting as there is a possibility of having two products: the endo and exo products. This is due to the fact that the dienophile is substituted and can approach in two different orientations. The exo product is formed when the bulk of the substituent approaches in such a way that it it pointing away from the pi-system of the diene. When it approaches with the bulk of the dienophile facing towards the pi system of the diene, the endo product is formed. This has implications for the energies of the products as will be discussed in the following sections.

[[File:Mo_2_eo1013.PNG|350px|thumb|center|Figure 5: MO diagram for the reaction of cyclohexadiene with 1,3-dioxole]]

The oxygen in either side of the dienophile have an electron donating effect on the p-orbitals of the double bond, causing the dienophile to be "electron rich" and raising the energy of the HOMO and LUMO, compared to ethene, as a result. As a consequence, as can illustrated in ''Figure 5'', the closest interaction is between the LUMO of the diene and the HOMO off the dienophile. Therefore, this is an example of an inverse electron demand reaction. (CLAYDEN)

===Analysis of Molecular Orbitals===
As mentioned before, the oxygens on the dioxole work to raise the energy of the HOMO and LUMO of the diene compared to ethene. This increases the energy gap and leads to weaker interactions. An example of this is the HOMO-1 which is still lower in energy than the HOMO of the reactants as it only experiences a slight destabilisation. Only orbitals of the same symmetry can interact as seen below in ''Table 5'' and ''Table 6''.

JMOL BLUB 2 + 3

===Thermochemical Analysis===
<center>
{| class="wikitable" border="1"
|+ Table 7: Thermochemical data for the reaction of cyclohexadiene with 1,3-dioxole
! Product
! Reaction Barrier in kJ mol<sup>-1</sup>
! Reaction Energy in kJ mol<sup>-1</sup>
|-
| Endo || 158.47 || -68.75
|-
| Exo || 166.30 || -65.15
|}
</center>

GaussView 5.0.9 also calculates the free energies of these geometries which can allow for an in-depth analysis of the energetics of the reaction. A summary of this data is presented in ''Table 7''. The reaction barrier is calculated as the difference in energy between the TS and the starting materials. The endo product has a lower reaction barrier compared to the exo product, making it the kinetically-preferred product. This can be attributed to the extra stabilisation present in the endo transition state as a result of the secondary orbital interactions between the oxygens and the pi system on the diene. ''Figure 6'' shows the orbital interaction between the oxygen (red atoms) with the double bond from.

[[File:Oxygen_interaction_eo1013.PNG|350px|thumb|center|Figure 6: MO depicted by GaussView 5.0.9 showing the secondary orbital interactions in the endo TS.]]

The reaction energy is calculated as the free energy difference between the products and the reactants. Comparing the two shows that the endo reaction has a more negative reaction energy compared to the exo reaction, making the endo product the thermodynamically-preferred product. This can be rationalised, as seen in ''Figure 7'', by the location of the CH<sub>2</sub>s on the-5 membered ring. There is some steric clash with the CH<sub>2</sub> fragments in the exo product with he CH<sub>2</sub>s on the bridging carbons which isn't present in the endo product (making it more thermodynamically stable).

[[File:Interaction_eo1013.PNG|350px|thumb|center|Figure 7: A diagram showing the steric clashing of the CH<sub>2</sub> fragments.]]

The endo product is both the kinetic and thermodynamic product. This also agrees with experimental observations stating that in a [4+2] cycloaddition, the endo product is preferred, even if the exo product is more stable, due to favourable secondary orbital interactions in the TS.

===Relevant Files===
1,3-Dioxole (B3LYP-Optimised): [[File:DIOXOLE_B3LYP_eo1013.LOG]]

Cyclohexadiene (B3LYP-Optimised): [[File:CYCLOHEXADIENE_B3LYP_eo1013.LOG]]

Endo Product (B3LYP-Optimised): [[File:ENDO_PRODUCT_PM6_eo1013.LOG]]

Exo Product (B3LYP-Optimised): [[File:EXO_PRODUCT_END_B3LYP_eo1013.LOG]]

IRC of Endo Reaction (PM6 Optimised): [[File:IRC_PM6_ENDO_eo1013.LOG]]

IRC of Exo Reaction (PM6 Optimised): [[File:IRC_EXO_PM6_eo1013.LOG]]

==Exercise 3: O-xylylene + SO<sub>2</sub>==
[[File:Rxn_scheme_3_eo1013.PNG|350px|thumb|center|Figure 8: MO diagram for the reaction of o-xylylene with SO<sub>2</sub>]]

This is another example of another interesting Diels-Alder reaction ([4+2] cycloaddition). As well as having the endo and exo products, this reaction can react to give the chelotropic product where a 5-membered ring is formed with two new bonds both formed to the sulphur. The other caveat to this reaction is that the reaction can occur on the double bonds within the ring to produce three more products: endo, exo and chelotropic. The analysis will be discussed below.

===IRCs of the Exocyclic Reaction===
The IRCs were run showing the geometries along the reaction coordinate. From ''Figure 9'' and ''Figure 10'' is can be seen that the exo and endo reaction proceed with asynchronous bonding, with the oxygen bonding before the sulphur. ''Figure 11'' clearly shows that the chelotropic reaction bonding in a synchronous fashion.

<center>
[[File:Exo_irc_eo1013.gif|x500px|thumb|center|Figure 9: IRC showing the formation of the exo product]]
</center>

<center>
[[File:Endo_irc_eo1013.gif|x500px|thumb|center|Figure 10: IRC showing the formation of the endo product]]
</center>

<center>
[[File:Che_irc_eo1013.gif|x500px|thumb|center|Figure 11: IRC showing the formation of the cheloptopic product]]
</center>

===Thermochemical Analysis===
<center>
{| class="wikitable" border="1"
|+ Table 8: Thermochemical data for the reaction of o-xylylene with SO<sub>2</sub>
! Product
! Reaction Barrier in kJ mol<sup>-1</sup>
! Reaction Energy in kJ mol<sup>-1</sup>
|-
| Endo || 80.12 || -100.66
|-
| Exo || 84.11 || -101.31
|-
| Cheletropic || 102.44 || -157.65
|}
</center>

GaussView 5.0.9 was used to calculate the energetics of the three reactions at the PM6 level. From ''Table 8'' it can be seen that the chelotropic product has the lowest reaction energy and is therefore the thermodynamic product. A consideration of the bond enthalpies involved makes this quite clear, the formation of C-O and S-O is less favorable compared to the formation of S=O and S-C. (bonds REF) It also has the highest energy TS largely due to the the 5-membered ring in the TS which suffers from ring strain compared to 6-membered TS in the endo and exo reaction pathways. Because of this higher energy transition state, the other products will be expected to form in a greater proportion under equilibrium conditions.

[[File:Rxn_profile_3_eo1013.png|450px|thumb|right|Figure 12: Approximate Reaction profile of all three reaction pathways investigated for the reaction of o-xylylene with SO<sub>2</sub>]]

''Figure 12'' illustrates that the endo product has the lowest energy TS and is therefore the kinetic product. These reactions are all very favourable due to the fact that an aromatic ring in formed afterwards. The stabilisation due to aromatisiation is very desired as we can see that ir is large enough to compensate for the high TS energy of the chelotropic reaction. Looking at the IRCs we can see that the aromatic ring forms before the other bonds in the reaction.

===Relevant Files===
Sulphur Dioxide (PM6 Optimised): [[File:SO2_PM6_EO1013.LOG]]

O-xylylene (PM6 Optimised): [[File:XYLYLENE_NEW_PM6_EO1013.LOG]]

Chelotropic TS (PM6 Optimised): [[File:TS_OPTIMISED_FINAL_PM6_che_eo1013.LOG]]

Exo TS (PM6 Optimised): [[File:TS_PM6_FINAL_EXO_eo1013.LOG]]

Endo TS (PM6 Optimised): [[File:TS_PM6_ENDO_FINAL_eo1013.LOG]]

Chelotropic Product (PM6 Optimised): [[File:PRODUCTS_PM6_che_eo1013.LOG]]

Exo Product (PM6 Optimised): [[File:EXO_PRODUCT_PM6_FINAL_eo1013.LOG]]

Endo Product (PM6 Optimised): [[File:PRODUCTS_PM6_ENDO_FINAL_eo1013.LOG]]

===Alternative Reaction Pathway===
<center>
{| class="wikitable" border="1"
|+ Table 9: Thermochemical data for the reaction (alternative pathway) of o-xylylene with SO<sub>2</sub>
! Product
! Reaction Barrier in kJ mol<sup>-1</sup>
! Reaction Energy in kJ mol<sup>-1</sup>
|-
| Endo || 110.34 || 14.62
|-
| Exo || 118.18 || 19.06
|}
</center>

From ''Table 9'', it is clear that the products are less stable than the sum of the energies of the reactants at infinite separation, this is a strong indication that the reaction requires some energy input in order for it to occur (endothermic reaction). The reaction barriers are a lot higher in comparison to those in ''Table 8'' which makes sense as there is the lack of stablisation gained from forming an aromatic ring from this pathway. The IRCs (''Figure 13'' and ''Figure 14'') are shown below.

<center>
[[File:ALT_EXO_IRC_eo1013.gif|x500px|thumb|center|Figure 13: IRC showing the formation of the exo product through the alternative pathway]]
</center>

<center>
[[File:ALT_ENDO_IRC_eo1013.gif|x500px|thumb|center|Figure 14: IRC showing the formation of the endo product through the alternative pathway]]
</center>

===Relevant Files (Alternative Pathway)===

Alternative Exo TS (PM6 Optimised): [[File:TS_EXO_FINAL_PM6_ALT_eo1013.LOG]]

Alternative Endo TS (PM6 Optimised): [[File:TS_ENDO_FINAL_PM6_ALT_eo1013.LOG]]

Alternative Exo Product (PM6 Optimised): [[File:PRODUCT_EXO_PM6_ALT_eo013.LOG]]

Alternative Endo Product (PM6 Optimised): [[File:PRODUCT_ENDO_PM6_ALT_eo1013.LOG]]

==Conclusion==
In conclusion, the results from this lab agree with the established theory around Diels-Alder reactions. Using the PM6 allows for quick calculations that may not be so reliable but aid an understanding of the underlying chemistry. The B3LYP calculations are very reliable but are more expensive in terms of computational cost. GaussView 5.0.9 has proven to be a very useful tool in analysing the thermochemical data of reactions and visualising the MOs to understand favourable orientations for successful reactions.

''Exercise 1'' was useful in understanding the advantages and limitations of the computational methods chosen. Analyzing and comparing the C-C bond lengths reflected how close GaussView 5.0.9 can get to literature values. ''Exercise 2'' required more in-depth analysis of the energies of the optimised geometries and shows how effective computational chemistry can be in predicting the major product of a reaction. ''Exercise 3'' highlighted the importance of utilising our chemical intuition along with the computational methods to investigate alternative pathways to rationalise their feasibility which could prove useful in determining possible side reactions.

All in all, these exercises have shown that the computational approach is a very powerful one indeed and can be used to predict the course, outcomes and shortcomings of a reaction before even entering the lab. This has some very beneficial implications namely in the fact that money can be saved rather than being spent on reagents for a reaction that will not yield desired products. It also proves to be a very useful tool in understanding reaction dynamics/mechanisms.

Rep:Mod:EO1013TS

2017-12-19T22:26:53Z

Eo1013: /* Exercise 3: O-xylylene + SO2 */

==Introduction==
GaussView 5.0.9 is a very powerful program that allows for complex quantum mechanical calculation to be performed on molecules. It was used to investigate several aspects of three Diels-Alder reactions, the orbital interactions (primary and secondary) were moedlled and closely inspected as well as the energies and transition states to better understand the reaction paths of the examples studied.

===Potential Energy Surfaces (PES)===
The concept of PES is fundamental in computational chemistry and has allowed for many breakthroughs. A PES displays the relationship between the energy of a molecule and its geometry.

<math display="block">\text{Equation 1: General Time-dependent Schrödinger equation: } i \hbar \frac{\partial}{\partial t}\Psi(\mathbf{r},t) = \hat H \Psi(\mathbf{r},t)</math>

The energies can be calculated using different computational methods that simplify and solve the Schrödinger equation (''Eqn 1'') using approximations allowing PES to be generated in very little time. A PES conatains a lot of information, namely global and local minima that represent stable confomers/rotamers of the same molecule with the transition state that links them.
(reference=hhttps://is.muni.cz/el/1431/podzim2015/C9920/um/The_concept_of_PES.pdf

===The Transition State (TS) and Minima===
In GaussView 5.0.9 there are various methods (discussed below) to allow for the calculation of energies after optimising a particular geometry to a minimum energy taking into account electron repulsion and several other factors. Methods have also been devised, making use of known atomic separations during transitions to hazard a guess at the TS before performing optimising calculations and running an Intrinsic Reaction Coordinate (IRC) calculation can be performed to plot a reaction profile diagram.

sencond year screencap

The value of gradient on the PES at the minimum and at the transition structure will both be zero. Minima will have a positive value for the second derivative in every axial direction of the energy potential surface whereas a TS will have a positive value for the second derivative (saddle point) in all axial directions apart from in the reaction coordinate. This means that at a minima, movement in any direction either side of that point will results in a geometry with a higher energy. The same is true for the TS but there is a decrease in energy in one dimension which is known as the reaction pathway (Figure 1). The PES has 3N-6 dimensions, where N is the number of atoms in the molecule of study, corresponding to the degrees of freedom available to the molecule. Running an IRC calculation on the Ts structure allows as to track the geometries along this pathway. (ANA CITATION 1)

The TS is a saddle point and just like a minima or a maxima, its first derivative will be zero. The difference however is apparent when you take the second derivative, which is done using a Hessian matrix in GaussView 5.0.9. The second derivative correlates to the energy and therefore the frequency and force constant of the vibrations in the molecule. As a result, minima always have positive force constants (increases in energy) and the TS, being a saddle point, will have at least one negative force constant (producing an imaginary vibration) which corresponds to the reaction pathway.

===Methods to Locate The TS===
In this investigation, three main methods were used to find the transition state.

'''Method 1:''' This method only works if one has prior knowledge of the transition state. The transition state is guessed using empirically observed bond lengths and a minimisation calculation is performed. If these lengths are wrong, undesired structures could form.

'''Method 2:''' This method also requires prior knowledge of the transition state. A guess of the TS is made and the bonds involved in the reaction are frozen before a minimisation calculation is performed. This structure is then optimised to a TS and is more reliable that '''Method 1'''.

'''Method 3:''' This method does not require prior knowledge of the transition state as you start with the product or reactants (optimised to a minimum). Bonds are then added or removed to closer resemble the TS and similar to '''Method 2''', these are frozen to obtain a minimum. However, It is not very reliable for TS geometries that do not resemble
the minima.

===Computational Methods===
The PM6 and B3LYP methods were used in this lab. PM6 is a semi-empirical method which simplifies the Hartree-Fock method by using empirical data and pre-determined integrals to solve Hamiltonian (the energy operator of the Schrödinger equation) and as a result, runs very quickly as less calculations need to be performed. With all the approximations and generic data used in this method, results are often inaccurate. (pm6 citation!)

B3LYP, on the other hand, is a hybrid method that uses elements of Hartree-Fock and Density Funtional Theory (DFT). This method is more expensive than the PM6 as it doesn't use pre-determined integrals: it uses the DFT method to calculate all of the terms of the Hamiltonian apart from the exchange correlation term which is done using a HF method. It gives a very reliable results. (QUANTUM BIBLE and QUORA).

==Exercise 1: Butadiene + Ethene==
[[File:Reaction_scheme_1_eo1013.png|350px|thumb|center|Figure 1: Reaction Scheme for Butadiene with Ethene]]

This reaction is a [4+2] cycloaddition. Butadiene and ethene react together to form cyclohexene. The diene is more electron-rich than the dienophile. As can be seen from ''Figure 2'', the HOMO of butadiene contributes more to the HOMO-1 of the TS. In addition, the LUMO on ethene contributes more to the LUMO+1 which shows that HOMO of butadiene is lower in energy than the LUMO of ethene. This is an example of a normal electron demand reaction as the closest interaction is between the HOMO of the diene and the LUMO off the dienophile.(CLAYDEN)

[[File:MO_1_eo1013.jpg|350px|thumb|center|Figure 2: MO Diagram showing orbital interactions in the reaction of Butadiene with Ethene]]

===Analysis of Molecular Orbitals===
A non-zero overlap integral is required in order for an orbital interaction to be favourable. Orbitals involved in this interaction must have the same symmetry as the overlap integral is proportional to the spatial overlap of the orbitals in question. For a non zero overlap, the orbitals must both be symmetric or asymmetric to give overall symmetric function. An anti-symmetric function will be gained when you combine orbitals of different symmetry which will leads overlap integral being zero.(CITE ATKINS AD)

Jmol BLURB 1

Looking at the HOMO and the LUMO of the TS in ''Table 3'', it is clear that they are formed from the HOMO of ethene and the LUMO of butadiene, both being symmetric orbitals. The opposite interaction from two antisymetic orbitals, the HOMO of butadiene and LUMO of ethene, give the HOMO-1 and the LUMO+1 of the TS. This clearly demonstrates that reactions can only be allowed when orbitals of the same symmetry can interact. Transition states that are of a geometry where orbitals of opposite symmetry are forced to interact will most likely lead to an unsuccessful reaction.

===Analysis of Bond Lengths===
<center>
{| class="wikitable" border="1"
|+ Table 4: Bond lengths (from ''Figure 1'') during the course of the reaction (Å)
! Bonds
! Cyclohexene
! Transition State
! Butadiene and Ethene
|-
| '''C1-C2''' || 1.501 || 1.380 || 1.335
|-
| '''C2-C3''' || 1.338 || 1.441 || 1.468
|-
| '''C3-C4''' || 1.501 || 1.380 || 1.335
|-
| '''C4-C5''' || 1.540 || 2.115 || ----
|-
| '''C5-C6''' || 1.541 || 1.382 || 1.327
|-
| '''C6-C1''' || 1.540 || 2.115 || ----
|}
</center>

A typical carbon to carbon single bond length is 1.54 Å and a double bond is 1.34 Å.(CITE) These are a direct match with the bond lengths predicted by Gaussian. C1-C2 and C3-C4 are a lot shorter due to the pulling effect of the higher electron density in C2-C3. As the carbons change from and sp3 hybridised orbitals to sp2, the bond lengths shorten and vice versa. Both double bonds on butadiene also lengthen as they change from sp2 to sp3 hybridisation. The two new bonds (C4-C5 and C6-C1) that form in the TS have a bond length (2.115 Å) that is smaller than two times the Van der Waal radius of carbon (1.7 Å) showing that the two molecules are starting to interact during the transition state and get shorter once the bond forms into a single C-C bond.(VdW reference)

===The Transition State===
<center>
<jmol>
<jmolApplet>
<title></title><color>white</color><size>350</size>
<uploadedFileContents>BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 7; frank off; vector on; vector scale -4; vector 0.04; color vectors red</script>
<name>CPD_Dimer_TS</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Toggle vibrate</text>
<target>CPD_Dimer_TS</target>
</jmolbutton>
</jmol>
</center>

The vibration above (click toggle vibration) corresponds to the negative frequency in the TS calculations a result of the negative force constant. The bond formation is synchronous as the carbons at both ends of the new bonds are moving at the same time in the TS. This can also seen in the IRC (Figure 3) as the bonds are formed at the same time.

<center>
[[File:IRC.gif|350px|thumb|center|Figure 3: IRC showing the formation of the two new bonds]]
</center>

===Relevant Files===
Product (PM6-Optimised): [[File:PRODUCTS_PM6_eo1016.LOG]]

TS of Reaction (PM6 Optimised): [[File:BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG]]

IRC of Reaction: [[File:BOTH_INITIAL_IRC_TS_PM6_eo1013.LOG]]

==Exercise 2: Reaction of Cyclohexadiene + 1,3-Dioxole==
[[File:Rxn_scheme_eo1013.png|350px|thumb|center|Figure 4: Reaction Scheme for cyclohexadiene with 1,3-dioxole]]
This Diels-Alder reaction ([4+2] cycloaddition) is particularly interesting as there is a possibility of having two products: the endo and exo products. This is due to the fact that the dienophile is substituted and can approach in two different orientations. The exo product is formed when the bulk of the substituent approaches in such a way that it it pointing away from the pi-system of the diene. When it approaches with the bulk of the dienophile facing towards the pi system of the diene, the endo product is formed. This has implications for the energies of the products as will be discussed in the following sections.

[[File:Mo_2_eo1013.PNG|350px|thumb|center|Figure 5: MO diagram for the reaction of cyclohexadiene with 1,3-dioxole]]

The oxygen in either side of the dienophile have an electron donating effect on the p-orbitals of the double bond, causing the dienophile to be "electron rich" and raising the energy of the HOMO and LUMO, compared to ethene, as a result. As a consequence, as can illustrated in ''Figure 5'', the closest interaction is between the LUMO of the diene and the HOMO off the dienophile. Therefore, this is an example of an inverse electron demand reaction. (CLAYDEN)

===Analysis of Molecular Orbitals===
As mentioned before, the oxygens on the dioxole work to raise the energy of the HOMO and LUMO of the diene compared to ethene. This increases the energy gap and leads to weaker interactions. An example of this is the HOMO-1 which is still lower in energy than the HOMO of the reactants as it only experiences a slight destabilisation. Only orbitals of the same symmetry can interact as seen below in ''Table 5'' and ''Table 6''.

JMOL BLUB 2 + 3

===Thermochemical Analysis===
<center>
{| class="wikitable" border="1"
|+ Table 7: Thermochemical data for the reaction of cyclohexadiene with 1,3-dioxole
! Product
! Reaction Barrier in kJ mol<sup>-1</sup>
! Reaction Energy in kJ mol<sup>-1</sup>
|-
| Endo || 158.47 || -68.75
|-
| Exo || 166.30 || -65.15
|}
</center>

GaussView 5.0.9 also calculates the free energies of these geometries which can allow for an in-depth analysis of the energetics of the reaction. A summary of this data is presented in ''Table 7''. The reaction barrier is calculated as the difference in energy between the TS and the starting materials. The endo product has a lower reaction barrier compared to the exo product, making it the kinetically-preferred product. This can be attributed to the extra stabilisation present in the endo transition state as a result of the secondary orbital interactions between the oxygens and the pi system on the diene. ''Figure 6'' shows the orbital interaction between the oxygen (red atoms) with the double bond from.

[[File:Oxygen_interaction_eo1013.PNG|350px|thumb|center|Figure 6: MO depicted by GaussView 5.0.9 showing the secondary orbital interactions in the endo TS.]]

The reaction energy is calculated as the free energy difference between the products and the reactants. Comparing the two shows that the endo reaction has a more negative reaction energy compared to the exo reaction, making the endo product the thermodynamically-preferred product. This can be rationalised, as seen in ''Figure 7'', by the location of the CH<sub>2</sub>s on the-5 membered ring. There is some steric clash with the CH<sub>2</sub> fragments in the exo product with he CH<sub>2</sub>s on the bridging carbons which isn't present in the endo product (making it more thermodynamically stable).

[[File:Interaction_eo1013.PNG|350px|thumb|center|Figure 7: A diagram showing the steric clashing of the CH<sub>2</sub> fragments.]]

The endo product is both the kinetic and thermodynamic product.

===Relevant Files===
1,3-Dioxole (B3LYP-Optimised): [[File:DIOXOLE_B3LYP_eo1013.LOG]]

Cyclohexadiene (B3LYP-Optimised): [[File:CYCLOHEXADIENE_B3LYP_eo1013.LOG]]

Endo Product (B3LYP-Optimised): [[File:ENDO_PRODUCT_PM6_eo1013.LOG]]

Exo Product (B3LYP-Optimised): [[File:EXO_PRODUCT_END_B3LYP_eo1013.LOG]]

IRC of Endo Reaction (PM6 Optimised): [[File:IRC_PM6_ENDO_eo1013.LOG]]

IRC of Exo Reaction (PM6 Optimised): [[File:IRC_EXO_PM6_eo1013.LOG]]

==Exercise 3: O-xylylene + SO<sub>2</sub>==
[[File:Rxn_scheme_3_eo1013.PNG|350px|thumb|center|Figure 8: MO diagram for the reaction of o-xylylene with SO<sub>2</sub>]]

This is another example of another interesting Diels-Alder reaction ([4+2] cycloaddition). As well as having the endo and exo products, this reaction can react to give the chelotropic product where a 5-membered ring is formed with two new bonds both formed to the sulphur. The other caveat to this reaction is that the reaction can occur on the double bonds within the ring to produce three more products: endo, exo and chelotropic. The analysis will be discussed below.

===IRCs of the Exocyclic Reaction===
The IRCs were run showing the geometries along the reaction coordinate. From ''Figure 9'' and ''Figure 10'' is can be seen that the exo and endo reaction proceed with asynchronous bonding, with the oxygen bonding before the sulphur. ''Figure 11'' clearly shows that the chelotropic reaction bonding in a synchronous fashion.

<center>
[[File:Exo_irc_eo1013.gif|x500px|thumb|center|Figure 9: IRC showing the formation of the exo product]]
</center>

<center>
[[File:Endo_irc_eo1013.gif|x500px|thumb|center|Figure 10: IRC showing the formation of the endo product]]
</center>

<center>
[[File:Che_irc_eo1013.gif|x500px|thumb|center|Figure 11: IRC showing the formation of the cheloptopic product]]
</center>

===Thermochemical Analysis===
<center>
{| class="wikitable" border="1"
|+ Table 8: Thermochemical data for the reaction of o-xylylene with SO<sub>2</sub>
! Product
! Reaction Barrier in kJ mol<sup>-1</sup>
! Reaction Energy in kJ mol<sup>-1</sup>
|-
| Endo || 80.12 || -100.66
|-
| Exo || 84.11 || -101.31
|-
| Cheletropic || 102.44 || -157.65
|}
</center>

GaussView 5.0.9 was used to calculate the energetics of the three reactions at the PM6 level. From ''Table 8'' it can be seen that the chelotropic product has the lowest reaction energy and is therefore the thermodynamic product. A consideration of the bond enthalpies involved makes this quite clear, the formation of C-O and S-O is less favorable compared to the formation of S=O and S-C. (bonds REF) It also has the highest energy TS largely due to the the 5-membered ring in the TS which suffers from ring strain compared to 6-membered TS in the endo and exo reaction pathways. Because of this higher energy transition state, the other products will be expected to form in a greater proportion under equilibrium conditions.

[[File:Rxn_profile_3_eo1013.png|450px|thumb|right|Figure 12: Approximate Reaction profile of all three reaction pathways investigated for the reaction of o-xylylene with SO<sub>2</sub>]]

''Figure 12'' illustrates that the endo product has the lowest energy TS and is therefore the kinetic product. These reactions are all very favourable due to the fact that an aromatic ring in formed afterwards. The stabilisation due to aromatisiation is very desired as we can see that ir is large enough to compensate for the high TS energy of the chelotropic reaction. Looking at the IRCs we can see that the aromatic ring forms before the other bonds in the reaction.

===Relevant Files===
Sulphur Dioxide (PM6 Optimised): [[File:SO2_PM6_EO1013.LOG]]

O-xylylene (PM6 Optimised): [[File:XYLYLENE_NEW_PM6_EO1013.LOG]]

Chelotropic TS (PM6 Optimised): [[File:TS_OPTIMISED_FINAL_PM6_che_eo1013.LOG]]

Exo TS (PM6 Optimised): [[File:TS_PM6_FINAL_EXO_eo1013.LOG]]

Endo TS (PM6 Optimised): [[File:TS_PM6_ENDO_FINAL_eo1013.LOG]]

Chelotropic Product (PM6 Optimised): [[File:PRODUCTS_PM6_che_eo1013.LOG]]

Exo Product (PM6 Optimised): [[File:EXO_PRODUCT_PM6_FINAL_eo1013.LOG]]

Endo Product (PM6 Optimised): [[File:PRODUCTS_PM6_ENDO_FINAL_eo1013.LOG]]

===Alternative Reaction Pathway===
<center>
{| class="wikitable" border="1"
|+ Table 9: Thermochemical data for the reaction (alternative pathway) of o-xylylene with SO<sub>2</sub>
! Product
! Reaction Barrier in kJ mol<sup>-1</sup>
! Reaction Energy in kJ mol<sup>-1</sup>
|-
| Endo || 110.34 || 14.62
|-
| Exo || 118.18 || 19.06
|}
</center>

From ''Table 9'', it is clear that the products are less stable than the sum of the energies of the reactants at infinite separation, this is a strong indication that the reaction requires some energy input in order for it to occur (endothermic reaction). The reaction barriers are a lot higher in comparison to those in ''Table 8'' which makes sense as there is the lack of stablisation gained from forming an aromatic ring from this pathway. The IRCs (''Figure 13'' and ''Figure 14'') are shown below.

<center>
[[File:ALT_EXO_IRC_eo1013.gif|x500px|thumb|center|Figure 13: IRC showing the formation of the exo product through the alternative pathway]]
</center>

<center>
[[File:ALT_ENDO_IRC_eo1013.gif|x500px|thumb|center|Figure 14: IRC showing the formation of the endo product through the alternative pathway]]
</center>

===Relevant Files (Alternative Pathway)===

Alternative Exo TS (PM6 Optimised): [[File:TS_EXO_FINAL_PM6_ALT_eo1013.LOG]]

Alternative Endo TS (PM6 Optimised): [[File:TS_ENDO_FINAL_PM6_ALT_eo1013.LOG]]

Alternative Exo Product (PM6 Optimised): [[File:PRODUCT_EXO_PM6_ALT_eo013.LOG]]

Alternative Endo Product (PM6 Optimised): [[File:PRODUCT_ENDO_PM6_ALT_eo1013.LOG]]

File:PRODUCT ENDO PM6 ALT eo1013.LOG

2017-12-19T22:26:47Z

Eo1013:

File:TS ENDO FINAL PM6 ALT eo1013.LOG

2017-12-19T22:26:25Z

Eo1013:

File:PRODUCT EXO PM6 ALT eo013.LOG

2017-12-19T22:25:58Z

Eo1013:

File:TS EXO FINAL PM6 ALT eo1013.LOG

2017-12-19T22:25:32Z

Eo1013:

File:ALT ENDO IRC eo1013.gif

2017-12-19T22:22:29Z

Eo1013:

Rep:Mod:EO1013TS

2017-12-19T22:22:17Z

Eo1013: /* Alternative Reaction Pathway */

File:ALT EXO IRC eo1013.gif

2017-12-19T22:21:36Z

Eo1013:

Rep:Mod:EO1013TS

2017-12-19T22:10:29Z

Eo1013: /* Exercise 3: O-xylylene + SO2 */

Rep:Mod:EO1013TS

2017-12-19T22:05:58Z

Eo1013: /* Relevant Files */

File:PRODUCTS PM6 che eo1013.LOG

2017-12-19T22:04:59Z

Eo1013: Eo1013 uploaded a new version of File:PRODUCTS PM6 che eo1013.LOG

Rep:Mod:EO1013TS

2017-12-19T22:03:32Z

Eo1013: /* Relevant Files */

File:TS PM6 ENDO FINAL eo1013.LOG

2017-12-19T22:03:23Z

Eo1013:

File:PRODUCTS PM6 ENDO FINAL eo1013.LOG

2017-12-19T22:03:01Z

Eo1013:

File:EXO PRODUCT PM6 FINAL eo1013.LOG

2017-12-19T22:02:19Z

Eo1013:

File:TS PM6 FINAL EXO eo1013.LOG

2017-12-19T22:01:50Z

Eo1013:

File:PRODUCTS PM6 che eo1013.LOG

2017-12-19T22:00:04Z

Eo1013:

File:TS OPTIMISED FINAL PM6 che eo1013.LOG

2017-12-19T21:58:38Z

Eo1013:

File:XYLYLENE NEW PM6 EO1013.LOG

2017-12-19T21:57:17Z

Eo1013:

File:SO2 PM6 EO1013.LOG

2017-12-19T21:56:56Z

Eo1013:

Rep:Mod:EO1013TS

2017-12-19T21:43:43Z

Eo1013: /* Exercise 3: O-xylylene + SO2 */

Rep:Mod:EO1013TS

2017-12-19T21:40:17Z

Eo1013: /* Thermochemical Analysis */

Rep:Mod:EO1013TS

2017-12-19T21:39:38Z

Eo1013: /* Thermochemical Analysis */

File:Rxn profile 3 eo1013.png

2017-12-19T21:37:52Z

Eo1013: Eo1013 uploaded a new version of File:Rxn profile 3 eo1013.png

File:Rxn profile 3 eo1013.png

2017-12-19T21:36:12Z

Eo1013:

Rep:Mod:EO1013TS

2017-12-19T20:20:03Z

Eo1013: /* Thermochemical Analysis */

Rep:Mod:EO1013TS

2017-12-19T20:16:11Z

Eo1013: /* Exercise 3: O-xylylene + SO2 */

File:Che irc eo1013.gif

2017-12-19T20:14:41Z

Eo1013: Eo1013 uploaded a new version of File:Che irc eo1013.gif

File:Che irc eo1013.gif

2017-12-19T20:13:58Z

Eo1013: Eo1013 uploaded a new version of File:Che irc eo1013.gif

Rep:Mod:EO1013TS

2017-12-19T20:12:06Z

Eo1013: /* IRCs of the Exocyclic Reaction */

File:Exo irc eo1013.gif

2017-12-19T20:11:55Z

Eo1013:

File:Endo irc eo1013.gif

2017-12-19T20:09:25Z

Eo1013:

Rep:Mod:EO1013TS

2017-12-19T20:06:47Z

Eo1013: /* IRCs of the Exocyclic Reaction */

Rep:Mod:EO1013TS

2017-12-19T20:06:13Z

Eo1013: /* IRCs of the Exocyclic Reaction */

Rep:Mod:EO1013TS

2017-12-19T20:04:48Z

Eo1013: /* IRCs of the Exocyclic Reaction */

Rep:Mod:EO1013TS

2017-12-19T20:03:28Z

Eo1013: /* IRCs of the Exocyclic Reaction */

Rep:Mod:EO1013TS

2017-12-19T20:02:49Z

Eo1013: /* IRCs of the Exocyclic Reaction */

File:Che irc eo1013.gif

2017-12-19T20:02:16Z

Eo1013:

File:Chelo irc eo1013.gif

2017-12-19T19:59:49Z

Eo1013: Eo1013 uploaded a new version of File:Chelo irc eo1013.gif

Rep:Mod:EO1013TS

2017-12-19T19:59:12Z

Eo1013: /* IRCs of the Exocyclic Reaction */