ChemWiki - User contributions [en]

Rep:Mod:cc5115TS

2018-02-14T11:24:50Z

Cc5115: /* Analysis of the vibrations */

= Y3C Transition states and Reactivity =

== Introduction ==

This section aims to illustrate the 3 different computational techniques that can be utilised in order to analyse the transition state (TS) of a reaction. The TS is the state which has the highest energy along a reaction coordinate, as a result it is the least stable state. In the reaction, the reactants needs to have a certain amount of energy in order to surpass the activation barrier, also known as the transition state energy, and reach the product state. This computational lab allows for calculations leading to the location of the TS. The structure of the TS is crucial in determining the mechanism of a reaction.

A potential energy surface (PES) has a 3N-6 dimension, which coincides to the degrees of freedom that the molecule has, where N is the number of atoms that the molecule possesses. In a 3-D PES, the saddle point (also called the TS), is a local mixami amidst 2 minima, and can be sometimes identified through secondary derivatives as it would be negative in one direction and positive in all other directions.

There are 3 calculation methods available in order to determine the structure of the TS.

1. The first and fastest method requires only one step where a guessed structure of the TS is optimised to give an optimised TS. This means that one will need of the TS to quite an extent, furthermore this method is rather unreliable as there is a high chance that the guessed TS is incorrectly drawn.

2. The second method works from a pre-frozen guess structure of the TS where the reacting termini of the reactants are frozen in space before the remaining structure is optimised to a minima. After that, the molecules are optimised as a transition state. This allows for a more reliable representation of the TS. This method is sufficient for Exercise 1.

3. The third method is the longest and most reliable method. Here, one starts by either optimising from the reactants or the products to a minima. For the reactant case, each reactants are optimised to a minima, arranged to resemble the TS and the reacting termini are frozen and the rest of the method 2 is repeated. A similar case occurs with the product; when the product is optimised to a minima, the bonds formed in the reactions are removed, the 2 fragments are arranged to resemble the TS and the reacting termini are frozen and method 2 was used once more. This method allows for the most reliable representation of the TS and is used for Exercise 2 & 3.

In this computational lab, two methods of calculation were used on Gaussian in order to find the TS. During the optimisation, the position of the molecule is decided as it is built in Gaussian. The time-independent Schrödinger equation was solved whilst utilising the Born-Oppenheimer approximation in order to find the energy and the wavefunction φ which represents the electronic states for the fixed nuclear positions and is dependent on on frozen nuclei positions. This is also known as the self-consistent field method (SCF). The two methods employed are the semi-empirical method PM6, which is usually performed first and sometimes followed by the Density Functional Theory (DFT) method B3LYP. The semi-empirical method PM6, although based on the Hartree-Fock formalism, this method uses many approximations based on experimental data in order to solve the Schrodinger equations. This method is usually fast and reliable, but can be easily countered if the environment of the molecule that is being computed is not similar enough to the approximated parameters of this method. The other method is B3LYP, a hydrid functional which utilises the DFT in order to calculate the majority of the Hamiltonian while a small portion still utilises the Hartree-Fock theory to calculate the exchange integral term. B3LYP stands for Becke, 3-parameter, Lee-Yang-Parr and uses a 6-31G basis set as the electronic wavefunction in order to produce more accurate results at the cost of increased calculation time.

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

[[File:Ex1 general.png|thumb|x700px|700px|centre|Figure 1: Formation of Cyclohaxadiene]]

Also known as the Diels-Alder reaction, this exercise investigates the well-known [4+2] cycloaddition between a conjugated diene (butadiene) and a dienophile (ethylene). The electrophilic reaction involves 4 pi-electrons from the diene and 2 pi-electrons from the alkene, and is a popular method to form regio- and stereochemically controlled 6-membered rings.

Method 2 was used to compute the transition state (TS) for this exercise. All steps are optimised to the PM6 level. First, the reactants are optimised to a minimum. The carbons at the reacting termini were then frozen at around 2.20 Å before optimised to a minimum to give a frozen-guess TS. Then finally, the molecule was optimised as a TS and an IRC was performed in order to confirm and locate the transition state.

=== Analysis of the Molecular Orbitals (MO) ===

The Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) for the reactants and the TS are shown below and its energies were recorded in order to produce the MO diagram as shown in figure 2.

{| class="wikitable"
! Ethene - HOMO
! Ethene - LUMO
! Butadiene - HOMO
! Butadiene - LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Cc5115 exer1finalMO.png|thumb|x800px|800px|left|Figure 2: MO Diagram for the formation of Transition State of the Diels-Alder Reaction]]

The symmetric TS HOMO and LUMO are formed through the interactions between the HOMO of ethylene and the LUMO of butadiene, both of which are symmetric. On the other hand, the LUMO of ethylene and the HOMO of butadiene, both of which are asymmetric, interacts to give an asymmetric HOMO-1 and LUMO+1. What can be concluded about the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed, and that the reaction is forbidden when the symmetry of the molecular orbitals aren't the same. The orbital overlap integral, S<sub>AB</sub>, is a quantitative measure of orbital overlap of two different atoms. Orbitals of the same symmetry will lead to constructive overlap and gives a non-zero value while orbitals of different symmetry will lead to destructive overlap and an orbital overlap integral of zero. Thus the overlap integral are:

- Non-zero for symmetric-symmetric interaction

- Non-zero for asymmetric-asymmetric interaction

- Zero for symmetric-asymmetric interaction

As observed in the MO diagram, the energy gap between the HOMO and LUMO for butadiene is smaller that those for ethylene due to butadiene being more electron rich than ethylene. Furthermore, in a normal MO diagram, the bonding MO formed should have a lower energy compared to both atomic orbitals (AO) whilst the anti-bonding MO formed should have a higher energy than both AOs. The reason why figure 3 goes against the tide is because the MOs formed corresponds to the transition state where the electrons are very delocalised within the chemical environment of the molecule.

==== LOG Files ====

[[:File:Cc5115_ETHENE_MO.LOG]]

[[:File:Cc5115_BUTADIENE_MO.LOG]]

[[:File:Cc5115_OPT_MO.LOG]]

=== Analysis of the C-C bond lengths ===

{| class="wikitable"
! Bond Lengths (Å)
! C1-C2
! C2-C3
! C3-C4
! C4-C5
! C5-C6
! C6-C1
|-
| Ethylene
|
|
|
|
| 1.36
|
|-
| Butadiene
| 1.36
| 1.54
| 1.36
|
|
|
|-
| Transition State
| 1.38
| 1.41
| 1.38
| 2.11
| 1.38
| 2.12
|-
| Cyclohexadiene
| 1.49
| 1.33
| 1.49
| 1.54
| 1.54
| 1.54
|}

The numbering of the carbon bonds are according to the labels on figure 1. The typical C-C bond lengths are as follows:

{| class="wikitable"
! Bond Type
! Bond Length (Å)
|-
| sp<sup>3</sup>-sp<sup>3</sup> C-C bond
| 1.54
|-
| sp<sup>3</sup>-sp<sup>2</sup> C-C bond
| 1.50
|-
| sp<sup>2</sup>-sp<sup>2</sup> C-C bond
| 1.47
|-
| sp<sup>2</sup>-sp<sup>2</sup> C=C bond
| 1.34
|}

When the reaction proceeds to the transition state, the sp<sup>2</sup>-sp<sup>2</sup> C5-C6 bond (originally ethylene) becomes longer as the carbons starts to change from sp<sup>2</sup> hybridised to sp<sup>3</sup> hybridised.
This trait is also apparent with C1-C2 and C3-C4 bonds where it once was the double bonds on butadiene, however, the increase in length of these bonds is less than that of C5-C6 due to the formation of a new double bond between C2 and C3, thus these carbons still remain sp<sup>2</sup> hybridised. This also leads to the next observation, where the C2-C3 bond decreases in length as it moves from the reactants to the transition state then the product, cyclohexadiene. This is because it is changing from a sp<sup>3</sup>-sp<sup>3</sup> C-C bond to a sp<sup>2</sup>-sp<sup>2</sup> C=C bond where the increase in s character shortens the bond lengths. This reaction also leads to the formation of 2 new bonds, namely C4-C5 and C6-C1. The Van der Waals radius of a carbon atom is 1.7 Å, and so the distance between 2 carbon atoms should be 3.4 Å, which is relatively longer than the bonds C4-C5 and C6-C1 which has a length of 2.11 and 2.12 Å respectively. This shows that the bonds are already partially formed in the transition state and they are beginning to interact together. This bond then settled at 1.54 Å in the product which matches with the typical bond length for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond.

=== Analysis of the vibrations ===

The animation for the first vibration is shown below. As observed, the formation of the 2 new bonds are synchronous as the reacting termini of butadiene and ethylene approaches each other at the same rate.

{| class="wikitable"
! <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 2;rotate x -20; </script>
<uploadedFileContents>Cc5115 OPT MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

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

[[File:Cc5115 Exercise 2 generl.png|thumb|x700px|700px|centre|Figure 3: Reaction Scheme]]

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via either the endo or exo pathways to form 2 products with different stereochemistry. Method 3 was employed in order to compute the TS for this exercise. This time, the structures were further optimised with B3LYP/6-31G method and the results are shown and discussed below.

=== Analysis of Molecular Orbitals ===

[[File:Cc5115 Endo MO Exercise 2.png|thumb|x500px|500px|left|Figure 4: MO Diagram for the Endo TS]]

[[File:Cc5115 Exo MO Exercise 2.png|thumb|x500px|500px|right|Figure 5: MO Diagram for the Exo TS]]

There are two types of Diels-Alder (DA) reactions: one is with a normal electron demand where the dienophile is electron deficient and the diene is electron rich, and the other is with an inverse electron demand where the dienophile is electron rich and the diene is electron deficient.

For a normal electron demand DA reaction, the dienophile low-lying LUMO interacts with the diene HOMO which has a high energy. However, observing the energies of the reactants and the transition states, the MO diagram shows that this particular DA reaction has an inverse electron demand where the dienophile (1,3-dioxole) is electron rich (higher in energy) and the diene (cyclohexadiene) is electron poor (lower in energy). The interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene thus leads to the HOMO and LUMO of the transition state. Although opposing that of a normal electron demand DA, this reaction still follows the Woodword-Hoffman rule and is thermally allowed.

Similar to exercise 1, MOs of the same symmetry interact; the symmetrical dienophile HOMO and the diene LUMO interacts to give a symmetrical TS HOMO and LUMO, while the asymmetrical dienophile LUMO and diene HOMO gives the asymmetrical TS HOMO-1 and LUMO+1. It is also observable that the endo TS HOMO has a lower energy than the exo TS HOMO which suggests that the endo reaction is favoured. This will be discussed further in the Thermochemistry section of this exercise.

{| class="wikitable"
! ENDO TS - HOMO -1
! ENDO TS - HOMO
! ENDO TS - LUMO
! ENDO TS - LUMO +1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Log Files ====

[[File:Cc5115 ENDO B3.LOG]]

[[File:Cc5115 PLEASE WORK B3.LOG]]

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +149.70
| -77.52
|-
| Exo
| +157.52
| -73.92
|}

As discussed briefly in the introduction, the reactants need to pass the activation barrier (transition state) in order to reach to the products. The table regarding the reaction barriers and energies shows that the activation barrier for the endo reaction is less than that of the exo reaction, more-so confirming that the endo reaction is kinetically favoured. This links to the lower energy that the endo TS HOMO has compared to the exo TS. This observance can be explained by secondary orbital interation (SOI). The 2 non-bonding oxygen p-orbitals containing electron lone pairs can overlap with the LUMO of the diene through space thus stabilising the TS and consequentially lowering reaction barrier. However, the more negative reaction energy of the endo reaction can be explained with sterics; in the exo transition state, the steric interaction between the sp<sup>3</sup> bridging carbons and the rest of the 1,3-dioxole structure results in the exo product being higher in energy.

{| class="wikitable"
! Exo Secondary MO
! Endo Secondary MO
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

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

[[File:Ex3 general.png|thumb|x700px|700px|centre|Figure 6: Reaction Scheme]]

=== IRC ===

{| class="wikitable"
! [[File:Cc5115 Exo IRC gif.gif|thumb|x500px|500px|left|IRC for Exo Product]]
! [[File:Cc5115 Endo IRC gif.gif|thumb|x500px|500px|left|IRC for Endo Product]]
! [[File:Chelatropic IRC gif.gif|thumb|x500px|500px|left|IRC for Chelatropic Product]]
|}

IRC (intrinsic reaction coordinate) show how reactions move in space during its reaction to form products. From the IRC animations, it can be seen that the formation of the new bonds differ to that of exercise 1. Here, in the exo and endo pathways, the formation of the 2 new bonds are asynchronous as one bond forms before the other. However, the bonds form synchronously in the chelatropic reaction leading to the symmetrical product.

The IRC reaction pathways also show a smaller activation barrier compared to that of exercise 1. This is because xylylene is highly unstable. Xylylene can exist with 4π electrons making it anti-aromatic, or either with 6π electrons an a diradical which is very unstable. On the flipside, the product formed is aromatic making the DA reaction extremely favourable. Naphthalene forces the diene to be rigid in its positions easing the overlap capabilities of the diene with the dienophile. This can be observed in the animation as naphthalene doesn't have to go through major rearrangements in order to form the products.

In the reaction, naphthalene initially has a C=C bond length of 1.35 Å and a C-C bond length averaging around 1.51 Å. This changes as the product is formed where all the carbon-carbon bonds on the 6 membered rings become 1.47 Å in length suggesting the formation of an aromatic 6-membered ring where the π electrons are delocalised throughout the ring. The change in bond length can also be seen with careful observation of the animations.

==== Log Files ====

[[File:Cc5115 chelatropic IRC.LOG]]

[[File:Cc5115 endoex3 IRC.LOG]]

[[File:Cc5115 exoex3 IRC.LOG]]

=== Thermochemistry ===

[[File:Cc5115 Energy Diagram Ex3.png|thumb|x500px|600px|right|Figure 7: Reaction profile for the 3 different pathways]]

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +79.85
| -100.95
|-
| Exo
| +83.82
| -101.59
|-
| Chelatropic
| +102.16
| -157.93
|}

Significantly resembling to exercise 2, exercise 3 features the endo pathway being kinetically favoured as its activation energy has the least energy compared to the other pathway. Again, this is due to the overlap between the oxygen p-orbitals overlapping with the π-orbitals of the xylylene ring. However, the difference in activation and reaction energies between the exo and endo pathways do not differ that much due to the SOI not contributing significantly in the TS and there are little steric difference between the two products. For the chelatropic product, there is a hugh drop in reaction energy. Observing the product, the large sulfur atom forming a 5-membered ring decreases the ring-strain making the product relatively stable compared to the products from the DA reaction.

=== Cyclisation at the other reaction site ===

{| class="wikitable"
! [[File:Cc5115 IRC exo reaction site b.gif|thumb|x500px|500px|left|IRC for Exo Product at reaction site B]]
! [[File:Cc5115 IRC endo reaction site b.gif|thumb|x500px|500px|left|IRC for Endo Product at reaction site B]]
|}

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +110.06
| -14.33
|-
| Exo
| +117.90
| -18.78
|}

For this exercise, the Diels-Alder reaction can also take place at the other reaction site as illustrated in the animations. As seen from the table of reaction barrier and energy, the endo product is both kinetically and thermodynamically favoured as its activation energy is lower (TS has lower energy) as well as its reaction energy (product has a lower energy and thus more stable). This alternative pathway, however, is not favoured compared to the previous DA reaction since an aromatic 6-membered ring did not form during this reaction. This leads to higher activation energies and well as higher reaction energies.

==== Log Files ====

[[File:Cc5115 IRC 2 endo.LOG]]

[[File:Cc5115 IRC exo.LOG]]

== Conclusion ==

Gaussian was used to calculate the geometries of the transition states and the TS was validated by a correct imaginary frequency from frequency calculations as well as the correct pathways along the reaction coordinate from IRC. In this exercise, the transition states of the DA and a chelatropic reaction was investigated using the PM6 and B3LYP calculation methods. Exercise 1 investigated the carbon-carbon bond lengths of the reactants, TS and products in the reaction between ethylene and butadiene. The bond lengths matched well with expectations. Exercise 2 investigated the inverse-electron demand DA reaction through the construction of a MO diagram and it was concluded that the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed. Here, the endothermic pathway gave the kinetically and thermodynamically favoured product as expected. Exercise 3 also investigated the chelatropic reaction alongside the DA reaction and, similar to exercise 2, the endothermic pathway resulted in a kinetically and thermodynamically favoured product. An alternative reaction site was also investigated which was concluded to be less favourable to the original DA reaction site as an aromatic 6-membered ring did not form.

Rep:Mod:cc5115TS

2018-02-14T11:24:01Z

Cc5115: /* Y3C Transition states and Reactivity */

= Y3C Transition states and Reactivity =

== Introduction ==

This section aims to illustrate the 3 different computational techniques that can be utilised in order to analyse the transition state (TS) of a reaction. The TS is the state which has the highest energy along a reaction coordinate, as a result it is the least stable state. In the reaction, the reactants needs to have a certain amount of energy in order to surpass the activation barrier, also known as the transition state energy, and reach the product state. This computational lab allows for calculations leading to the location of the TS. The structure of the TS is crucial in determining the mechanism of a reaction.

A potential energy surface (PES) has a 3N-6 dimension, which coincides to the degrees of freedom that the molecule has, where N is the number of atoms that the molecule possesses. In a 3-D PES, the saddle point (also called the TS), is a local mixami amidst 2 minima, and can be sometimes identified through secondary derivatives as it would be negative in one direction and positive in all other directions.

There are 3 calculation methods available in order to determine the structure of the TS.

1. The first and fastest method requires only one step where a guessed structure of the TS is optimised to give an optimised TS. This means that one will need of the TS to quite an extent, furthermore this method is rather unreliable as there is a high chance that the guessed TS is incorrectly drawn.

2. The second method works from a pre-frozen guess structure of the TS where the reacting termini of the reactants are frozen in space before the remaining structure is optimised to a minima. After that, the molecules are optimised as a transition state. This allows for a more reliable representation of the TS. This method is sufficient for Exercise 1.

3. The third method is the longest and most reliable method. Here, one starts by either optimising from the reactants or the products to a minima. For the reactant case, each reactants are optimised to a minima, arranged to resemble the TS and the reacting termini are frozen and the rest of the method 2 is repeated. A similar case occurs with the product; when the product is optimised to a minima, the bonds formed in the reactions are removed, the 2 fragments are arranged to resemble the TS and the reacting termini are frozen and method 2 was used once more. This method allows for the most reliable representation of the TS and is used for Exercise 2 & 3.

In this computational lab, two methods of calculation were used on Gaussian in order to find the TS. During the optimisation, the position of the molecule is decided as it is built in Gaussian. The time-independent Schrödinger equation was solved whilst utilising the Born-Oppenheimer approximation in order to find the energy and the wavefunction φ which represents the electronic states for the fixed nuclear positions and is dependent on on frozen nuclei positions. This is also known as the self-consistent field method (SCF). The two methods employed are the semi-empirical method PM6, which is usually performed first and sometimes followed by the Density Functional Theory (DFT) method B3LYP. The semi-empirical method PM6, although based on the Hartree-Fock formalism, this method uses many approximations based on experimental data in order to solve the Schrodinger equations. This method is usually fast and reliable, but can be easily countered if the environment of the molecule that is being computed is not similar enough to the approximated parameters of this method. The other method is B3LYP, a hydrid functional which utilises the DFT in order to calculate the majority of the Hamiltonian while a small portion still utilises the Hartree-Fock theory to calculate the exchange integral term. B3LYP stands for Becke, 3-parameter, Lee-Yang-Parr and uses a 6-31G basis set as the electronic wavefunction in order to produce more accurate results at the cost of increased calculation time.

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

[[File:Ex1 general.png|thumb|x700px|700px|centre|Figure 1: Formation of Cyclohaxadiene]]

Also known as the Diels-Alder reaction, this exercise investigates the well-known [4+2] cycloaddition between a conjugated diene (butadiene) and a dienophile (ethylene). The electrophilic reaction involves 4 pi-electrons from the diene and 2 pi-electrons from the alkene, and is a popular method to form regio- and stereochemically controlled 6-membered rings.

Method 2 was used to compute the transition state (TS) for this exercise. All steps are optimised to the PM6 level. First, the reactants are optimised to a minimum. The carbons at the reacting termini were then frozen at around 2.20 Å before optimised to a minimum to give a frozen-guess TS. Then finally, the molecule was optimised as a TS and an IRC was performed in order to confirm and locate the transition state.

=== Analysis of the Molecular Orbitals (MO) ===

The Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) for the reactants and the TS are shown below and its energies were recorded in order to produce the MO diagram as shown in figure 2.

{| class="wikitable"
! Ethene - HOMO
! Ethene - LUMO
! Butadiene - HOMO
! Butadiene - LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Cc5115 exer1finalMO.png|thumb|x800px|800px|left|Figure 2: MO Diagram for the formation of Transition State of the Diels-Alder Reaction]]

The symmetric TS HOMO and LUMO are formed through the interactions between the HOMO of ethylene and the LUMO of butadiene, both of which are symmetric. On the other hand, the LUMO of ethylene and the HOMO of butadiene, both of which are asymmetric, interacts to give an asymmetric HOMO-1 and LUMO+1. What can be concluded about the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed, and that the reaction is forbidden when the symmetry of the molecular orbitals aren't the same. The orbital overlap integral, S<sub>AB</sub>, is a quantitative measure of orbital overlap of two different atoms. Orbitals of the same symmetry will lead to constructive overlap and gives a non-zero value while orbitals of different symmetry will lead to destructive overlap and an orbital overlap integral of zero. Thus the overlap integral are:

- Non-zero for symmetric-symmetric interaction

- Non-zero for asymmetric-asymmetric interaction

- Zero for symmetric-asymmetric interaction

As observed in the MO diagram, the energy gap between the HOMO and LUMO for butadiene is smaller that those for ethylene due to butadiene being more electron rich than ethylene. Furthermore, in a normal MO diagram, the bonding MO formed should have a lower energy compared to both atomic orbitals (AO) whilst the anti-bonding MO formed should have a higher energy than both AOs. The reason why figure 3 goes against the tide is because the MOs formed corresponds to the transition state where the electrons are very delocalised within the chemical environment of the molecule.

==== LOG Files ====

[[:File:Cc5115_ETHENE_MO.LOG]]

[[:File:Cc5115_BUTADIENE_MO.LOG]]

[[:File:Cc5115_OPT_MO.LOG]]

=== Analysis of the C-C bond lengths ===

{| class="wikitable"
! Bond Lengths (Å)
! C1-C2
! C2-C3
! C3-C4
! C4-C5
! C5-C6
! C6-C1
|-
| Ethylene
|
|
|
|
| 1.36
|
|-
| Butadiene
| 1.36
| 1.54
| 1.36
|
|
|
|-
| Transition State
| 1.38
| 1.41
| 1.38
| 2.11
| 1.38
| 2.12
|-
| Cyclohexadiene
| 1.49
| 1.33
| 1.49
| 1.54
| 1.54
| 1.54
|}

The numbering of the carbon bonds are according to the labels on figure 1. The typical C-C bond lengths are as follows:

{| class="wikitable"
! Bond Type
! Bond Length (Å)
|-
| sp<sup>3</sup>-sp<sup>3</sup> C-C bond
| 1.54
|-
| sp<sup>3</sup>-sp<sup>2</sup> C-C bond
| 1.50
|-
| sp<sup>2</sup>-sp<sup>2</sup> C-C bond
| 1.47
|-
| sp<sup>2</sup>-sp<sup>2</sup> C=C bond
| 1.34
|}

When the reaction proceeds to the transition state, the sp<sup>2</sup>-sp<sup>2</sup> C5-C6 bond (originally ethylene) becomes longer as the carbons starts to change from sp<sup>2</sup> hybridised to sp<sup>3</sup> hybridised.
This trait is also apparent with C1-C2 and C3-C4 bonds where it once was the double bonds on butadiene, however, the increase in length of these bonds is less than that of C5-C6 due to the formation of a new double bond between C2 and C3, thus these carbons still remain sp<sup>2</sup> hybridised. This also leads to the next observation, where the C2-C3 bond decreases in length as it moves from the reactants to the transition state then the product, cyclohexadiene. This is because it is changing from a sp<sup>3</sup>-sp<sup>3</sup> C-C bond to a sp<sup>2</sup>-sp<sup>2</sup> C=C bond where the increase in s character shortens the bond lengths. This reaction also leads to the formation of 2 new bonds, namely C4-C5 and C6-C1. The Van der Waals radius of a carbon atom is 1.7 Å, and so the distance between 2 carbon atoms should be 3.4 Å, which is relatively longer than the bonds C4-C5 and C6-C1 which has a length of 2.11 and 2.12 Å respectively. This shows that the bonds are already partially formed in the transition state and they are beginning to interact together. This bond then settled at 1.54 Å in the product which matches with the typical bond length for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond.

=== Analysis of the vibrations ===

The animation for the first vibration is shown below. As observed, the formation of the 2 new bonds are synchronous as the reacting termini of butadiene and ethylene approaches each other at the same rate.

{| class="wikitable"
! <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 2;rotate x -20; </script>
<uploadedFileContents>Cc5115 OPT MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| The vibrations
|}

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

[[File:Cc5115 Exercise 2 generl.png|thumb|x700px|700px|centre|Figure 3: Reaction Scheme]]

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via either the endo or exo pathways to form 2 products with different stereochemistry. Method 3 was employed in order to compute the TS for this exercise. This time, the structures were further optimised with B3LYP/6-31G method and the results are shown and discussed below.

=== Analysis of Molecular Orbitals ===

[[File:Cc5115 Endo MO Exercise 2.png|thumb|x500px|500px|left|Figure 4: MO Diagram for the Endo TS]]

[[File:Cc5115 Exo MO Exercise 2.png|thumb|x500px|500px|right|Figure 5: MO Diagram for the Exo TS]]

There are two types of Diels-Alder (DA) reactions: one is with a normal electron demand where the dienophile is electron deficient and the diene is electron rich, and the other is with an inverse electron demand where the dienophile is electron rich and the diene is electron deficient.

For a normal electron demand DA reaction, the dienophile low-lying LUMO interacts with the diene HOMO which has a high energy. However, observing the energies of the reactants and the transition states, the MO diagram shows that this particular DA reaction has an inverse electron demand where the dienophile (1,3-dioxole) is electron rich (higher in energy) and the diene (cyclohexadiene) is electron poor (lower in energy). The interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene thus leads to the HOMO and LUMO of the transition state. Although opposing that of a normal electron demand DA, this reaction still follows the Woodword-Hoffman rule and is thermally allowed.

Similar to exercise 1, MOs of the same symmetry interact; the symmetrical dienophile HOMO and the diene LUMO interacts to give a symmetrical TS HOMO and LUMO, while the asymmetrical dienophile LUMO and diene HOMO gives the asymmetrical TS HOMO-1 and LUMO+1. It is also observable that the endo TS HOMO has a lower energy than the exo TS HOMO which suggests that the endo reaction is favoured. This will be discussed further in the Thermochemistry section of this exercise.

{| class="wikitable"
! ENDO TS - HOMO -1
! ENDO TS - HOMO
! ENDO TS - LUMO
! ENDO TS - LUMO +1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Log Files ====

[[File:Cc5115 ENDO B3.LOG]]

[[File:Cc5115 PLEASE WORK B3.LOG]]

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +149.70
| -77.52
|-
| Exo
| +157.52
| -73.92
|}

As discussed briefly in the introduction, the reactants need to pass the activation barrier (transition state) in order to reach to the products. The table regarding the reaction barriers and energies shows that the activation barrier for the endo reaction is less than that of the exo reaction, more-so confirming that the endo reaction is kinetically favoured. This links to the lower energy that the endo TS HOMO has compared to the exo TS. This observance can be explained by secondary orbital interation (SOI). The 2 non-bonding oxygen p-orbitals containing electron lone pairs can overlap with the LUMO of the diene through space thus stabilising the TS and consequentially lowering reaction barrier. However, the more negative reaction energy of the endo reaction can be explained with sterics; in the exo transition state, the steric interaction between the sp<sup>3</sup> bridging carbons and the rest of the 1,3-dioxole structure results in the exo product being higher in energy.

{| class="wikitable"
! Exo Secondary MO
! Endo Secondary MO
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

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

[[File:Ex3 general.png|thumb|x700px|700px|centre|Figure 6: Reaction Scheme]]

=== IRC ===

{| class="wikitable"
! [[File:Cc5115 Exo IRC gif.gif|thumb|x500px|500px|left|IRC for Exo Product]]
! [[File:Cc5115 Endo IRC gif.gif|thumb|x500px|500px|left|IRC for Endo Product]]
! [[File:Chelatropic IRC gif.gif|thumb|x500px|500px|left|IRC for Chelatropic Product]]
|}

IRC (intrinsic reaction coordinate) show how reactions move in space during its reaction to form products. From the IRC animations, it can be seen that the formation of the new bonds differ to that of exercise 1. Here, in the exo and endo pathways, the formation of the 2 new bonds are asynchronous as one bond forms before the other. However, the bonds form synchronously in the chelatropic reaction leading to the symmetrical product.

The IRC reaction pathways also show a smaller activation barrier compared to that of exercise 1. This is because xylylene is highly unstable. Xylylene can exist with 4π electrons making it anti-aromatic, or either with 6π electrons an a diradical which is very unstable. On the flipside, the product formed is aromatic making the DA reaction extremely favourable. Naphthalene forces the diene to be rigid in its positions easing the overlap capabilities of the diene with the dienophile. This can be observed in the animation as naphthalene doesn't have to go through major rearrangements in order to form the products.

In the reaction, naphthalene initially has a C=C bond length of 1.35 Å and a C-C bond length averaging around 1.51 Å. This changes as the product is formed where all the carbon-carbon bonds on the 6 membered rings become 1.47 Å in length suggesting the formation of an aromatic 6-membered ring where the π electrons are delocalised throughout the ring. The change in bond length can also be seen with careful observation of the animations.

==== Log Files ====

[[File:Cc5115 chelatropic IRC.LOG]]

[[File:Cc5115 endoex3 IRC.LOG]]

[[File:Cc5115 exoex3 IRC.LOG]]

=== Thermochemistry ===

[[File:Cc5115 Energy Diagram Ex3.png|thumb|x500px|600px|right|Figure 7: Reaction profile for the 3 different pathways]]

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +79.85
| -100.95
|-
| Exo
| +83.82
| -101.59
|-
| Chelatropic
| +102.16
| -157.93
|}

Significantly resembling to exercise 2, exercise 3 features the endo pathway being kinetically favoured as its activation energy has the least energy compared to the other pathway. Again, this is due to the overlap between the oxygen p-orbitals overlapping with the π-orbitals of the xylylene ring. However, the difference in activation and reaction energies between the exo and endo pathways do not differ that much due to the SOI not contributing significantly in the TS and there are little steric difference between the two products. For the chelatropic product, there is a hugh drop in reaction energy. Observing the product, the large sulfur atom forming a 5-membered ring decreases the ring-strain making the product relatively stable compared to the products from the DA reaction.

=== Cyclisation at the other reaction site ===

{| class="wikitable"
! [[File:Cc5115 IRC exo reaction site b.gif|thumb|x500px|500px|left|IRC for Exo Product at reaction site B]]
! [[File:Cc5115 IRC endo reaction site b.gif|thumb|x500px|500px|left|IRC for Endo Product at reaction site B]]
|}

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +110.06
| -14.33
|-
| Exo
| +117.90
| -18.78
|}

For this exercise, the Diels-Alder reaction can also take place at the other reaction site as illustrated in the animations. As seen from the table of reaction barrier and energy, the endo product is both kinetically and thermodynamically favoured as its activation energy is lower (TS has lower energy) as well as its reaction energy (product has a lower energy and thus more stable). This alternative pathway, however, is not favoured compared to the previous DA reaction since an aromatic 6-membered ring did not form during this reaction. This leads to higher activation energies and well as higher reaction energies.

==== Log Files ====

[[File:Cc5115 IRC 2 endo.LOG]]

[[File:Cc5115 IRC exo.LOG]]

== Conclusion ==

Gaussian was used to calculate the geometries of the transition states and the TS was validated by a correct imaginary frequency from frequency calculations as well as the correct pathways along the reaction coordinate from IRC. In this exercise, the transition states of the DA and a chelatropic reaction was investigated using the PM6 and B3LYP calculation methods. Exercise 1 investigated the carbon-carbon bond lengths of the reactants, TS and products in the reaction between ethylene and butadiene. The bond lengths matched well with expectations. Exercise 2 investigated the inverse-electron demand DA reaction through the construction of a MO diagram and it was concluded that the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed. Here, the endothermic pathway gave the kinetically and thermodynamically favoured product as expected. Exercise 3 also investigated the chelatropic reaction alongside the DA reaction and, similar to exercise 2, the endothermic pathway resulted in a kinetically and thermodynamically favoured product. An alternative reaction site was also investigated which was concluded to be less favourable to the original DA reaction site as an aromatic 6-membered ring did not form.

Rep:Mod:cc5115TS

2018-02-14T11:22:59Z

Cc5115: /* Exercise 3: Diels-Alder vs Cheletropic */

= Y3C Transition states and Reactivity =

== Introduction ==

This section aims to illustrate the 3 different computational techniques that can be utilised in order to analyse the transition state (TS) of a reaction. The TS is the state which has the highest energy along a reaction coordinate, as a result it is the least stable state. In the reaction, the reactants needs to have a certain amount of energy in order to surpass the activation barrier, also known as the transition state energy, and reach the product state. This computational lab allows for calculations leading to the location of the TS. The structure of the TS is crucial in determining the mechanism of a reaction.

A potential energy surface (PES) has a 3N-6 dimension, which coincides to the degrees of freedom that the molecule has, where N is the number of atoms that the molecule possesses. In a 3-D PES, the saddle point (also called the TS), is a local mixami amidst 2 minima, and can be sometimes identified through secondary derivatives as it would be negative in one direction and positive in all other directions.

There are 3 calculation methods available in order to determine the structure of the TS.

1. The first and fastest method requires only one step where a guessed structure of the TS is optimised to give an optimised TS. This means that one will need of the TS to quite an extent, furthermore this method is rather unreliable as there is a high chance that the guessed TS is incorrectly drawn.

2. The second method works from a pre-frozen guess structure of the TS where the reacting termini of the reactants are frozen in space before the remaining structure is optimised to a minima. After that, the molecules are optimised as a transition state. This allows for a more reliable representation of the TS. This method is sufficient for Exercise 1.

3. The third method is the longest and most reliable method. Here, one starts by either optimising from the reactants or the products to a minima. For the reactant case, each reactants are optimised to a minima, arranged to resemble the TS and the reacting termini are frozen and the rest of the method 2 is repeated. A similar case occurs with the product; when the product is optimised to a minima, the bonds formed in the reactions are removed, the 2 fragments are arranged to resemble the TS and the reacting termini are frozen and method 2 was used once more. This method allows for the most reliable representation of the TS and is used for Exercise 2 & 3.

In this computational lab, two methods of calculation were used on Gaussian in order to find the TS. During the optimisation, the position of the molecule is decided as it is built in Gaussian. The time-independent Schrödinger equation was solved whilst utilising the Born-Oppenheimer approximation in order to find the energy and the wavefunction φ which represents the electronic states for the fixed nuclear positions and is dependent on on frozen nuclei positions. This is also known as the self-consistent field method (SCF). The two methods employed are the semi-empirical method PM6, which is usually performed first and sometimes followed by the Density Functional Theory (DFT) method B3LYP. The semi-empirical method PM6, although based on the Hartree-Fock formalism, this method uses many approximations based on experimental data in order to solve the Schrodinger equations. This method is usually fast and reliable, but can be easily countered if the environment of the molecule that is being computed is not similar enough to the approximated parameters of this method. The other method is B3LYP, a hydrid functional which utilises the DFT in order to calculate the majority of the Hamiltonian while a small portion still utilises the Hartree-Fock theory to calculate the exchange integral term. B3LYP stands for Becke, 3-parameter, Lee-Yang-Parr and uses a 6-31G basis set as the electronic wavefunction in order to produce more accurate results at the cost of increased calculation time.

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

[[File:Ex1 general.png|thumb|x700px|700px|centre|Figure 1: Formation of Cyclohaxadiene]]

Also known as the Diels-Alder reaction, this exercise investigates the well-known [4+2] cycloaddition between a conjugated diene (butadiene) and a dienophile (ethylene). The electrophilic reaction involves 4 pi-electrons from the diene and 2 pi-electrons from the alkene, and is a popular method to form regio- and stereochemically controlled 6-membered rings.

Method 2 was used to compute the transition state (TS) for this exercise. All steps are optimised to the PM6 level. First, the reactants are optimised to a minimum. The carbons at the reacting termini were then frozen at around 2.20 Å before optimised to a minimum to give a frozen-guess TS. Then finally, the molecule was optimised as a TS and an IRC was performed in order to confirm and locate the transition state.

=== Analysis of the Molecular Orbitals (MO) ===

The Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) for the reactants and the TS are shown below and its energies were recorded in order to produce the MO diagram as shown in figure 2.

{| class="wikitable"
! Ethene - HOMO
! Ethene - LUMO
! Butadiene - HOMO
! Butadiene - LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Cc5115 exer1finalMO.png|thumb|x800px|800px|left|Figure 2: MO Diagram for the formation of Transition State of the Diels-Alder Reaction]]

The symmetric TS HOMO and LUMO are formed through the interactions between the HOMO of ethylene and the LUMO of butadiene, both of which are symmetric. On the other hand, the LUMO of ethylene and the HOMO of butadiene, both of which are asymmetric, interacts to give an asymmetric HOMO-1 and LUMO+1. What can be concluded about the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed, and that the reaction is forbidden when the symmetry of the molecular orbitals aren't the same. The orbital overlap integral, S<sub>AB</sub>, is a quantitative measure of orbital overlap of two different atoms. Orbitals of the same symmetry will lead to constructive overlap and gives a non-zero value while orbitals of different symmetry will lead to destructive overlap and an orbital overlap integral of zero. Thus the overlap integral are:

- Non-zero for symmetric-symmetric interaction

- Non-zero for asymmetric-asymmetric interaction

- Zero for symmetric-asymmetric interaction

As observed in the MO diagram, the energy gap between the HOMO and LUMO for butadiene is smaller that those for ethylene due to butadiene being more electron rich than ethylene. Furthermore, in a normal MO diagram, the bonding MO formed should have a lower energy compared to both atomic orbitals (AO) whilst the anti-bonding MO formed should have a higher energy than both AOs. The reason why figure 3 goes against the tide is because the MOs formed corresponds to the transition state where the electrons are very delocalised within the chemical environment of the molecule.

==== LOG Files ====

[[:File:Cc5115_ETHENE_MO.LOG]]

[[:File:Cc5115_BUTADIENE_MO.LOG]]

[[:File:Cc5115_OPT_MO.LOG]]

=== Analysis of the C-C bond lengths ===

{| class="wikitable"
! Bond Lengths (Å)
! C1-C2
! C2-C3
! C3-C4
! C4-C5
! C5-C6
! C6-C1
|-
| Ethylene
|
|
|
|
| 1.36
|
|-
| Butadiene
| 1.36
| 1.54
| 1.36
|
|
|
|-
| Transition State
| 1.38
| 1.41
| 1.38
| 2.11
| 1.38
| 2.12
|-
| Cyclohexadiene
| 1.49
| 1.33
| 1.49
| 1.54
| 1.54
| 1.54
|}

The numbering of the carbon bonds are according to the labels on figure 1. The typical C-C bond lengths are as follows:

{| class="wikitable"
! Bond Type
! Bond Length (Å)
|-
| sp<sup>3</sup>-sp<sup>3</sup> C-C bond
| 1.54
|-
| sp<sup>3</sup>-sp<sup>2</sup> C-C bond
| 1.50
|-
| sp<sup>2</sup>-sp<sup>2</sup> C-C bond
| 1.47
|-
| sp<sup>2</sup>-sp<sup>2</sup> C=C bond
| 1.34
|}

When the reaction proceeds to the transition state, the sp<sup>2</sup>-sp<sup>2</sup> C5-C6 bond (originally ethylene) becomes longer as the carbons starts to change from sp<sup>2</sup> hybridised to sp<sup>3</sup> hybridised.
This trait is also apparent with C1-C2 and C3-C4 bonds where it once was the double bonds on butadiene, however, the increase in length of these bonds is less than that of C5-C6 due to the formation of a new double bond between C2 and C3, thus these carbons still remain sp<sup>2</sup> hybridised. This also leads to the next observation, where the C2-C3 bond decreases in length as it moves from the reactants to the transition state then the product, cyclohexadiene. This is because it is changing from a sp<sup>3</sup>-sp<sup>3</sup> C-C bond to a sp<sup>2</sup>-sp<sup>2</sup> C=C bond where the increase in s character shortens the bond lengths. This reaction also leads to the formation of 2 new bonds, namely C4-C5 and C6-C1. The Van der Waals radius of a carbon atom is 1.7 Å, and so the distance between 2 carbon atoms should be 3.4 Å, which is relatively longer than the bonds C4-C5 and C6-C1 which has a length of 2.11 and 2.12 Å respectively. This shows that the bonds are already partially formed in the transition state and they are beginning to interact together. This bond then settled at 1.54 Å in the product which matches with the typical bond length for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond.

=== Analysis of the vibrations ===

The animation for the first vibration is shown below. As observed, the formation of the 2 new bonds are synchronous as the reacting termini of butadiene and ethylene approaches each other at the same rate.

{| class="wikitable"
! <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 2;rotate x -20; </script>
<uploadedFileContents>Cc5115 OPT MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| The vibrations
|}

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

[[File:Cc5115 Exercise 2 generl.png|thumb|x700px|700px|centre|Figure 3: Reaction Scheme]]

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via either the endo or exo pathways to form 2 products with different stereochemistry. Method 3 was employed in order to compute the TS for this exercise. This time, the structures were further optimised with B3LYP/6-31G method and the results are shown and discussed below.

=== Analysis of Molecular Orbitals ===

[[File:Cc5115 Endo MO Exercise 2.png|thumb|x500px|500px|left|Figure 4: MO Diagram for the Endo TS]]

[[File:Cc5115 Exo MO Exercise 2.png|thumb|x500px|500px|right|Figure 5: MO Diagram for the Exo TS]]

There are two types of Diels-Alder (DA) reactions: one is with a normal electron demand where the dienophile is electron deficient and the diene is electron rich, and the other is with an inverse electron demand where the dienophile is electron rich and the diene is electron deficient.

For a normal electron demand DA reaction, the dienophile low-lying LUMO interacts with the diene HOMO which has a high energy. However, observing the energies of the reactants and the transition states, the MO diagram shows that this particular DA reaction has an inverse electron demand where the dienophile (1,3-dioxole) is electron rich (higher in energy) and the diene (cyclohexadiene) is electron poor (lower in energy). The interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene thus leads to the HOMO and LUMO of the transition state. Although opposing that of a normal electron demand DA, this reaction still follows the Woodword-Hoffman rule and is thermally allowed.

Similar to exercise 1, MOs of the same symmetry interact; the symmetrical dienophile HOMO and the diene LUMO interacts to give a symmetrical TS HOMO and LUMO, while the asymmetrical dienophile LUMO and diene HOMO gives the asymmetrical TS HOMO-1 and LUMO+1. It is also observable that the endo TS HOMO has a lower energy than the exo TS HOMO which suggests that the endo reaction is favoured. This will be discussed further in the Thermochemistry section of this exercise.

{| class="wikitable"
! ENDO TS - HOMO -1
! ENDO TS - HOMO
! ENDO TS - LUMO
! ENDO TS - LUMO +1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Log Files ====

[[File:Cc5115 ENDO B3.LOG]]

[[File:Cc5115 PLEASE WORK B3.LOG]]

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +149.70
| -77.52
|-
| Exo
| +157.52
| -73.92
|}

As discussed briefly in the introduction, the reactants need to pass the activation barrier (transition state) in order to reach to the products. The table regarding the reaction barriers and energies shows that the activation barrier for the endo reaction is less than that of the exo reaction, more-so confirming that the endo reaction is kinetically favoured. This links to the lower energy that the endo TS HOMO has compared to the exo TS. This observance can be explained by secondary orbital interation (SOI). The 2 non-bonding oxygen p-orbitals containing electron lone pairs can overlap with the LUMO of the diene through space thus stabilising the TS and consequentially lowering reaction barrier. However, the more negative reaction energy of the endo reaction can be explained with sterics; in the exo transition state, the steric interaction between the sp<sup>3</sup> bridging carbons and the rest of the 1,3-dioxole structure results in the exo product being higher in energy.

{| class="wikitable"
! Exo Secondary MO
! Endo Secondary MO
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

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

[[File:Ex3 general.png|thumb|x500px|500px|centre|Figure 6: Reaction Scheme]]

=== IRC ===

{| class="wikitable"
! [[File:Cc5115 Exo IRC gif.gif|thumb|x500px|500px|left|IRC for Exo Product]]
! [[File:Cc5115 Endo IRC gif.gif|thumb|x500px|500px|left|IRC for Endo Product]]
! [[File:Chelatropic IRC gif.gif|thumb|x500px|500px|left|IRC for Chelatropic Product]]
|}

IRC (intrinsic reaction coordinate) show how reactions move in space during its reaction to form products. From the IRC animations, it can be seen that the formation of the new bonds differ to that of exercise 1. Here, in the exo and endo pathways, the formation of the 2 new bonds are asynchronous as one bond forms before the other. However, the bonds form synchronously in the chelatropic reaction leading to the symmetrical product.

The IRC reaction pathways also show a smaller activation barrier compared to that of exercise 1. This is because xylylene is highly unstable. Xylylene can exist with 4π electrons making it anti-aromatic, or either with 6π electrons an a diradical which is very unstable. On the flipside, the product formed is aromatic making the DA reaction extremely favourable. Naphthalene forces the diene to be rigid in its positions easing the overlap capabilities of the diene with the dienophile. This can be observed in the animation as naphthalene doesn't have to go through major rearrangements in order to form the products.

In the reaction, naphthalene initially has a C=C bond length of 1.35 Å and a C-C bond length averaging around 1.51 Å. This changes as the product is formed where all the carbon-carbon bonds on the 6 membered rings become 1.47 Å in length suggesting the formation of an aromatic 6-membered ring where the π electrons are delocalised throughout the ring. The change in bond length can also be seen with careful observation of the animations.

==== Log Files ====

[[File:Cc5115 chelatropic IRC.LOG]]

[[File:Cc5115 endoex3 IRC.LOG]]

[[File:Cc5115 exoex3 IRC.LOG]]

=== Thermochemistry ===

[[File:Cc5115 Energy Diagram Ex3.png|thumb|x500px|600px|right|Figure 6: Reaction profile for the 3 different pathways]]

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +79.85
| -100.95
|-
| Exo
| +83.82
| -101.59
|-
| Chelatropic
| +102.16
| -157.93
|}

Significantly resembling to exercise 2, exercise 3 features the endo pathway being kinetically favoured as its activation energy has the least energy compared to the other pathway. Again, this is due to the overlap between the oxygen p-orbitals overlapping with the π-orbitals of the xylylene ring. However, the difference in activation and reaction energies between the exo and endo pathways do not differ that much due to the SOI not contributing significantly in the TS and there are little steric difference between the two products. For the chelatropic product, there is a hugh drop in reaction energy. Observing the product, the large sulfur atom forming a 5-membered ring decreases the ring-strain making the product relatively stable compared to the products from the DA reaction.

=== Cyclisation at the other reaction site ===

{| class="wikitable"
! [[File:Cc5115 IRC exo reaction site b.gif|thumb|x500px|500px|left|IRC for Exo Product at reaction site B]]
! [[File:Cc5115 IRC endo reaction site b.gif|thumb|x500px|500px|left|IRC for Endo Product at reaction site B]]
|}

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +110.06
| -14.33
|-
| Exo
| +117.90
| -18.78
|}

For this exercise, the Diels-Alder reaction can also take place at the other reaction site as illustrated in the animations. As seen from the table of reaction barrier and energy, the endo product is both kinetically and thermodynamically favoured as its activation energy is lower (TS has lower energy) as well as its reaction energy (product has a lower energy and thus more stable). This alternative pathway, however, is not favoured compared to the previous DA reaction since an aromatic 6-membered ring did not form during this reaction. This leads to higher activation energies and well as higher reaction energies.

==== Log Files ====

[[File:Cc5115 IRC 2 endo.LOG]]

[[File:Cc5115 IRC exo.LOG]]

== Conclusion ==

Gaussian was used to calculate the geometries of the transition states and the TS was validated by a correct imaginary frequency from frequency calculations as well as the correct pathways along the reaction coordinate from IRC. In this exercise, the transition states of the DA and a chelatropic reaction was investigated using the PM6 and B3LYP calculation methods. Exercise 1 investigated the carbon-carbon bond lengths of the reactants, TS and products in the reaction between ethylene and butadiene. The bond lengths matched well with expectations. Exercise 2 investigated the inverse-electron demand DA reaction through the construction of a MO diagram and it was concluded that the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed. Here, the endothermic pathway gave the kinetically and thermodynamically favoured product as expected. Exercise 3 also investigated the chelatropic reaction alongside the DA reaction and, similar to exercise 2, the endothermic pathway resulted in a kinetically and thermodynamically favoured product. An alternative reaction site was also investigated which was concluded to be less favourable to the original DA reaction site as an aromatic 6-membered ring did not form.

File:Ex3 general.png

2018-02-14T11:22:28Z

Cc5115:

Rep:Mod:cc5115TS

2018-02-14T11:15:18Z

Cc5115: /* Y3C Transition states and Reactivity */

= Y3C Transition states and Reactivity =

== Introduction ==

This section aims to illustrate the 3 different computational techniques that can be utilised in order to analyse the transition state (TS) of a reaction. The TS is the state which has the highest energy along a reaction coordinate, as a result it is the least stable state. In the reaction, the reactants needs to have a certain amount of energy in order to surpass the activation barrier, also known as the transition state energy, and reach the product state. This computational lab allows for calculations leading to the location of the TS. The structure of the TS is crucial in determining the mechanism of a reaction.

A potential energy surface (PES) has a 3N-6 dimension, which coincides to the degrees of freedom that the molecule has, where N is the number of atoms that the molecule possesses. In a 3-D PES, the saddle point (also called the TS), is a local mixami amidst 2 minima, and can be sometimes identified through secondary derivatives as it would be negative in one direction and positive in all other directions.

There are 3 calculation methods available in order to determine the structure of the TS.

1. The first and fastest method requires only one step where a guessed structure of the TS is optimised to give an optimised TS. This means that one will need of the TS to quite an extent, furthermore this method is rather unreliable as there is a high chance that the guessed TS is incorrectly drawn.

2. The second method works from a pre-frozen guess structure of the TS where the reacting termini of the reactants are frozen in space before the remaining structure is optimised to a minima. After that, the molecules are optimised as a transition state. This allows for a more reliable representation of the TS. This method is sufficient for Exercise 1.

3. The third method is the longest and most reliable method. Here, one starts by either optimising from the reactants or the products to a minima. For the reactant case, each reactants are optimised to a minima, arranged to resemble the TS and the reacting termini are frozen and the rest of the method 2 is repeated. A similar case occurs with the product; when the product is optimised to a minima, the bonds formed in the reactions are removed, the 2 fragments are arranged to resemble the TS and the reacting termini are frozen and method 2 was used once more. This method allows for the most reliable representation of the TS and is used for Exercise 2 & 3.

In this computational lab, two methods of calculation were used on Gaussian in order to find the TS. During the optimisation, the position of the molecule is decided as it is built in Gaussian. The time-independent Schrödinger equation was solved whilst utilising the Born-Oppenheimer approximation in order to find the energy and the wavefunction φ which represents the electronic states for the fixed nuclear positions and is dependent on on frozen nuclei positions. This is also known as the self-consistent field method (SCF). The two methods employed are the semi-empirical method PM6, which is usually performed first and sometimes followed by the Density Functional Theory (DFT) method B3LYP. The semi-empirical method PM6, although based on the Hartree-Fock formalism, this method uses many approximations based on experimental data in order to solve the Schrodinger equations. This method is usually fast and reliable, but can be easily countered if the environment of the molecule that is being computed is not similar enough to the approximated parameters of this method. The other method is B3LYP, a hydrid functional which utilises the DFT in order to calculate the majority of the Hamiltonian while a small portion still utilises the Hartree-Fock theory to calculate the exchange integral term. B3LYP stands for Becke, 3-parameter, Lee-Yang-Parr and uses a 6-31G basis set as the electronic wavefunction in order to produce more accurate results at the cost of increased calculation time.

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

[[File:Ex1 general.png|thumb|x700px|700px|centre|Figure 1: Formation of Cyclohaxadiene]]

Also known as the Diels-Alder reaction, this exercise investigates the well-known [4+2] cycloaddition between a conjugated diene (butadiene) and a dienophile (ethylene). The electrophilic reaction involves 4 pi-electrons from the diene and 2 pi-electrons from the alkene, and is a popular method to form regio- and stereochemically controlled 6-membered rings.

Method 2 was used to compute the transition state (TS) for this exercise. All steps are optimised to the PM6 level. First, the reactants are optimised to a minimum. The carbons at the reacting termini were then frozen at around 2.20 Å before optimised to a minimum to give a frozen-guess TS. Then finally, the molecule was optimised as a TS and an IRC was performed in order to confirm and locate the transition state.

=== Analysis of the Molecular Orbitals (MO) ===

The Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) for the reactants and the TS are shown below and its energies were recorded in order to produce the MO diagram as shown in figure 2.

{| class="wikitable"
! Ethene - HOMO
! Ethene - LUMO
! Butadiene - HOMO
! Butadiene - LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Cc5115 exer1finalMO.png|thumb|x800px|800px|left|Figure 2: MO Diagram for the formation of Transition State of the Diels-Alder Reaction]]

The symmetric TS HOMO and LUMO are formed through the interactions between the HOMO of ethylene and the LUMO of butadiene, both of which are symmetric. On the other hand, the LUMO of ethylene and the HOMO of butadiene, both of which are asymmetric, interacts to give an asymmetric HOMO-1 and LUMO+1. What can be concluded about the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed, and that the reaction is forbidden when the symmetry of the molecular orbitals aren't the same. The orbital overlap integral, S<sub>AB</sub>, is a quantitative measure of orbital overlap of two different atoms. Orbitals of the same symmetry will lead to constructive overlap and gives a non-zero value while orbitals of different symmetry will lead to destructive overlap and an orbital overlap integral of zero. Thus the overlap integral are:

- Non-zero for symmetric-symmetric interaction

- Non-zero for asymmetric-asymmetric interaction

- Zero for symmetric-asymmetric interaction

As observed in the MO diagram, the energy gap between the HOMO and LUMO for butadiene is smaller that those for ethylene due to butadiene being more electron rich than ethylene. Furthermore, in a normal MO diagram, the bonding MO formed should have a lower energy compared to both atomic orbitals (AO) whilst the anti-bonding MO formed should have a higher energy than both AOs. The reason why figure 3 goes against the tide is because the MOs formed corresponds to the transition state where the electrons are very delocalised within the chemical environment of the molecule.

==== LOG Files ====

[[:File:Cc5115_ETHENE_MO.LOG]]

[[:File:Cc5115_BUTADIENE_MO.LOG]]

[[:File:Cc5115_OPT_MO.LOG]]

=== Analysis of the C-C bond lengths ===

{| class="wikitable"
! Bond Lengths (Å)
! C1-C2
! C2-C3
! C3-C4
! C4-C5
! C5-C6
! C6-C1
|-
| Ethylene
|
|
|
|
| 1.36
|
|-
| Butadiene
| 1.36
| 1.54
| 1.36
|
|
|
|-
| Transition State
| 1.38
| 1.41
| 1.38
| 2.11
| 1.38
| 2.12
|-
| Cyclohexadiene
| 1.49
| 1.33
| 1.49
| 1.54
| 1.54
| 1.54
|}

The numbering of the carbon bonds are according to the labels on figure 1. The typical C-C bond lengths are as follows:

{| class="wikitable"
! Bond Type
! Bond Length (Å)
|-
| sp<sup>3</sup>-sp<sup>3</sup> C-C bond
| 1.54
|-
| sp<sup>3</sup>-sp<sup>2</sup> C-C bond
| 1.50
|-
| sp<sup>2</sup>-sp<sup>2</sup> C-C bond
| 1.47
|-
| sp<sup>2</sup>-sp<sup>2</sup> C=C bond
| 1.34
|}

When the reaction proceeds to the transition state, the sp<sup>2</sup>-sp<sup>2</sup> C5-C6 bond (originally ethylene) becomes longer as the carbons starts to change from sp<sup>2</sup> hybridised to sp<sup>3</sup> hybridised.
This trait is also apparent with C1-C2 and C3-C4 bonds where it once was the double bonds on butadiene, however, the increase in length of these bonds is less than that of C5-C6 due to the formation of a new double bond between C2 and C3, thus these carbons still remain sp<sup>2</sup> hybridised. This also leads to the next observation, where the C2-C3 bond decreases in length as it moves from the reactants to the transition state then the product, cyclohexadiene. This is because it is changing from a sp<sup>3</sup>-sp<sup>3</sup> C-C bond to a sp<sup>2</sup>-sp<sup>2</sup> C=C bond where the increase in s character shortens the bond lengths. This reaction also leads to the formation of 2 new bonds, namely C4-C5 and C6-C1. The Van der Waals radius of a carbon atom is 1.7 Å, and so the distance between 2 carbon atoms should be 3.4 Å, which is relatively longer than the bonds C4-C5 and C6-C1 which has a length of 2.11 and 2.12 Å respectively. This shows that the bonds are already partially formed in the transition state and they are beginning to interact together. This bond then settled at 1.54 Å in the product which matches with the typical bond length for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond.

=== Analysis of the vibrations ===

The animation for the first vibration is shown below. As observed, the formation of the 2 new bonds are synchronous as the reacting termini of butadiene and ethylene approaches each other at the same rate.

{| class="wikitable"
! <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 2;rotate x -20; </script>
<uploadedFileContents>Cc5115 OPT MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| The vibrations
|}

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

[[File:Cc5115 Exercise 2 generl.png|thumb|x700px|700px|centre|Figure 3: Reaction Scheme]]

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via either the endo or exo pathways to form 2 products with different stereochemistry. Method 3 was employed in order to compute the TS for this exercise. This time, the structures were further optimised with B3LYP/6-31G method and the results are shown and discussed below.

=== Analysis of Molecular Orbitals ===

[[File:Cc5115 Endo MO Exercise 2.png|thumb|x500px|500px|left|Figure 4: MO Diagram for the Endo TS]]

[[File:Cc5115 Exo MO Exercise 2.png|thumb|x500px|500px|right|Figure 5: MO Diagram for the Exo TS]]

There are two types of Diels-Alder (DA) reactions: one is with a normal electron demand where the dienophile is electron deficient and the diene is electron rich, and the other is with an inverse electron demand where the dienophile is electron rich and the diene is electron deficient.

For a normal electron demand DA reaction, the dienophile low-lying LUMO interacts with the diene HOMO which has a high energy. However, observing the energies of the reactants and the transition states, the MO diagram shows that this particular DA reaction has an inverse electron demand where the dienophile (1,3-dioxole) is electron rich (higher in energy) and the diene (cyclohexadiene) is electron poor (lower in energy). The interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene thus leads to the HOMO and LUMO of the transition state. Although opposing that of a normal electron demand DA, this reaction still follows the Woodword-Hoffman rule and is thermally allowed.

Similar to exercise 1, MOs of the same symmetry interact; the symmetrical dienophile HOMO and the diene LUMO interacts to give a symmetrical TS HOMO and LUMO, while the asymmetrical dienophile LUMO and diene HOMO gives the asymmetrical TS HOMO-1 and LUMO+1. It is also observable that the endo TS HOMO has a lower energy than the exo TS HOMO which suggests that the endo reaction is favoured. This will be discussed further in the Thermochemistry section of this exercise.

{| class="wikitable"
! ENDO TS - HOMO -1
! ENDO TS - HOMO
! ENDO TS - LUMO
! ENDO TS - LUMO +1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Log Files ====

[[File:Cc5115 ENDO B3.LOG]]

[[File:Cc5115 PLEASE WORK B3.LOG]]

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +149.70
| -77.52
|-
| Exo
| +157.52
| -73.92
|}

As discussed briefly in the introduction, the reactants need to pass the activation barrier (transition state) in order to reach to the products. The table regarding the reaction barriers and energies shows that the activation barrier for the endo reaction is less than that of the exo reaction, more-so confirming that the endo reaction is kinetically favoured. This links to the lower energy that the endo TS HOMO has compared to the exo TS. This observance can be explained by secondary orbital interation (SOI). The 2 non-bonding oxygen p-orbitals containing electron lone pairs can overlap with the LUMO of the diene through space thus stabilising the TS and consequentially lowering reaction barrier. However, the more negative reaction energy of the endo reaction can be explained with sterics; in the exo transition state, the steric interaction between the sp<sup>3</sup> bridging carbons and the rest of the 1,3-dioxole structure results in the exo product being higher in energy.

{| class="wikitable"
! Exo Secondary MO
! Endo Secondary MO
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

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

=== IRC ===

{| class="wikitable"
! [[File:Cc5115 Exo IRC gif.gif|thumb|x500px|500px|left|IRC for Exo Product]]
! [[File:Cc5115 Endo IRC gif.gif|thumb|x500px|500px|left|IRC for Endo Product]]
! [[File:Chelatropic IRC gif.gif|thumb|x500px|500px|left|IRC for Chelatropic Product]]
|}

IRC (intrinsic reaction coordinate) show how reactions move in space during its reaction to form products. From the IRC animations, it can be seen that the formation of the new bonds differ to that of exercise 1. Here, in the exo and endo pathways, the formation of the 2 new bonds are asynchronous as one bond forms before the other. However, the bonds form synchronously in the chelatropic reaction leading to the symmetrical product.

The IRC reaction pathways also show a smaller activation barrier compared to that of exercise 1. This is because xylylene is highly unstable. Xylylene can exist with 4π electrons making it anti-aromatic, or either with 6π electrons an a diradical which is very unstable. On the flipside, the product formed is aromatic making the DA reaction extremely favourable. Naphthalene forces the diene to be rigid in its positions easing the overlap capabilities of the diene with the dienophile. This can be observed in the animation as naphthalene doesn't have to go through major rearrangements in order to form the products.

In the reaction, naphthalene initially has a C=C bond length of 1.35 Å and a C-C bond length averaging around 1.51 Å. This changes as the product is formed where all the carbon-carbon bonds on the 6 membered rings become 1.47 Å in length suggesting the formation of an aromatic 6-membered ring where the π electrons are delocalised throughout the ring. The change in bond length can also be seen with careful observation of the animations.

==== Log Files ====

[[File:Cc5115 chelatropic IRC.LOG]]

[[File:Cc5115 endoex3 IRC.LOG]]

[[File:Cc5115 exoex3 IRC.LOG]]

=== Thermochemistry ===

[[File:Cc5115 Energy Diagram Ex3.png|thumb|x500px|600px|right|Figure 6: Reaction profile for the 3 different pathways]]

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +79.85
| -100.95
|-
| Exo
| +83.82
| -101.59
|-
| Chelatropic
| +102.16
| -157.93
|}

Significantly resembling to exercise 2, exercise 3 features the endo pathway being kinetically favoured as its activation energy has the least energy compared to the other pathway. Again, this is due to the overlap between the oxygen p-orbitals overlapping with the π-orbitals of the xylylene ring. However, the difference in activation and reaction energies between the exo and endo pathways do not differ that much due to the SOI not contributing significantly in the TS and there are little steric difference between the two products. For the chelatropic product, there is a hugh drop in reaction energy. Observing the product, the large sulfur atom forming a 5-membered ring decreases the ring-strain making the product relatively stable compared to the products from the DA reaction.

=== Cyclisation at the other reaction site ===

{| class="wikitable"
! [[File:Cc5115 IRC exo reaction site b.gif|thumb|x500px|500px|left|IRC for Exo Product at reaction site B]]
! [[File:Cc5115 IRC endo reaction site b.gif|thumb|x500px|500px|left|IRC for Endo Product at reaction site B]]
|}

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +110.06
| -14.33
|-
| Exo
| +117.90
| -18.78
|}

For this exercise, the Diels-Alder reaction can also take place at the other reaction site as illustrated in the animations. As seen from the table of reaction barrier and energy, the endo product is both kinetically and thermodynamically favoured as its activation energy is lower (TS has lower energy) as well as its reaction energy (product has a lower energy and thus more stable). This alternative pathway, however, is not favoured compared to the previous DA reaction since an aromatic 6-membered ring did not form during this reaction. This leads to higher activation energies and well as higher reaction energies.

==== Log Files ====

[[File:Cc5115 IRC 2 endo.LOG]]

[[File:Cc5115 IRC exo.LOG]]

== Conclusion ==

Gaussian was used to calculate the geometries of the transition states and the TS was validated by a correct imaginary frequency from frequency calculations as well as the correct pathways along the reaction coordinate from IRC. In this exercise, the transition states of the DA and a chelatropic reaction was investigated using the PM6 and B3LYP calculation methods. Exercise 1 investigated the carbon-carbon bond lengths of the reactants, TS and products in the reaction between ethylene and butadiene. The bond lengths matched well with expectations. Exercise 2 investigated the inverse-electron demand DA reaction through the construction of a MO diagram and it was concluded that the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed. Here, the endothermic pathway gave the kinetically and thermodynamically favoured product as expected. Exercise 3 also investigated the chelatropic reaction alongside the DA reaction and, similar to exercise 2, the endothermic pathway resulted in a kinetically and thermodynamically favoured product. An alternative reaction site was also investigated which was concluded to be less favourable to the original DA reaction site as an aromatic 6-membered ring did not form.

Rep:Mod:cc5115TS

2018-02-14T11:14:16Z

Cc5115: /* IRC */

= Y3C Transition states and Reactivity =

== Introduction ==

This section aims to illustrate the 3 different computational techniques that can be utilised in order to analyse the transition state (TS) of a reaction. The TS is the state which has the highest energy along a reaction coordinate, as a result it is the least stable state. In the reaction, the reactants needs to have a certain amount of energy in order to surpass the activation barrier, also known as the transition state energy, and reach the product state. This computational lab allows for calculations leading to the location of the TS. The structure of the TS is crucial in determining the mechanism of a reaction.

A potential energy surface (PES) has a 3N-6 dimension, which coincides to the degrees of freedom that the molecule has, where N is the number of atoms that the molecule possesses. In a 3-D PES, the saddle point (also called the TS), is a local mixami amidst 2 minima, and can be sometimes identified through secondary derivatives as it would be negative in one direction and positive in all other directions.

There are 3 calculation methods available in order to determine the structure of the TS.

1. The first and fastest method requires only one step where a guessed structure of the TS is optimised to give an optimised TS. This means that one will need of the TS to quite an extent, furthermore this method is rather unreliable as there is a high chance that the guessed TS is incorrectly drawn.

2. The second method works from a pre-frozen guess structure of the TS where the reacting termini of the reactants are frozen in space before the remaining structure is optimised to a minima. After that, the molecules are optimised as a transition state. This allows for a more reliable representation of the TS. This method is sufficient for Exercise 1.

3. The third method is the longest and most reliable method. Here, one starts by either optimising from the reactants or the products to a minima. For the reactant case, each reactants are optimised to a minima, arranged to resemble the TS and the reacting termini are frozen and the rest of the method 2 is repeated. A similar case occurs with the product; when the product is optimised to a minima, the bonds formed in the reactions are removed, the 2 fragments are arranged to resemble the TS and the reacting termini are frozen and method 2 was used once more. This method allows for the most reliable representation of the TS and is used for Exercise 2 & 3.

In this computational lab, two methods of calculation were used on Gaussian in order to find the TS. During the optimisation, the position of the molecule is decided as it is built in Gaussian. The time-independent Schrödinger equation was solved whilst utilising the Born-Oppenheimer approximation in order to find the energy and the wavefunction φ which represents the electronic states for the fixed nuclear positions and is dependent on on frozen nuclei positions. This is also known as the self-consistent field method (SCF). The two methods employed are the semi-empirical method PM6, which is usually performed first and sometimes followed by the Density Functional Theory (DFT) method B3LYP. The semi-empirical method PM6, although based on the Hartree-Fock formalism, this method uses many approximations based on experimental data in order to solve the Schrodinger equations. This method is usually fast and reliable, but can be easily countered if the environment of the molecule that is being computed is not similar enough to the approximated parameters of this method. The other method is B3LYP, a hydrid functional which utilises the DFT in order to calculate the majority of the Hamiltonian while a small portion still utilises the Hartree-Fock theory to calculate the exchange integral term. B3LYP stands for Becke, 3-parameter, Lee-Yang-Parr and uses a 6-31G basis set as the electronic wavefunction in order to produce more accurate results at the cost of increased calculation time.

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

[[File:Ex1 general.png|thumb|x700px|700px|centre|Figure 1: Formation of Cyclohaxadiene]]

Also known as the Diels-Alder reaction, this exercise investigates the well-known [4+2] cycloaddition between a conjugated diene (butadiene) and a dienophile (ethylene). The electrophilic reaction involves 4 pi-electrons from the diene and 2 pi-electrons from the alkene, and is a popular method to form regio- and stereochemically controlled 6-membered rings.

Method 2 was used to compute the transition state (TS) for this exercise. All steps are optimised to the PM6 level. First, the reactants are optimised to a minimum. The carbons at the reacting termini were then frozen at around 2.20 Å before optimised to a minimum to give a frozen-guess TS. Then finally, the molecule was optimised as a TS and an IRC was performed in order to confirm and locate the transition state.

=== Analysis of the Molecular Orbitals (MO) ===

The Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) for the reactants and the TS are shown below and its energies were recorded in order to produce the MO diagram as shown in figure 2.

{| class="wikitable"
! Ethene - HOMO
! Ethene - LUMO
! Butadiene - HOMO
! Butadiene - LUMO
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Cc5115 exer1finalMO.png|thumb|x800px|800px|left|Figure 2: MO Diagram for the formation of Transition State of the Diels-Alder Reaction]]

The symmetric TS HOMO and LUMO are formed through the interactions between the HOMO of ethylene and the LUMO of butadiene, both of which are symmetric. On the other hand, the LUMO of ethylene and the HOMO of butadiene, both of which are asymmetric, interacts to give an asymmetric HOMO-1 and LUMO+1. What can be concluded about the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed, and that the reaction is forbidden when the symmetry of the molecular orbitals aren't the same. The orbital overlap integral, S<sub>AB</sub>, is a quantitative measure of orbital overlap of two different atoms. Orbitals of the same symmetry will lead to constructive overlap and gives a non-zero value while orbitals of different symmetry will lead to destructive overlap and an orbital overlap integral of zero. Thus the overlap integral are:

- Non-zero for symmetric-symmetric interaction

- Non-zero for asymmetric-asymmetric interaction

- Zero for symmetric-asymmetric interaction

As observed in the MO diagram, the energy gap between the HOMO and LUMO for butadiene is smaller that those for ethylene due to butadiene being more electron rich than ethylene. Furthermore, in a normal MO diagram, the bonding MO formed should have a lower energy compared to both atomic orbitals (AO) whilst the anti-bonding MO formed should have a higher energy than both AOs. The reason why figure 3 goes against the tide is because the MOs formed corresponds to the transition state where the electrons are very delocalised within the chemical environment of the molecule.

==== LOG Files ====

[[:File:Cc5115_ETHENE_MO.LOG]]

[[:File:Cc5115_BUTADIENE_MO.LOG]]

[[:File:Cc5115_OPT_MO.LOG]]

=== Analysis of the C-C bond lengths ===

{| class="wikitable"
! Bond Lengths (Å)
! C1-C2
! C2-C3
! C3-C4
! C4-C5
! C5-C6
! C6-C1
|-
| Ethylene
|
|
|
|
| 1.36
|
|-
| Butadiene
| 1.36
| 1.54
| 1.36
|
|
|
|-
| Transition State
| 1.38
| 1.41
| 1.38
| 2.11
| 1.38
| 2.12
|-
| Cyclohexadiene
| 1.49
| 1.33
| 1.49
| 1.54
| 1.54
| 1.54
|}

The numbering of the carbon bonds are according to the labels on figure 1. The typical C-C bond lengths are as follows:

{| class="wikitable"
! Bond Type
! Bond Length (Å)
|-
| sp<sup>3</sup>-sp<sup>3</sup> C-C bond
| 1.54
|-
| sp<sup>3</sup>-sp<sup>2</sup> C-C bond
| 1.50
|-
| sp<sup>2</sup>-sp<sup>2</sup> C-C bond
| 1.47
|-
| sp<sup>2</sup>-sp<sup>2</sup> C=C bond
| 1.34
|}

When the reaction proceeds to the transition state, the sp<sup>2</sup>-sp<sup>2</sup> C5-C6 bond (originally ethylene) becomes longer as the carbons starts to change from sp<sup>2</sup> hybridised to sp<sup>3</sup> hybridised.
This trait is also apparent with C1-C2 and C3-C4 bonds where it once was the double bonds on butadiene, however, the increase in length of these bonds is less than that of C5-C6 due to the formation of a new double bond between C2 and C3, thus these carbons still remain sp<sup>2</sup> hybridised. This also leads to the next observation, where the C2-C3 bond decreases in length as it moves from the reactants to the transition state then the product, cyclohexadiene. This is because it is changing from a sp<sup>3</sup>-sp<sup>3</sup> C-C bond to a sp<sup>2</sup>-sp<sup>2</sup> C=C bond where the increase in s character shortens the bond lengths. This reaction also leads to the formation of 2 new bonds, namely C4-C5 and C6-C1. The Van der Waals radius of a carbon atom is 1.7 Å, and so the distance between 2 carbon atoms should be 3.4 Å, which is relatively longer than the bonds C4-C5 and C6-C1 which has a length of 2.11 and 2.12 Å respectively. This shows that the bonds are already partially formed in the transition state and they are beginning to interact together. This bond then settled at 1.54 Å in the product which matches with the typical bond length for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond.

=== Analysis of the vibrations ===

The animation for the first vibration is shown below. As observed, the formation of the 2 new bonds are synchronous as the reacting termini of butadiene and ethylene approaches each other at the same rate.

{| class="wikitable"
! <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 2;rotate x -20; </script>
<uploadedFileContents>Cc5115 OPT MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| The vibrations
|}

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

[[File:Cc5115 Exercise 2 generl.png|thumb|x700px|700px|centre|Figure 3: Reaction Scheme]]

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via either the endo or exo pathways to form 2 products with different stereochemistry. Method 3 was employed in order to compute the TS for this exercise. This time, the structures were further optimised with B3LYP/6-31G method and the results are shown and discussed below.

=== Analysis of Molecular Orbitals ===

[[File:Cc5115 Endo MO Exercise 2.png|thumb|x500px|500px|left|Figure 4: MO Diagram for the Endo TS]]

[[File:Cc5115 Exo MO Exercise 2.png|thumb|x500px|500px|right|Figure 5: MO Diagram for the Exo TS]]

There are two types of Diels-Alder (DA) reactions: one is with a normal electron demand where the dienophile is electron deficient and the diene is electron rich, and the other is with an inverse electron demand where the dienophile is electron rich and the diene is electron deficient.

For a normal electron demand DA reaction, the dienophile low-lying LUMO interacts with the diene HOMO which has a high energy. However, observing the energies of the reactants and the transition states, the MO diagram shows that this particular DA reaction has an inverse electron demand where the dienophile (1,3-dioxole) is electron rich (higher in energy) and the diene (cyclohexadiene) is electron poor (lower in energy). The interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene thus leads to the HOMO and LUMO of the transition state. Although opposing that of a normal electron demand DA, this reaction still follows the Woodword-Hoffman rule and is thermally allowed.

Similar to exercise 1, MOs of the same symmetry interact; the symmetrical dienophile HOMO and the diene LUMO interacts to give a symmetrical TS HOMO and LUMO, while the asymmetrical dienophile LUMO and diene HOMO gives the asymmetrical TS HOMO-1 and LUMO+1. It is also observable that the endo TS HOMO has a lower energy than the exo TS HOMO which suggests that the endo reaction is favoured. This will be discussed further in the Thermochemistry section of this exercise.

{| class="wikitable"
! ENDO TS - HOMO -1
! ENDO TS - HOMO
! ENDO TS - LUMO
! ENDO TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Log Files ====

[[File:Cc5115 ENDO B3.LOG]]

[[File:Cc5115 PLEASE WORK B3.LOG]]

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +149.70
| -77.52
|-
| Exo
| +157.52
| -73.92
|}

As discussed briefly in the introduction, the reactants need to pass the activation barrier (transition state) in order to reach to the products. The table regarding the reaction barriers and energies shows that the activation barrier for the endo reaction is less than that of the exo reaction, more-so confirming that the endo reaction is kinetically favoured. This links to the lower energy that the endo TS HOMO has compared to the exo TS. This observance can be explained by secondary orbital interation (SOI). The 2 non-bonding oxygen p-orbitals containing electron lone pairs can overlap with the LUMO of the diene through space thus stabilising the TS and consequentially lowering reaction barrier. However, the more negative reaction energy of the endo reaction can be explained with sterics; in the exo transition state, the steric interaction between the sp<sup>3</sup> bridging carbons and the rest of the 1,3-dioxole structure results in the exo product being higher in energy.

{| class="wikitable"
! Exo Secondary MO
! Endo Secondary MO
|-
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

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

=== IRC ===

{| class="wikitable"
! [[File:Cc5115 Exo IRC gif.gif|thumb|x500px|500px|left|IRC for Exo Product]]
! [[File:Cc5115 Endo IRC gif.gif|thumb|x500px|500px|left|IRC for Endo Product]]
! [[File:Chelatropic IRC gif.gif|thumb|x500px|500px|left|IRC for Chelatropic Product]]
|}

IRC (intrinsic reaction coordinate) show how reactions move in space during its reaction to form products. From the IRC animations, it can be seen that the formation of the new bonds differ to that of exercise 1. Here, in the exo and endo pathways, the formation of the 2 new bonds are asynchronous as one bond forms before the other. However, the bonds form synchronously in the chelatropic reaction leading to the symmetrical product.

The IRC reaction pathways also show a smaller activation barrier compared to that of exercise 1. This is because xylylene is highly unstable. Xylylene can exist with 4π electrons making it anti-aromatic, or either with 6π electrons an a diradical which is very unstable. On the flipside, the product formed is aromatic making the DA reaction extremely favourable. Naphthalene forces the diene to be rigid in its positions easing the overlap capabilities of the diene with the dienophile. This can be observed in the animation as naphthalene doesn't have to go through major rearrangements in order to form the products.

In the reaction, naphthalene initially has a C=C bond length of 1.35 Å and a C-C bond length averaging around 1.51 Å. This changes as the product is formed where all the carbon-carbon bonds on the 6 membered rings become 1.47 Å in length suggesting the formation of an aromatic 6-membered ring where the π electrons are delocalised throughout the ring. The change in bond length can also be seen with careful observation of the animations.

==== Log Files ====

[[File:Cc5115 chelatropic IRC.LOG]]

[[File:Cc5115 endoex3 IRC.LOG]]

[[File:Cc5115 exoex3 IRC.LOG]]

=== Thermochemistry ===

[[File:Cc5115 Energy Diagram Ex3.png|thumb|x500px|600px|right|Figure 6: Reaction profile for the 3 different pathways]]

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +79.85
| -100.95
|-
| Exo
| +83.82
| -101.59
|-
| Chelatropic
| +102.16
| -157.93
|}

Significantly resembling to exercise 2, exercise 3 features the endo pathway being kinetically favoured as its activation energy has the least energy compared to the other pathway. Again, this is due to the overlap between the oxygen p-orbitals overlapping with the π-orbitals of the xylylene ring. However, the difference in activation and reaction energies between the exo and endo pathways do not differ that much due to the SOI not contributing significantly in the TS and there are little steric difference between the two products. For the chelatropic product, there is a hugh drop in reaction energy. Observing the product, the large sulfur atom forming a 5-membered ring decreases the ring-strain making the product relatively stable compared to the products from the DA reaction.

=== Cyclisation at the other reaction site ===

{| class="wikitable"
! [[File:Cc5115 IRC exo reaction site b.gif|thumb|x500px|500px|left|IRC for Exo Product at reaction site B]]
! [[File:Cc5115 IRC endo reaction site b.gif|thumb|x500px|500px|left|IRC for Endo Product at reaction site B]]
|}

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +110.06
| -14.33
|-
| Exo
| +117.90
| -18.78
|}

For this exercise, the Diels-Alder reaction can also take place at the other reaction site as illustrated in the animations. As seen from the table of reaction barrier and energy, the endo product is both kinetically and thermodynamically favoured as its activation energy is lower (TS has lower energy) as well as its reaction energy (product has a lower energy and thus more stable). This alternative pathway, however, is not favoured compared to the previous DA reaction since an aromatic 6-membered ring did not form during this reaction. This leads to higher activation energies and well as higher reaction energies.

==== Log Files ====

[[File:Cc5115 IRC 2 endo.LOG]]

[[File:Cc5115 IRC exo.LOG]]

== Conclusion ==

Gaussian was used to calculate the geometries of the transition states and the TS was validated by a correct imaginary frequency from frequency calculations as well as the correct pathways along the reaction coordinate from IRC. In this exercise, the transition states of the DA and a chelatropic reaction was investigated using the PM6 and B3LYP calculation methods. Exercise 1 investigated the carbon-carbon bond lengths of the reactants, TS and products in the reaction between ethylene and butadiene. The bond lengths matched well with expectations. Exercise 2 investigated the inverse-electron demand DA reaction through the construction of a MO diagram and it was concluded that the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed. Here, the endothermic pathway gave the kinetically and thermodynamically favoured product as expected. Exercise 3 also investigated the chelatropic reaction alongside the DA reaction and, similar to exercise 2, the endothermic pathway resulted in a kinetically and thermodynamically favoured product. An alternative reaction site was also investigated which was concluded to be less favourable to the original DA reaction site as an aromatic 6-membered ring did not form.

File:Cc5115 exoex3 IRC.LOG

2018-02-14T11:14:08Z

Cc5115:

File:Cc5115 endoex3 IRC.LOG

2018-02-14T11:13:42Z

Cc5115:

File:Cc5115 chelatropic IRC.LOG

2018-02-14T11:13:07Z

Cc5115:

Rep:Mod:cc5115TS

2018-02-14T11:12:12Z

Cc5115: /* Log Files */

= Y3C Transition states and Reactivity =

== Introduction ==

This section aims to illustrate the 3 different computational techniques that can be utilised in order to analyse the transition state (TS) of a reaction. The TS is the state which has the highest energy along a reaction coordinate, as a result it is the least stable state. In the reaction, the reactants needs to have a certain amount of energy in order to surpass the activation barrier, also known as the transition state energy, and reach the product state. This computational lab allows for calculations leading to the location of the TS. The structure of the TS is crucial in determining the mechanism of a reaction.

A potential energy surface (PES) has a 3N-6 dimension, which coincides to the degrees of freedom that the molecule has, where N is the number of atoms that the molecule possesses. In a 3-D PES, the saddle point (also called the TS), is a local mixami amidst 2 minima, and can be sometimes identified through secondary derivatives as it would be negative in one direction and positive in all other directions.

There are 3 calculation methods available in order to determine the structure of the TS.

1. The first and fastest method requires only one step where a guessed structure of the TS is optimised to give an optimised TS. This means that one will need of the TS to quite an extent, furthermore this method is rather unreliable as there is a high chance that the guessed TS is incorrectly drawn.

2. The second method works from a pre-frozen guess structure of the TS where the reacting termini of the reactants are frozen in space before the remaining structure is optimised to a minima. After that, the molecules are optimised as a transition state. This allows for a more reliable representation of the TS. This method is sufficient for Exercise 1.

3. The third method is the longest and most reliable method. Here, one starts by either optimising from the reactants or the products to a minima. For the reactant case, each reactants are optimised to a minima, arranged to resemble the TS and the reacting termini are frozen and the rest of the method 2 is repeated. A similar case occurs with the product; when the product is optimised to a minima, the bonds formed in the reactions are removed, the 2 fragments are arranged to resemble the TS and the reacting termini are frozen and method 2 was used once more. This method allows for the most reliable representation of the TS and is used for Exercise 2 & 3.

In this computational lab, two methods of calculation were used on Gaussian in order to find the TS. During the optimisation, the position of the molecule is decided as it is built in Gaussian. The time-independent Schrödinger equation was solved whilst utilising the Born-Oppenheimer approximation in order to find the energy and the wavefunction φ which represents the electronic states for the fixed nuclear positions and is dependent on on frozen nuclei positions. This is also known as the self-consistent field method (SCF). The two methods employed are the semi-empirical method PM6, which is usually performed first and sometimes followed by the Density Functional Theory (DFT) method B3LYP. The semi-empirical method PM6, although based on the Hartree-Fock formalism, this method uses many approximations based on experimental data in order to solve the Schrodinger equations. This method is usually fast and reliable, but can be easily countered if the environment of the molecule that is being computed is not similar enough to the approximated parameters of this method. The other method is B3LYP, a hydrid functional which utilises the DFT in order to calculate the majority of the Hamiltonian while a small portion still utilises the Hartree-Fock theory to calculate the exchange integral term. B3LYP stands for Becke, 3-parameter, Lee-Yang-Parr and uses a 6-31G basis set as the electronic wavefunction in order to produce more accurate results at the cost of increased calculation time.

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

[[File:Ex1 general.png|thumb|x700px|700px|centre|Figure 1: Formation of Cyclohaxadiene]]

Also known as the Diels-Alder reaction, this exercise investigates the well-known [4+2] cycloaddition between a conjugated diene (butadiene) and a dienophile (ethylene). The electrophilic reaction involves 4 pi-electrons from the diene and 2 pi-electrons from the alkene, and is a popular method to form regio- and stereochemically controlled 6-membered rings.

Method 2 was used to compute the transition state (TS) for this exercise. All steps are optimised to the PM6 level. First, the reactants are optimised to a minimum. The carbons at the reacting termini were then frozen at around 2.20 Å before optimised to a minimum to give a frozen-guess TS. Then finally, the molecule was optimised as a TS and an IRC was performed in order to confirm and locate the transition state.

=== Analysis of the Molecular Orbitals (MO) ===

The Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) for the reactants and the TS are shown below and its energies were recorded in order to produce the MO diagram as shown in figure 2.

{| class="wikitable"
! Ethene - HOMO
! Ethene - LUMO
! Butadiene - HOMO
! Butadiene - LUMO
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
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<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
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<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Cc5115 exer1finalMO.png|thumb|x800px|800px|left|Figure 2: MO Diagram for the formation of Transition State of the Diels-Alder Reaction]]

The symmetric TS HOMO and LUMO are formed through the interactions between the HOMO of ethylene and the LUMO of butadiene, both of which are symmetric. On the other hand, the LUMO of ethylene and the HOMO of butadiene, both of which are asymmetric, interacts to give an asymmetric HOMO-1 and LUMO+1. What can be concluded about the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed, and that the reaction is forbidden when the symmetry of the molecular orbitals aren't the same. The orbital overlap integral, S<sub>AB</sub>, is a quantitative measure of orbital overlap of two different atoms. Orbitals of the same symmetry will lead to constructive overlap and gives a non-zero value while orbitals of different symmetry will lead to destructive overlap and an orbital overlap integral of zero. Thus the overlap integral are:

- Non-zero for symmetric-symmetric interaction

- Non-zero for asymmetric-asymmetric interaction

- Zero for symmetric-asymmetric interaction

As observed in the MO diagram, the energy gap between the HOMO and LUMO for butadiene is smaller that those for ethylene due to butadiene being more electron rich than ethylene. Furthermore, in a normal MO diagram, the bonding MO formed should have a lower energy compared to both atomic orbitals (AO) whilst the anti-bonding MO formed should have a higher energy than both AOs. The reason why figure 3 goes against the tide is because the MOs formed corresponds to the transition state where the electrons are very delocalised within the chemical environment of the molecule.

==== LOG Files ====

[[:File:Cc5115_ETHENE_MO.LOG]]

[[:File:Cc5115_BUTADIENE_MO.LOG]]

[[:File:Cc5115_OPT_MO.LOG]]

=== Analysis of the C-C bond lengths ===

{| class="wikitable"
! Bond Lengths (Å)
! C1-C2
! C2-C3
! C3-C4
! C4-C5
! C5-C6
! C6-C1
|-
| Ethylene
|
|
|
|
| 1.36
|
|-
| Butadiene
| 1.36
| 1.54
| 1.36
|
|
|
|-
| Transition State
| 1.38
| 1.41
| 1.38
| 2.11
| 1.38
| 2.12
|-
| Cyclohexadiene
| 1.49
| 1.33
| 1.49
| 1.54
| 1.54
| 1.54
|}

The numbering of the carbon bonds are according to the labels on figure 1. The typical C-C bond lengths are as follows:

{| class="wikitable"
! Bond Type
! Bond Length (Å)
|-
| sp<sup>3</sup>-sp<sup>3</sup> C-C bond
| 1.54
|-
| sp<sup>3</sup>-sp<sup>2</sup> C-C bond
| 1.50
|-
| sp<sup>2</sup>-sp<sup>2</sup> C-C bond
| 1.47
|-
| sp<sup>2</sup>-sp<sup>2</sup> C=C bond
| 1.34
|}

When the reaction proceeds to the transition state, the sp<sup>2</sup>-sp<sup>2</sup> C5-C6 bond (originally ethylene) becomes longer as the carbons starts to change from sp<sup>2</sup> hybridised to sp<sup>3</sup> hybridised.
This trait is also apparent with C1-C2 and C3-C4 bonds where it once was the double bonds on butadiene, however, the increase in length of these bonds is less than that of C5-C6 due to the formation of a new double bond between C2 and C3, thus these carbons still remain sp<sup>2</sup> hybridised. This also leads to the next observation, where the C2-C3 bond decreases in length as it moves from the reactants to the transition state then the product, cyclohexadiene. This is because it is changing from a sp<sup>3</sup>-sp<sup>3</sup> C-C bond to a sp<sup>2</sup>-sp<sup>2</sup> C=C bond where the increase in s character shortens the bond lengths. This reaction also leads to the formation of 2 new bonds, namely C4-C5 and C6-C1. The Van der Waals radius of a carbon atom is 1.7 Å, and so the distance between 2 carbon atoms should be 3.4 Å, which is relatively longer than the bonds C4-C5 and C6-C1 which has a length of 2.11 and 2.12 Å respectively. This shows that the bonds are already partially formed in the transition state and they are beginning to interact together. This bond then settled at 1.54 Å in the product which matches with the typical bond length for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond.

=== Analysis of the vibrations ===

The animation for the first vibration is shown below. As observed, the formation of the 2 new bonds are synchronous as the reacting termini of butadiene and ethylene approaches each other at the same rate.

{| class="wikitable"
! <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 2;rotate x -20; </script>
<uploadedFileContents>Cc5115 OPT MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| The vibrations
|}

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

[[File:Cc5115 Exercise 2 generl.png|thumb|x700px|700px|centre|Figure 3: Reaction Scheme]]

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via either the endo or exo pathways to form 2 products with different stereochemistry. Method 3 was employed in order to compute the TS for this exercise. This time, the structures were further optimised with B3LYP/6-31G method and the results are shown and discussed below.

=== Analysis of Molecular Orbitals ===

[[File:Cc5115 Endo MO Exercise 2.png|thumb|x500px|500px|left|Figure 4: MO Diagram for the Endo TS]]

[[File:Cc5115 Exo MO Exercise 2.png|thumb|x500px|500px|right|Figure 5: MO Diagram for the Exo TS]]

There are two types of Diels-Alder (DA) reactions: one is with a normal electron demand where the dienophile is electron deficient and the diene is electron rich, and the other is with an inverse electron demand where the dienophile is electron rich and the diene is electron deficient.

For a normal electron demand DA reaction, the dienophile low-lying LUMO interacts with the diene HOMO which has a high energy. However, observing the energies of the reactants and the transition states, the MO diagram shows that this particular DA reaction has an inverse electron demand where the dienophile (1,3-dioxole) is electron rich (higher in energy) and the diene (cyclohexadiene) is electron poor (lower in energy). The interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene thus leads to the HOMO and LUMO of the transition state. Although opposing that of a normal electron demand DA, this reaction still follows the Woodword-Hoffman rule and is thermally allowed.

Similar to exercise 1, MOs of the same symmetry interact; the symmetrical dienophile HOMO and the diene LUMO interacts to give a symmetrical TS HOMO and LUMO, while the asymmetrical dienophile LUMO and diene HOMO gives the asymmetrical TS HOMO-1 and LUMO+1. It is also observable that the endo TS HOMO has a lower energy than the exo TS HOMO which suggests that the endo reaction is favoured. This will be discussed further in the Thermochemistry section of this exercise.

{| class="wikitable"
! ENDO TS - HOMO -1
! ENDO TS - HOMO
! ENDO TS - LUMO
! ENDO TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
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<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
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</jmolApplet>
</jmol>
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<size>300</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Log Files ====

[[File:Cc5115 ENDO B3.LOG]]

[[File:Cc5115 PLEASE WORK B3.LOG]]

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +149.70
| -77.52
|-
| Exo
| +157.52
| -73.92
|}

As discussed briefly in the introduction, the reactants need to pass the activation barrier (transition state) in order to reach to the products. The table regarding the reaction barriers and energies shows that the activation barrier for the endo reaction is less than that of the exo reaction, more-so confirming that the endo reaction is kinetically favoured. This links to the lower energy that the endo TS HOMO has compared to the exo TS. This observance can be explained by secondary orbital interation (SOI). The 2 non-bonding oxygen p-orbitals containing electron lone pairs can overlap with the LUMO of the diene through space thus stabilising the TS and consequentially lowering reaction barrier. However, the more negative reaction energy of the endo reaction can be explained with sterics; in the exo transition state, the steric interaction between the sp<sup>3</sup> bridging carbons and the rest of the 1,3-dioxole structure results in the exo product being higher in energy.

{| class="wikitable"
! Exo Secondary MO
! Endo Secondary MO
|-
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

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

=== IRC ===

{| class="wikitable"
! [[File:Cc5115 Exo IRC gif.gif|thumb|x500px|500px|left|IRC for Exo Product]]
! [[File:Cc5115 Endo IRC gif.gif|thumb|x500px|500px|left|IRC for Endo Product]]
! [[File:Chelatropic IRC gif.gif|thumb|x500px|500px|left|IRC for Chelatropic Product]]
|}

IRC (intrinsic reaction coordinate) show how reactions move in space during its reaction to form products. From the IRC animations, it can be seen that the formation of the new bonds differ to that of exercise 1. Here, in the exo and endo pathways, the formation of the 2 new bonds are asynchronous as one bond forms before the other. However, the bonds form synchronously in the chelatropic reaction leading to the symmetrical product.

The IRC reaction pathways also show a smaller activation barrier compared to that of exercise 1. This is because xylylene is highly unstable. Xylylene can exist with 4π electrons making it anti-aromatic, or either with 6π electrons an a diradical which is very unstable. On the flipside, the product formed is aromatic making the DA reaction extremely favourable. Naphthalene forces the diene to be rigid in its positions easing the overlap capabilities of the diene with the dienophile. This can be observed in the animation as naphthalene doesn't have to go through major rearrangements in order to form the products.

In the reaction, naphthalene initially has a C=C bond length of 1.35 Å and a C-C bond length averaging around 1.51 Å. This changes as the product is formed where all the carbon-carbon bonds on the 6 membered rings become 1.47 Å in length suggesting the formation of an aromatic 6-membered ring where the π electrons are delocalised throughout the ring. The change in bond length can also be seen with careful observation of the animations.

=== Thermochemistry ===

[[File:Cc5115 Energy Diagram Ex3.png|thumb|x500px|600px|right|Figure 6: Reaction profile for the 3 different pathways]]

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +79.85
| -100.95
|-
| Exo
| +83.82
| -101.59
|-
| Chelatropic
| +102.16
| -157.93
|}

Significantly resembling to exercise 2, exercise 3 features the endo pathway being kinetically favoured as its activation energy has the least energy compared to the other pathway. Again, this is due to the overlap between the oxygen p-orbitals overlapping with the π-orbitals of the xylylene ring. However, the difference in activation and reaction energies between the exo and endo pathways do not differ that much due to the SOI not contributing significantly in the TS and there are little steric difference between the two products. For the chelatropic product, there is a hugh drop in reaction energy. Observing the product, the large sulfur atom forming a 5-membered ring decreases the ring-strain making the product relatively stable compared to the products from the DA reaction.

=== Cyclisation at the other reaction site ===

{| class="wikitable"
! [[File:Cc5115 IRC exo reaction site b.gif|thumb|x500px|500px|left|IRC for Exo Product at reaction site B]]
! [[File:Cc5115 IRC endo reaction site b.gif|thumb|x500px|500px|left|IRC for Endo Product at reaction site B]]
|}

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +110.06
| -14.33
|-
| Exo
| +117.90
| -18.78
|}

For this exercise, the Diels-Alder reaction can also take place at the other reaction site as illustrated in the animations. As seen from the table of reaction barrier and energy, the endo product is both kinetically and thermodynamically favoured as its activation energy is lower (TS has lower energy) as well as its reaction energy (product has a lower energy and thus more stable). This alternative pathway, however, is not favoured compared to the previous DA reaction since an aromatic 6-membered ring did not form during this reaction. This leads to higher activation energies and well as higher reaction energies.

==== Log Files ====

[[File:Cc5115 IRC 2 endo.LOG]]

[[File:Cc5115 IRC exo.LOG]]

== Conclusion ==

Gaussian was used to calculate the geometries of the transition states and the TS was validated by a correct imaginary frequency from frequency calculations as well as the correct pathways along the reaction coordinate from IRC. In this exercise, the transition states of the DA and a chelatropic reaction was investigated using the PM6 and B3LYP calculation methods. Exercise 1 investigated the carbon-carbon bond lengths of the reactants, TS and products in the reaction between ethylene and butadiene. The bond lengths matched well with expectations. Exercise 2 investigated the inverse-electron demand DA reaction through the construction of a MO diagram and it was concluded that the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed. Here, the endothermic pathway gave the kinetically and thermodynamically favoured product as expected. Exercise 3 also investigated the chelatropic reaction alongside the DA reaction and, similar to exercise 2, the endothermic pathway resulted in a kinetically and thermodynamically favoured product. An alternative reaction site was also investigated which was concluded to be less favourable to the original DA reaction site as an aromatic 6-membered ring did not form.

File:Cc5115 IRC exo.LOG

2018-02-14T11:12:02Z

Cc5115:

File:Cc5115 IRC 2 endo.LOG

2018-02-14T11:11:34Z

Cc5115:

Rep:Mod:cc5115TS

2018-02-14T11:10:18Z

Cc5115: /* Cyclisation at the other reaction site */

= Y3C Transition states and Reactivity =

== Introduction ==

This section aims to illustrate the 3 different computational techniques that can be utilised in order to analyse the transition state (TS) of a reaction. The TS is the state which has the highest energy along a reaction coordinate, as a result it is the least stable state. In the reaction, the reactants needs to have a certain amount of energy in order to surpass the activation barrier, also known as the transition state energy, and reach the product state. This computational lab allows for calculations leading to the location of the TS. The structure of the TS is crucial in determining the mechanism of a reaction.

A potential energy surface (PES) has a 3N-6 dimension, which coincides to the degrees of freedom that the molecule has, where N is the number of atoms that the molecule possesses. In a 3-D PES, the saddle point (also called the TS), is a local mixami amidst 2 minima, and can be sometimes identified through secondary derivatives as it would be negative in one direction and positive in all other directions.

There are 3 calculation methods available in order to determine the structure of the TS.

1. The first and fastest method requires only one step where a guessed structure of the TS is optimised to give an optimised TS. This means that one will need of the TS to quite an extent, furthermore this method is rather unreliable as there is a high chance that the guessed TS is incorrectly drawn.

2. The second method works from a pre-frozen guess structure of the TS where the reacting termini of the reactants are frozen in space before the remaining structure is optimised to a minima. After that, the molecules are optimised as a transition state. This allows for a more reliable representation of the TS. This method is sufficient for Exercise 1.

3. The third method is the longest and most reliable method. Here, one starts by either optimising from the reactants or the products to a minima. For the reactant case, each reactants are optimised to a minima, arranged to resemble the TS and the reacting termini are frozen and the rest of the method 2 is repeated. A similar case occurs with the product; when the product is optimised to a minima, the bonds formed in the reactions are removed, the 2 fragments are arranged to resemble the TS and the reacting termini are frozen and method 2 was used once more. This method allows for the most reliable representation of the TS and is used for Exercise 2 & 3.

In this computational lab, two methods of calculation were used on Gaussian in order to find the TS. During the optimisation, the position of the molecule is decided as it is built in Gaussian. The time-independent Schrödinger equation was solved whilst utilising the Born-Oppenheimer approximation in order to find the energy and the wavefunction φ which represents the electronic states for the fixed nuclear positions and is dependent on on frozen nuclei positions. This is also known as the self-consistent field method (SCF). The two methods employed are the semi-empirical method PM6, which is usually performed first and sometimes followed by the Density Functional Theory (DFT) method B3LYP. The semi-empirical method PM6, although based on the Hartree-Fock formalism, this method uses many approximations based on experimental data in order to solve the Schrodinger equations. This method is usually fast and reliable, but can be easily countered if the environment of the molecule that is being computed is not similar enough to the approximated parameters of this method. The other method is B3LYP, a hydrid functional which utilises the DFT in order to calculate the majority of the Hamiltonian while a small portion still utilises the Hartree-Fock theory to calculate the exchange integral term. B3LYP stands for Becke, 3-parameter, Lee-Yang-Parr and uses a 6-31G basis set as the electronic wavefunction in order to produce more accurate results at the cost of increased calculation time.

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

[[File:Ex1 general.png|thumb|x700px|700px|centre|Figure 1: Formation of Cyclohaxadiene]]

Also known as the Diels-Alder reaction, this exercise investigates the well-known [4+2] cycloaddition between a conjugated diene (butadiene) and a dienophile (ethylene). The electrophilic reaction involves 4 pi-electrons from the diene and 2 pi-electrons from the alkene, and is a popular method to form regio- and stereochemically controlled 6-membered rings.

Method 2 was used to compute the transition state (TS) for this exercise. All steps are optimised to the PM6 level. First, the reactants are optimised to a minimum. The carbons at the reacting termini were then frozen at around 2.20 Å before optimised to a minimum to give a frozen-guess TS. Then finally, the molecule was optimised as a TS and an IRC was performed in order to confirm and locate the transition state.

=== Analysis of the Molecular Orbitals (MO) ===

The Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) for the reactants and the TS are shown below and its energies were recorded in order to produce the MO diagram as shown in figure 2.

{| class="wikitable"
! Ethene - HOMO
! Ethene - LUMO
! Butadiene - HOMO
! Butadiene - LUMO
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Cc5115 exer1finalMO.png|thumb|x800px|800px|left|Figure 2: MO Diagram for the formation of Transition State of the Diels-Alder Reaction]]

The symmetric TS HOMO and LUMO are formed through the interactions between the HOMO of ethylene and the LUMO of butadiene, both of which are symmetric. On the other hand, the LUMO of ethylene and the HOMO of butadiene, both of which are asymmetric, interacts to give an asymmetric HOMO-1 and LUMO+1. What can be concluded about the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed, and that the reaction is forbidden when the symmetry of the molecular orbitals aren't the same. The orbital overlap integral, S<sub>AB</sub>, is a quantitative measure of orbital overlap of two different atoms. Orbitals of the same symmetry will lead to constructive overlap and gives a non-zero value while orbitals of different symmetry will lead to destructive overlap and an orbital overlap integral of zero. Thus the overlap integral are:

- Non-zero for symmetric-symmetric interaction

- Non-zero for asymmetric-asymmetric interaction

- Zero for symmetric-asymmetric interaction

As observed in the MO diagram, the energy gap between the HOMO and LUMO for butadiene is smaller that those for ethylene due to butadiene being more electron rich than ethylene. Furthermore, in a normal MO diagram, the bonding MO formed should have a lower energy compared to both atomic orbitals (AO) whilst the anti-bonding MO formed should have a higher energy than both AOs. The reason why figure 3 goes against the tide is because the MOs formed corresponds to the transition state where the electrons are very delocalised within the chemical environment of the molecule.

==== LOG Files ====

[[:File:Cc5115_ETHENE_MO.LOG]]

[[:File:Cc5115_BUTADIENE_MO.LOG]]

[[:File:Cc5115_OPT_MO.LOG]]

=== Analysis of the C-C bond lengths ===

{| class="wikitable"
! Bond Lengths (Å)
! C1-C2
! C2-C3
! C3-C4
! C4-C5
! C5-C6
! C6-C1
|-
| Ethylene
|
|
|
|
| 1.36
|
|-
| Butadiene
| 1.36
| 1.54
| 1.36
|
|
|
|-
| Transition State
| 1.38
| 1.41
| 1.38
| 2.11
| 1.38
| 2.12
|-
| Cyclohexadiene
| 1.49
| 1.33
| 1.49
| 1.54
| 1.54
| 1.54
|}

The numbering of the carbon bonds are according to the labels on figure 1. The typical C-C bond lengths are as follows:

{| class="wikitable"
! Bond Type
! Bond Length (Å)
|-
| sp<sup>3</sup>-sp<sup>3</sup> C-C bond
| 1.54
|-
| sp<sup>3</sup>-sp<sup>2</sup> C-C bond
| 1.50
|-
| sp<sup>2</sup>-sp<sup>2</sup> C-C bond
| 1.47
|-
| sp<sup>2</sup>-sp<sup>2</sup> C=C bond
| 1.34
|}

When the reaction proceeds to the transition state, the sp<sup>2</sup>-sp<sup>2</sup> C5-C6 bond (originally ethylene) becomes longer as the carbons starts to change from sp<sup>2</sup> hybridised to sp<sup>3</sup> hybridised.
This trait is also apparent with C1-C2 and C3-C4 bonds where it once was the double bonds on butadiene, however, the increase in length of these bonds is less than that of C5-C6 due to the formation of a new double bond between C2 and C3, thus these carbons still remain sp<sup>2</sup> hybridised. This also leads to the next observation, where the C2-C3 bond decreases in length as it moves from the reactants to the transition state then the product, cyclohexadiene. This is because it is changing from a sp<sup>3</sup>-sp<sup>3</sup> C-C bond to a sp<sup>2</sup>-sp<sup>2</sup> C=C bond where the increase in s character shortens the bond lengths. This reaction also leads to the formation of 2 new bonds, namely C4-C5 and C6-C1. The Van der Waals radius of a carbon atom is 1.7 Å, and so the distance between 2 carbon atoms should be 3.4 Å, which is relatively longer than the bonds C4-C5 and C6-C1 which has a length of 2.11 and 2.12 Å respectively. This shows that the bonds are already partially formed in the transition state and they are beginning to interact together. This bond then settled at 1.54 Å in the product which matches with the typical bond length for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond.

=== Analysis of the vibrations ===

The animation for the first vibration is shown below. As observed, the formation of the 2 new bonds are synchronous as the reacting termini of butadiene and ethylene approaches each other at the same rate.

{| class="wikitable"
! <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 2;rotate x -20; </script>
<uploadedFileContents>Cc5115 OPT MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| The vibrations
|}

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

[[File:Cc5115 Exercise 2 generl.png|thumb|x700px|700px|centre|Figure 3: Reaction Scheme]]

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via either the endo or exo pathways to form 2 products with different stereochemistry. Method 3 was employed in order to compute the TS for this exercise. This time, the structures were further optimised with B3LYP/6-31G method and the results are shown and discussed below.

=== Analysis of Molecular Orbitals ===

[[File:Cc5115 Endo MO Exercise 2.png|thumb|x500px|500px|left|Figure 4: MO Diagram for the Endo TS]]

[[File:Cc5115 Exo MO Exercise 2.png|thumb|x500px|500px|right|Figure 5: MO Diagram for the Exo TS]]

There are two types of Diels-Alder (DA) reactions: one is with a normal electron demand where the dienophile is electron deficient and the diene is electron rich, and the other is with an inverse electron demand where the dienophile is electron rich and the diene is electron deficient.

For a normal electron demand DA reaction, the dienophile low-lying LUMO interacts with the diene HOMO which has a high energy. However, observing the energies of the reactants and the transition states, the MO diagram shows that this particular DA reaction has an inverse electron demand where the dienophile (1,3-dioxole) is electron rich (higher in energy) and the diene (cyclohexadiene) is electron poor (lower in energy). The interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene thus leads to the HOMO and LUMO of the transition state. Although opposing that of a normal electron demand DA, this reaction still follows the Woodword-Hoffman rule and is thermally allowed.

Similar to exercise 1, MOs of the same symmetry interact; the symmetrical dienophile HOMO and the diene LUMO interacts to give a symmetrical TS HOMO and LUMO, while the asymmetrical dienophile LUMO and diene HOMO gives the asymmetrical TS HOMO-1 and LUMO+1. It is also observable that the endo TS HOMO has a lower energy than the exo TS HOMO which suggests that the endo reaction is favoured. This will be discussed further in the Thermochemistry section of this exercise.

{| class="wikitable"
! ENDO TS - HOMO -1
! ENDO TS - HOMO
! ENDO TS - LUMO
! ENDO TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Log Files ====

[[File:Cc5115 ENDO B3.LOG]]

[[File:Cc5115 PLEASE WORK B3.LOG]]

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +149.70
| -77.52
|-
| Exo
| +157.52
| -73.92
|}

As discussed briefly in the introduction, the reactants need to pass the activation barrier (transition state) in order to reach to the products. The table regarding the reaction barriers and energies shows that the activation barrier for the endo reaction is less than that of the exo reaction, more-so confirming that the endo reaction is kinetically favoured. This links to the lower energy that the endo TS HOMO has compared to the exo TS. This observance can be explained by secondary orbital interation (SOI). The 2 non-bonding oxygen p-orbitals containing electron lone pairs can overlap with the LUMO of the diene through space thus stabilising the TS and consequentially lowering reaction barrier. However, the more negative reaction energy of the endo reaction can be explained with sterics; in the exo transition state, the steric interaction between the sp<sup>3</sup> bridging carbons and the rest of the 1,3-dioxole structure results in the exo product being higher in energy.

{| class="wikitable"
! Exo Secondary MO
! Endo Secondary MO
|-
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

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

=== IRC ===

{| class="wikitable"
! [[File:Cc5115 Exo IRC gif.gif|thumb|x500px|500px|left|IRC for Exo Product]]
! [[File:Cc5115 Endo IRC gif.gif|thumb|x500px|500px|left|IRC for Endo Product]]
! [[File:Chelatropic IRC gif.gif|thumb|x500px|500px|left|IRC for Chelatropic Product]]
|}

IRC (intrinsic reaction coordinate) show how reactions move in space during its reaction to form products. From the IRC animations, it can be seen that the formation of the new bonds differ to that of exercise 1. Here, in the exo and endo pathways, the formation of the 2 new bonds are asynchronous as one bond forms before the other. However, the bonds form synchronously in the chelatropic reaction leading to the symmetrical product.

The IRC reaction pathways also show a smaller activation barrier compared to that of exercise 1. This is because xylylene is highly unstable. Xylylene can exist with 4π electrons making it anti-aromatic, or either with 6π electrons an a diradical which is very unstable. On the flipside, the product formed is aromatic making the DA reaction extremely favourable. Naphthalene forces the diene to be rigid in its positions easing the overlap capabilities of the diene with the dienophile. This can be observed in the animation as naphthalene doesn't have to go through major rearrangements in order to form the products.

In the reaction, naphthalene initially has a C=C bond length of 1.35 Å and a C-C bond length averaging around 1.51 Å. This changes as the product is formed where all the carbon-carbon bonds on the 6 membered rings become 1.47 Å in length suggesting the formation of an aromatic 6-membered ring where the π electrons are delocalised throughout the ring. The change in bond length can also be seen with careful observation of the animations.

=== Thermochemistry ===

[[File:Cc5115 Energy Diagram Ex3.png|thumb|x500px|600px|right|Figure 6: Reaction profile for the 3 different pathways]]

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +79.85
| -100.95
|-
| Exo
| +83.82
| -101.59
|-
| Chelatropic
| +102.16
| -157.93
|}

Significantly resembling to exercise 2, exercise 3 features the endo pathway being kinetically favoured as its activation energy has the least energy compared to the other pathway. Again, this is due to the overlap between the oxygen p-orbitals overlapping with the π-orbitals of the xylylene ring. However, the difference in activation and reaction energies between the exo and endo pathways do not differ that much due to the SOI not contributing significantly in the TS and there are little steric difference between the two products. For the chelatropic product, there is a hugh drop in reaction energy. Observing the product, the large sulfur atom forming a 5-membered ring decreases the ring-strain making the product relatively stable compared to the products from the DA reaction.

=== Cyclisation at the other reaction site ===

{| class="wikitable"
! [[File:Cc5115 IRC exo reaction site b.gif|thumb|x500px|500px|left|IRC for Exo Product at reaction site B]]
! [[File:Cc5115 IRC endo reaction site b.gif|thumb|x500px|500px|left|IRC for Endo Product at reaction site B]]
|}

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +110.06
| -14.33
|-
| Exo
| +117.90
| -18.78
|}

For this exercise, the Diels-Alder reaction can also take place at the other reaction site as illustrated in the animations. As seen from the table of reaction barrier and energy, the endo product is both kinetically and thermodynamically favoured as its activation energy is lower (TS has lower energy) as well as its reaction energy (product has a lower energy and thus more stable). This alternative pathway, however, is not favoured compared to the previous DA reaction since an aromatic 6-membered ring did not form during this reaction. This leads to higher activation energies and well as higher reaction energies.

==== Log Files ====

[[File:Cc5115 IRC exo reaction site b.gif]]

[[File:Cc5115 IRC endo reaction site b.gif]]

== Conclusion ==

Gaussian was used to calculate the geometries of the transition states and the TS was validated by a correct imaginary frequency from frequency calculations as well as the correct pathways along the reaction coordinate from IRC. In this exercise, the transition states of the DA and a chelatropic reaction was investigated using the PM6 and B3LYP calculation methods. Exercise 1 investigated the carbon-carbon bond lengths of the reactants, TS and products in the reaction between ethylene and butadiene. The bond lengths matched well with expectations. Exercise 2 investigated the inverse-electron demand DA reaction through the construction of a MO diagram and it was concluded that the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed. Here, the endothermic pathway gave the kinetically and thermodynamically favoured product as expected. Exercise 3 also investigated the chelatropic reaction alongside the DA reaction and, similar to exercise 2, the endothermic pathway resulted in a kinetically and thermodynamically favoured product. An alternative reaction site was also investigated which was concluded to be less favourable to the original DA reaction site as an aromatic 6-membered ring did not form.

Rep:Mod:cc5115TS

2018-02-14T11:09:40Z

Cc5115: /* Conclusion */

= Y3C Transition states and Reactivity =

== Introduction ==

This section aims to illustrate the 3 different computational techniques that can be utilised in order to analyse the transition state (TS) of a reaction. The TS is the state which has the highest energy along a reaction coordinate, as a result it is the least stable state. In the reaction, the reactants needs to have a certain amount of energy in order to surpass the activation barrier, also known as the transition state energy, and reach the product state. This computational lab allows for calculations leading to the location of the TS. The structure of the TS is crucial in determining the mechanism of a reaction.

A potential energy surface (PES) has a 3N-6 dimension, which coincides to the degrees of freedom that the molecule has, where N is the number of atoms that the molecule possesses. In a 3-D PES, the saddle point (also called the TS), is a local mixami amidst 2 minima, and can be sometimes identified through secondary derivatives as it would be negative in one direction and positive in all other directions.

There are 3 calculation methods available in order to determine the structure of the TS.

1. The first and fastest method requires only one step where a guessed structure of the TS is optimised to give an optimised TS. This means that one will need of the TS to quite an extent, furthermore this method is rather unreliable as there is a high chance that the guessed TS is incorrectly drawn.

2. The second method works from a pre-frozen guess structure of the TS where the reacting termini of the reactants are frozen in space before the remaining structure is optimised to a minima. After that, the molecules are optimised as a transition state. This allows for a more reliable representation of the TS. This method is sufficient for Exercise 1.

3. The third method is the longest and most reliable method. Here, one starts by either optimising from the reactants or the products to a minima. For the reactant case, each reactants are optimised to a minima, arranged to resemble the TS and the reacting termini are frozen and the rest of the method 2 is repeated. A similar case occurs with the product; when the product is optimised to a minima, the bonds formed in the reactions are removed, the 2 fragments are arranged to resemble the TS and the reacting termini are frozen and method 2 was used once more. This method allows for the most reliable representation of the TS and is used for Exercise 2 & 3.

In this computational lab, two methods of calculation were used on Gaussian in order to find the TS. During the optimisation, the position of the molecule is decided as it is built in Gaussian. The time-independent Schrödinger equation was solved whilst utilising the Born-Oppenheimer approximation in order to find the energy and the wavefunction φ which represents the electronic states for the fixed nuclear positions and is dependent on on frozen nuclei positions. This is also known as the self-consistent field method (SCF). The two methods employed are the semi-empirical method PM6, which is usually performed first and sometimes followed by the Density Functional Theory (DFT) method B3LYP. The semi-empirical method PM6, although based on the Hartree-Fock formalism, this method uses many approximations based on experimental data in order to solve the Schrodinger equations. This method is usually fast and reliable, but can be easily countered if the environment of the molecule that is being computed is not similar enough to the approximated parameters of this method. The other method is B3LYP, a hydrid functional which utilises the DFT in order to calculate the majority of the Hamiltonian while a small portion still utilises the Hartree-Fock theory to calculate the exchange integral term. B3LYP stands for Becke, 3-parameter, Lee-Yang-Parr and uses a 6-31G basis set as the electronic wavefunction in order to produce more accurate results at the cost of increased calculation time.

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

[[File:Ex1 general.png|thumb|x700px|700px|centre|Figure 1: Formation of Cyclohaxadiene]]

Also known as the Diels-Alder reaction, this exercise investigates the well-known [4+2] cycloaddition between a conjugated diene (butadiene) and a dienophile (ethylene). The electrophilic reaction involves 4 pi-electrons from the diene and 2 pi-electrons from the alkene, and is a popular method to form regio- and stereochemically controlled 6-membered rings.

Method 2 was used to compute the transition state (TS) for this exercise. All steps are optimised to the PM6 level. First, the reactants are optimised to a minimum. The carbons at the reacting termini were then frozen at around 2.20 Å before optimised to a minimum to give a frozen-guess TS. Then finally, the molecule was optimised as a TS and an IRC was performed in order to confirm and locate the transition state.

=== Analysis of the Molecular Orbitals (MO) ===

The Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) for the reactants and the TS are shown below and its energies were recorded in order to produce the MO diagram as shown in figure 2.

{| class="wikitable"
! Ethene - HOMO
! Ethene - LUMO
! Butadiene - HOMO
! Butadiene - LUMO
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Cc5115 exer1finalMO.png|thumb|x800px|800px|left|Figure 2: MO Diagram for the formation of Transition State of the Diels-Alder Reaction]]

The symmetric TS HOMO and LUMO are formed through the interactions between the HOMO of ethylene and the LUMO of butadiene, both of which are symmetric. On the other hand, the LUMO of ethylene and the HOMO of butadiene, both of which are asymmetric, interacts to give an asymmetric HOMO-1 and LUMO+1. What can be concluded about the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed, and that the reaction is forbidden when the symmetry of the molecular orbitals aren't the same. The orbital overlap integral, S<sub>AB</sub>, is a quantitative measure of orbital overlap of two different atoms. Orbitals of the same symmetry will lead to constructive overlap and gives a non-zero value while orbitals of different symmetry will lead to destructive overlap and an orbital overlap integral of zero. Thus the overlap integral are:

- Non-zero for symmetric-symmetric interaction

- Non-zero for asymmetric-asymmetric interaction

- Zero for symmetric-asymmetric interaction

As observed in the MO diagram, the energy gap between the HOMO and LUMO for butadiene is smaller that those for ethylene due to butadiene being more electron rich than ethylene. Furthermore, in a normal MO diagram, the bonding MO formed should have a lower energy compared to both atomic orbitals (AO) whilst the anti-bonding MO formed should have a higher energy than both AOs. The reason why figure 3 goes against the tide is because the MOs formed corresponds to the transition state where the electrons are very delocalised within the chemical environment of the molecule.

==== LOG Files ====

[[:File:Cc5115_ETHENE_MO.LOG]]

[[:File:Cc5115_BUTADIENE_MO.LOG]]

[[:File:Cc5115_OPT_MO.LOG]]

=== Analysis of the C-C bond lengths ===

{| class="wikitable"
! Bond Lengths (Å)
! C1-C2
! C2-C3
! C3-C4
! C4-C5
! C5-C6
! C6-C1
|-
| Ethylene
|
|
|
|
| 1.36
|
|-
| Butadiene
| 1.36
| 1.54
| 1.36
|
|
|
|-
| Transition State
| 1.38
| 1.41
| 1.38
| 2.11
| 1.38
| 2.12
|-
| Cyclohexadiene
| 1.49
| 1.33
| 1.49
| 1.54
| 1.54
| 1.54
|}

The numbering of the carbon bonds are according to the labels on figure 1. The typical C-C bond lengths are as follows:

{| class="wikitable"
! Bond Type
! Bond Length (Å)
|-
| sp<sup>3</sup>-sp<sup>3</sup> C-C bond
| 1.54
|-
| sp<sup>3</sup>-sp<sup>2</sup> C-C bond
| 1.50
|-
| sp<sup>2</sup>-sp<sup>2</sup> C-C bond
| 1.47
|-
| sp<sup>2</sup>-sp<sup>2</sup> C=C bond
| 1.34
|}

When the reaction proceeds to the transition state, the sp<sup>2</sup>-sp<sup>2</sup> C5-C6 bond (originally ethylene) becomes longer as the carbons starts to change from sp<sup>2</sup> hybridised to sp<sup>3</sup> hybridised.
This trait is also apparent with C1-C2 and C3-C4 bonds where it once was the double bonds on butadiene, however, the increase in length of these bonds is less than that of C5-C6 due to the formation of a new double bond between C2 and C3, thus these carbons still remain sp<sup>2</sup> hybridised. This also leads to the next observation, where the C2-C3 bond decreases in length as it moves from the reactants to the transition state then the product, cyclohexadiene. This is because it is changing from a sp<sup>3</sup>-sp<sup>3</sup> C-C bond to a sp<sup>2</sup>-sp<sup>2</sup> C=C bond where the increase in s character shortens the bond lengths. This reaction also leads to the formation of 2 new bonds, namely C4-C5 and C6-C1. The Van der Waals radius of a carbon atom is 1.7 Å, and so the distance between 2 carbon atoms should be 3.4 Å, which is relatively longer than the bonds C4-C5 and C6-C1 which has a length of 2.11 and 2.12 Å respectively. This shows that the bonds are already partially formed in the transition state and they are beginning to interact together. This bond then settled at 1.54 Å in the product which matches with the typical bond length for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond.

=== Analysis of the vibrations ===

The animation for the first vibration is shown below. As observed, the formation of the 2 new bonds are synchronous as the reacting termini of butadiene and ethylene approaches each other at the same rate.

{| class="wikitable"
! <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 2;rotate x -20; </script>
<uploadedFileContents>Cc5115 OPT MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| The vibrations
|}

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

[[File:Cc5115 Exercise 2 generl.png|thumb|x700px|700px|centre|Figure 3: Reaction Scheme]]

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via either the endo or exo pathways to form 2 products with different stereochemistry. Method 3 was employed in order to compute the TS for this exercise. This time, the structures were further optimised with B3LYP/6-31G method and the results are shown and discussed below.

=== Analysis of Molecular Orbitals ===

[[File:Cc5115 Endo MO Exercise 2.png|thumb|x500px|500px|left|Figure 4: MO Diagram for the Endo TS]]

[[File:Cc5115 Exo MO Exercise 2.png|thumb|x500px|500px|right|Figure 5: MO Diagram for the Exo TS]]

There are two types of Diels-Alder (DA) reactions: one is with a normal electron demand where the dienophile is electron deficient and the diene is electron rich, and the other is with an inverse electron demand where the dienophile is electron rich and the diene is electron deficient.

For a normal electron demand DA reaction, the dienophile low-lying LUMO interacts with the diene HOMO which has a high energy. However, observing the energies of the reactants and the transition states, the MO diagram shows that this particular DA reaction has an inverse electron demand where the dienophile (1,3-dioxole) is electron rich (higher in energy) and the diene (cyclohexadiene) is electron poor (lower in energy). The interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene thus leads to the HOMO and LUMO of the transition state. Although opposing that of a normal electron demand DA, this reaction still follows the Woodword-Hoffman rule and is thermally allowed.

Similar to exercise 1, MOs of the same symmetry interact; the symmetrical dienophile HOMO and the diene LUMO interacts to give a symmetrical TS HOMO and LUMO, while the asymmetrical dienophile LUMO and diene HOMO gives the asymmetrical TS HOMO-1 and LUMO+1. It is also observable that the endo TS HOMO has a lower energy than the exo TS HOMO which suggests that the endo reaction is favoured. This will be discussed further in the Thermochemistry section of this exercise.

{| class="wikitable"
! ENDO TS - HOMO -1
! ENDO TS - HOMO
! ENDO TS - LUMO
! ENDO TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Log Files ====

[[File:Cc5115 ENDO B3.LOG]]

[[File:Cc5115 PLEASE WORK B3.LOG]]

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +149.70
| -77.52
|-
| Exo
| +157.52
| -73.92
|}

As discussed briefly in the introduction, the reactants need to pass the activation barrier (transition state) in order to reach to the products. The table regarding the reaction barriers and energies shows that the activation barrier for the endo reaction is less than that of the exo reaction, more-so confirming that the endo reaction is kinetically favoured. This links to the lower energy that the endo TS HOMO has compared to the exo TS. This observance can be explained by secondary orbital interation (SOI). The 2 non-bonding oxygen p-orbitals containing electron lone pairs can overlap with the LUMO of the diene through space thus stabilising the TS and consequentially lowering reaction barrier. However, the more negative reaction energy of the endo reaction can be explained with sterics; in the exo transition state, the steric interaction between the sp<sup>3</sup> bridging carbons and the rest of the 1,3-dioxole structure results in the exo product being higher in energy.

{| class="wikitable"
! Exo Secondary MO
! Endo Secondary MO
|-
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

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

=== IRC ===

{| class="wikitable"
! [[File:Cc5115 Exo IRC gif.gif|thumb|x500px|500px|left|IRC for Exo Product]]
! [[File:Cc5115 Endo IRC gif.gif|thumb|x500px|500px|left|IRC for Endo Product]]
! [[File:Chelatropic IRC gif.gif|thumb|x500px|500px|left|IRC for Chelatropic Product]]
|}

IRC (intrinsic reaction coordinate) show how reactions move in space during its reaction to form products. From the IRC animations, it can be seen that the formation of the new bonds differ to that of exercise 1. Here, in the exo and endo pathways, the formation of the 2 new bonds are asynchronous as one bond forms before the other. However, the bonds form synchronously in the chelatropic reaction leading to the symmetrical product.

The IRC reaction pathways also show a smaller activation barrier compared to that of exercise 1. This is because xylylene is highly unstable. Xylylene can exist with 4π electrons making it anti-aromatic, or either with 6π electrons an a diradical which is very unstable. On the flipside, the product formed is aromatic making the DA reaction extremely favourable. Naphthalene forces the diene to be rigid in its positions easing the overlap capabilities of the diene with the dienophile. This can be observed in the animation as naphthalene doesn't have to go through major rearrangements in order to form the products.

In the reaction, naphthalene initially has a C=C bond length of 1.35 Å and a C-C bond length averaging around 1.51 Å. This changes as the product is formed where all the carbon-carbon bonds on the 6 membered rings become 1.47 Å in length suggesting the formation of an aromatic 6-membered ring where the π electrons are delocalised throughout the ring. The change in bond length can also be seen with careful observation of the animations.

=== Thermochemistry ===

[[File:Cc5115 Energy Diagram Ex3.png|thumb|x500px|600px|right|Figure 6: Reaction profile for the 3 different pathways]]

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +79.85
| -100.95
|-
| Exo
| +83.82
| -101.59
|-
| Chelatropic
| +102.16
| -157.93
|}

Significantly resembling to exercise 2, exercise 3 features the endo pathway being kinetically favoured as its activation energy has the least energy compared to the other pathway. Again, this is due to the overlap between the oxygen p-orbitals overlapping with the π-orbitals of the xylylene ring. However, the difference in activation and reaction energies between the exo and endo pathways do not differ that much due to the SOI not contributing significantly in the TS and there are little steric difference between the two products. For the chelatropic product, there is a hugh drop in reaction energy. Observing the product, the large sulfur atom forming a 5-membered ring decreases the ring-strain making the product relatively stable compared to the products from the DA reaction.

=== Cyclisation at the other reaction site ===

{| class="wikitable"
! [[File:Cc5115 IRC exo reaction site b.gif|thumb|x500px|500px|left|IRC for Exo Product at reaction site B]]
! [[File:Cc5115 IRC endo reaction site b.gif|thumb|x500px|500px|left|IRC for Endo Product at reaction site B]]
|}

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +110.06
| -14.33
|-
| Exo
| +117.90
| -18.78
|}

For this exercise, the Diels-Alder reaction can also take place at the other reaction site as illustrated in the animations. As seen from the table of reaction barrier and energy, the endo product is both kinetically and thermodynamically favoured as its activation energy is lower (TS has lower energy) as well as its reaction energy (product has a lower energy and thus more stable). This alternative pathway, however, is not favoured compared to the previous DA reaction since an aromatic 6-membered ring did not form during this reaction. This leads to higher activation energies and well as higher reaction energies.

== Conclusion ==

Gaussian was used to calculate the geometries of the transition states and the TS was validated by a correct imaginary frequency from frequency calculations as well as the correct pathways along the reaction coordinate from IRC. In this exercise, the transition states of the DA and a chelatropic reaction was investigated using the PM6 and B3LYP calculation methods. Exercise 1 investigated the carbon-carbon bond lengths of the reactants, TS and products in the reaction between ethylene and butadiene. The bond lengths matched well with expectations. Exercise 2 investigated the inverse-electron demand DA reaction through the construction of a MO diagram and it was concluded that the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed. Here, the endothermic pathway gave the kinetically and thermodynamically favoured product as expected. Exercise 3 also investigated the chelatropic reaction alongside the DA reaction and, similar to exercise 2, the endothermic pathway resulted in a kinetically and thermodynamically favoured product. An alternative reaction site was also investigated which was concluded to be less favourable to the original DA reaction site as an aromatic 6-membered ring did not form.

Rep:Mod:cc5115TS

2018-02-14T10:58:25Z

Cc5115: /* Cyclisation at the other reaction site */

= Y3C Transition states and Reactivity =

== Introduction ==

This section aims to illustrate the 3 different computational techniques that can be utilised in order to analyse the transition state (TS) of a reaction. The TS is the state which has the highest energy along a reaction coordinate, as a result it is the least stable state. In the reaction, the reactants needs to have a certain amount of energy in order to surpass the activation barrier, also known as the transition state energy, and reach the product state. This computational lab allows for calculations leading to the location of the TS. The structure of the TS is crucial in determining the mechanism of a reaction.

A potential energy surface (PES) has a 3N-6 dimension, which coincides to the degrees of freedom that the molecule has, where N is the number of atoms that the molecule possesses. In a 3-D PES, the saddle point (also called the TS), is a local mixami amidst 2 minima, and can be sometimes identified through secondary derivatives as it would be negative in one direction and positive in all other directions.

There are 3 calculation methods available in order to determine the structure of the TS.

1. The first and fastest method requires only one step where a guessed structure of the TS is optimised to give an optimised TS. This means that one will need of the TS to quite an extent, furthermore this method is rather unreliable as there is a high chance that the guessed TS is incorrectly drawn.

2. The second method works from a pre-frozen guess structure of the TS where the reacting termini of the reactants are frozen in space before the remaining structure is optimised to a minima. After that, the molecules are optimised as a transition state. This allows for a more reliable representation of the TS. This method is sufficient for Exercise 1.

3. The third method is the longest and most reliable method. Here, one starts by either optimising from the reactants or the products to a minima. For the reactant case, each reactants are optimised to a minima, arranged to resemble the TS and the reacting termini are frozen and the rest of the method 2 is repeated. A similar case occurs with the product; when the product is optimised to a minima, the bonds formed in the reactions are removed, the 2 fragments are arranged to resemble the TS and the reacting termini are frozen and method 2 was used once more. This method allows for the most reliable representation of the TS and is used for Exercise 2 & 3.

In this computational lab, two methods of calculation were used on Gaussian in order to find the TS. During the optimisation, the position of the molecule is decided as it is built in Gaussian. The time-independent Schrödinger equation was solved whilst utilising the Born-Oppenheimer approximation in order to find the energy and the wavefunction φ which represents the electronic states for the fixed nuclear positions and is dependent on on frozen nuclei positions. This is also known as the self-consistent field method (SCF). The two methods employed are the semi-empirical method PM6, which is usually performed first and sometimes followed by the Density Functional Theory (DFT) method B3LYP. The semi-empirical method PM6, although based on the Hartree-Fock formalism, this method uses many approximations based on experimental data in order to solve the Schrodinger equations. This method is usually fast and reliable, but can be easily countered if the environment of the molecule that is being computed is not similar enough to the approximated parameters of this method. The other method is B3LYP, a hydrid functional which utilises the DFT in order to calculate the majority of the Hamiltonian while a small portion still utilises the Hartree-Fock theory to calculate the exchange integral term. B3LYP stands for Becke, 3-parameter, Lee-Yang-Parr and uses a 6-31G basis set as the electronic wavefunction in order to produce more accurate results at the cost of increased calculation time.

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

[[File:Ex1 general.png|thumb|x700px|700px|centre|Figure 1: Formation of Cyclohaxadiene]]

Also known as the Diels-Alder reaction, this exercise investigates the well-known [4+2] cycloaddition between a conjugated diene (butadiene) and a dienophile (ethylene). The electrophilic reaction involves 4 pi-electrons from the diene and 2 pi-electrons from the alkene, and is a popular method to form regio- and stereochemically controlled 6-membered rings.

Method 2 was used to compute the transition state (TS) for this exercise. All steps are optimised to the PM6 level. First, the reactants are optimised to a minimum. The carbons at the reacting termini were then frozen at around 2.20 Å before optimised to a minimum to give a frozen-guess TS. Then finally, the molecule was optimised as a TS and an IRC was performed in order to confirm and locate the transition state.

=== Analysis of the Molecular Orbitals (MO) ===

The Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) for the reactants and the TS are shown below and its energies were recorded in order to produce the MO diagram as shown in figure 2.

{| class="wikitable"
! Ethene - HOMO
! Ethene - LUMO
! Butadiene - HOMO
! Butadiene - LUMO
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Cc5115 exer1finalMO.png|thumb|x800px|800px|left|Figure 2: MO Diagram for the formation of Transition State of the Diels-Alder Reaction]]

The symmetric TS HOMO and LUMO are formed through the interactions between the HOMO of ethylene and the LUMO of butadiene, both of which are symmetric. On the other hand, the LUMO of ethylene and the HOMO of butadiene, both of which are asymmetric, interacts to give an asymmetric HOMO-1 and LUMO+1. What can be concluded about the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed, and that the reaction is forbidden when the symmetry of the molecular orbitals aren't the same. The orbital overlap integral, S<sub>AB</sub>, is a quantitative measure of orbital overlap of two different atoms. Orbitals of the same symmetry will lead to constructive overlap and gives a non-zero value while orbitals of different symmetry will lead to destructive overlap and an orbital overlap integral of zero. Thus the overlap integral are:

- Non-zero for symmetric-symmetric interaction

- Non-zero for asymmetric-asymmetric interaction

- Zero for symmetric-asymmetric interaction

As observed in the MO diagram, the energy gap between the HOMO and LUMO for butadiene is smaller that those for ethylene due to butadiene being more electron rich than ethylene. Furthermore, in a normal MO diagram, the bonding MO formed should have a lower energy compared to both atomic orbitals (AO) whilst the anti-bonding MO formed should have a higher energy than both AOs. The reason why figure 3 goes against the tide is because the MOs formed corresponds to the transition state where the electrons are very delocalised within the chemical environment of the molecule.

==== LOG Files ====

[[:File:Cc5115_ETHENE_MO.LOG]]

[[:File:Cc5115_BUTADIENE_MO.LOG]]

[[:File:Cc5115_OPT_MO.LOG]]

=== Analysis of the C-C bond lengths ===

{| class="wikitable"
! Bond Lengths (Å)
! C1-C2
! C2-C3
! C3-C4
! C4-C5
! C5-C6
! C6-C1
|-
| Ethylene
|
|
|
|
| 1.36
|
|-
| Butadiene
| 1.36
| 1.54
| 1.36
|
|
|
|-
| Transition State
| 1.38
| 1.41
| 1.38
| 2.11
| 1.38
| 2.12
|-
| Cyclohexadiene
| 1.49
| 1.33
| 1.49
| 1.54
| 1.54
| 1.54
|}

The numbering of the carbon bonds are according to the labels on figure 1. The typical C-C bond lengths are as follows:

{| class="wikitable"
! Bond Type
! Bond Length (Å)
|-
| sp<sup>3</sup>-sp<sup>3</sup> C-C bond
| 1.54
|-
| sp<sup>3</sup>-sp<sup>2</sup> C-C bond
| 1.50
|-
| sp<sup>2</sup>-sp<sup>2</sup> C-C bond
| 1.47
|-
| sp<sup>2</sup>-sp<sup>2</sup> C=C bond
| 1.34
|}

When the reaction proceeds to the transition state, the sp<sup>2</sup>-sp<sup>2</sup> C5-C6 bond (originally ethylene) becomes longer as the carbons starts to change from sp<sup>2</sup> hybridised to sp<sup>3</sup> hybridised.
This trait is also apparent with C1-C2 and C3-C4 bonds where it once was the double bonds on butadiene, however, the increase in length of these bonds is less than that of C5-C6 due to the formation of a new double bond between C2 and C3, thus these carbons still remain sp<sup>2</sup> hybridised. This also leads to the next observation, where the C2-C3 bond decreases in length as it moves from the reactants to the transition state then the product, cyclohexadiene. This is because it is changing from a sp<sup>3</sup>-sp<sup>3</sup> C-C bond to a sp<sup>2</sup>-sp<sup>2</sup> C=C bond where the increase in s character shortens the bond lengths. This reaction also leads to the formation of 2 new bonds, namely C4-C5 and C6-C1. The Van der Waals radius of a carbon atom is 1.7 Å, and so the distance between 2 carbon atoms should be 3.4 Å, which is relatively longer than the bonds C4-C5 and C6-C1 which has a length of 2.11 and 2.12 Å respectively. This shows that the bonds are already partially formed in the transition state and they are beginning to interact together. This bond then settled at 1.54 Å in the product which matches with the typical bond length for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond.

=== Analysis of the vibrations ===

The animation for the first vibration is shown below. As observed, the formation of the 2 new bonds are synchronous as the reacting termini of butadiene and ethylene approaches each other at the same rate.

{| class="wikitable"
! <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 2;rotate x -20; </script>
<uploadedFileContents>Cc5115 OPT MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| The vibrations
|}

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

[[File:Cc5115 Exercise 2 generl.png|thumb|x700px|700px|centre|Figure 3: Reaction Scheme]]

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via either the endo or exo pathways to form 2 products with different stereochemistry. Method 3 was employed in order to compute the TS for this exercise. This time, the structures were further optimised with B3LYP/6-31G method and the results are shown and discussed below.

=== Analysis of Molecular Orbitals ===

[[File:Cc5115 Endo MO Exercise 2.png|thumb|x500px|500px|left|Figure 4: MO Diagram for the Endo TS]]

[[File:Cc5115 Exo MO Exercise 2.png|thumb|x500px|500px|right|Figure 5: MO Diagram for the Exo TS]]

There are two types of Diels-Alder (DA) reactions: one is with a normal electron demand where the dienophile is electron deficient and the diene is electron rich, and the other is with an inverse electron demand where the dienophile is electron rich and the diene is electron deficient.

For a normal electron demand DA reaction, the dienophile low-lying LUMO interacts with the diene HOMO which has a high energy. However, observing the energies of the reactants and the transition states, the MO diagram shows that this particular DA reaction has an inverse electron demand where the dienophile (1,3-dioxole) is electron rich (higher in energy) and the diene (cyclohexadiene) is electron poor (lower in energy). The interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene thus leads to the HOMO and LUMO of the transition state. Although opposing that of a normal electron demand DA, this reaction still follows the Woodword-Hoffman rule and is thermally allowed.

Similar to exercise 1, MOs of the same symmetry interact; the symmetrical dienophile HOMO and the diene LUMO interacts to give a symmetrical TS HOMO and LUMO, while the asymmetrical dienophile LUMO and diene HOMO gives the asymmetrical TS HOMO-1 and LUMO+1. It is also observable that the endo TS HOMO has a lower energy than the exo TS HOMO which suggests that the endo reaction is favoured. This will be discussed further in the Thermochemistry section of this exercise.

{| class="wikitable"
! ENDO TS - HOMO -1
! ENDO TS - HOMO
! ENDO TS - LUMO
! ENDO TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Log Files ====

[[File:Cc5115 ENDO B3.LOG]]

[[File:Cc5115 PLEASE WORK B3.LOG]]

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +149.70
| -77.52
|-
| Exo
| +157.52
| -73.92
|}

As discussed briefly in the introduction, the reactants need to pass the activation barrier (transition state) in order to reach to the products. The table regarding the reaction barriers and energies shows that the activation barrier for the endo reaction is less than that of the exo reaction, more-so confirming that the endo reaction is kinetically favoured. This links to the lower energy that the endo TS HOMO has compared to the exo TS. This observance can be explained by secondary orbital interation (SOI). The 2 non-bonding oxygen p-orbitals containing electron lone pairs can overlap with the LUMO of the diene through space thus stabilising the TS and consequentially lowering reaction barrier. However, the more negative reaction energy of the endo reaction can be explained with sterics; in the exo transition state, the steric interaction between the sp<sup>3</sup> bridging carbons and the rest of the 1,3-dioxole structure results in the exo product being higher in energy.

{| class="wikitable"
! Exo Secondary MO
! Endo Secondary MO
|-
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

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

=== IRC ===

{| class="wikitable"
! [[File:Cc5115 Exo IRC gif.gif|thumb|x500px|500px|left|IRC for Exo Product]]
! [[File:Cc5115 Endo IRC gif.gif|thumb|x500px|500px|left|IRC for Endo Product]]
! [[File:Chelatropic IRC gif.gif|thumb|x500px|500px|left|IRC for Chelatropic Product]]
|}

IRC (intrinsic reaction coordinate) show how reactions move in space during its reaction to form products. From the IRC animations, it can be seen that the formation of the new bonds differ to that of exercise 1. Here, in the exo and endo pathways, the formation of the 2 new bonds are asynchronous as one bond forms before the other. However, the bonds form synchronously in the chelatropic reaction leading to the symmetrical product.

The IRC reaction pathways also show a smaller activation barrier compared to that of exercise 1. This is because xylylene is highly unstable. Xylylene can exist with 4π electrons making it anti-aromatic, or either with 6π electrons an a diradical which is very unstable. On the flipside, the product formed is aromatic making the DA reaction extremely favourable. Naphthalene forces the diene to be rigid in its positions easing the overlap capabilities of the diene with the dienophile. This can be observed in the animation as naphthalene doesn't have to go through major rearrangements in order to form the products.

In the reaction, naphthalene initially has a C=C bond length of 1.35 Å and a C-C bond length averaging around 1.51 Å. This changes as the product is formed where all the carbon-carbon bonds on the 6 membered rings become 1.47 Å in length suggesting the formation of an aromatic 6-membered ring where the π electrons are delocalised throughout the ring. The change in bond length can also be seen with careful observation of the animations.

=== Thermochemistry ===

[[File:Cc5115 Energy Diagram Ex3.png|thumb|x500px|600px|right|Figure 6: Reaction profile for the 3 different pathways]]

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +79.85
| -100.95
|-
| Exo
| +83.82
| -101.59
|-
| Chelatropic
| +102.16
| -157.93
|}

Significantly resembling to exercise 2, exercise 3 features the endo pathway being kinetically favoured as its activation energy has the least energy compared to the other pathway. Again, this is due to the overlap between the oxygen p-orbitals overlapping with the π-orbitals of the xylylene ring. However, the difference in activation and reaction energies between the exo and endo pathways do not differ that much due to the SOI not contributing significantly in the TS and there are little steric difference between the two products. For the chelatropic product, there is a hugh drop in reaction energy. Observing the product, the large sulfur atom forming a 5-membered ring decreases the ring-strain making the product relatively stable compared to the products from the DA reaction.

=== Cyclisation at the other reaction site ===

{| class="wikitable"
! [[File:Cc5115 IRC exo reaction site b.gif|thumb|x500px|500px|left|IRC for Exo Product at reaction site B]]
! [[File:Cc5115 IRC endo reaction site b.gif|thumb|x500px|500px|left|IRC for Endo Product at reaction site B]]
|}

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +110.06
| -14.33
|-
| Exo
| +117.90
| -18.78
|}

For this exercise, the Diels-Alder reaction can also take place at the other reaction site as illustrated in the animations. As seen from the table of reaction barrier and energy, the endo product is both kinetically and thermodynamically favoured as its activation energy is lower (TS has lower energy) as well as its reaction energy (product has a lower energy and thus more stable). This alternative pathway, however, is not favoured compared to the previous DA reaction since an aromatic 6-membered ring did not form during this reaction. This leads to higher activation energies and well as higher reaction energies.

== Conclusion ==

Gaussian was used to calculate the geometries of the transition states using the PM6 and the B3LYP methods. The TS was validated by a correct imaginary frequency from frequency calculations as well as the correct pathways along the reaction coordinate from IRC.

Rep:Mod:cc5115TS

2018-02-14T10:54:30Z

Cc5115: /* Thermochemistry */

= Y3C Transition states and Reactivity =

== Introduction ==

This section aims to illustrate the 3 different computational techniques that can be utilised in order to analyse the transition state (TS) of a reaction. The TS is the state which has the highest energy along a reaction coordinate, as a result it is the least stable state. In the reaction, the reactants needs to have a certain amount of energy in order to surpass the activation barrier, also known as the transition state energy, and reach the product state. This computational lab allows for calculations leading to the location of the TS. The structure of the TS is crucial in determining the mechanism of a reaction.

A potential energy surface (PES) has a 3N-6 dimension, which coincides to the degrees of freedom that the molecule has, where N is the number of atoms that the molecule possesses. In a 3-D PES, the saddle point (also called the TS), is a local mixami amidst 2 minima, and can be sometimes identified through secondary derivatives as it would be negative in one direction and positive in all other directions.

There are 3 calculation methods available in order to determine the structure of the TS.

1. The first and fastest method requires only one step where a guessed structure of the TS is optimised to give an optimised TS. This means that one will need of the TS to quite an extent, furthermore this method is rather unreliable as there is a high chance that the guessed TS is incorrectly drawn.

2. The second method works from a pre-frozen guess structure of the TS where the reacting termini of the reactants are frozen in space before the remaining structure is optimised to a minima. After that, the molecules are optimised as a transition state. This allows for a more reliable representation of the TS. This method is sufficient for Exercise 1.

3. The third method is the longest and most reliable method. Here, one starts by either optimising from the reactants or the products to a minima. For the reactant case, each reactants are optimised to a minima, arranged to resemble the TS and the reacting termini are frozen and the rest of the method 2 is repeated. A similar case occurs with the product; when the product is optimised to a minima, the bonds formed in the reactions are removed, the 2 fragments are arranged to resemble the TS and the reacting termini are frozen and method 2 was used once more. This method allows for the most reliable representation of the TS and is used for Exercise 2 & 3.

In this computational lab, two methods of calculation were used on Gaussian in order to find the TS. During the optimisation, the position of the molecule is decided as it is built in Gaussian. The time-independent Schrödinger equation was solved whilst utilising the Born-Oppenheimer approximation in order to find the energy and the wavefunction φ which represents the electronic states for the fixed nuclear positions and is dependent on on frozen nuclei positions. This is also known as the self-consistent field method (SCF). The two methods employed are the semi-empirical method PM6, which is usually performed first and sometimes followed by the Density Functional Theory (DFT) method B3LYP. The semi-empirical method PM6, although based on the Hartree-Fock formalism, this method uses many approximations based on experimental data in order to solve the Schrodinger equations. This method is usually fast and reliable, but can be easily countered if the environment of the molecule that is being computed is not similar enough to the approximated parameters of this method. The other method is B3LYP, a hydrid functional which utilises the DFT in order to calculate the majority of the Hamiltonian while a small portion still utilises the Hartree-Fock theory to calculate the exchange integral term. B3LYP stands for Becke, 3-parameter, Lee-Yang-Parr and uses a 6-31G basis set as the electronic wavefunction in order to produce more accurate results at the cost of increased calculation time.

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

[[File:Ex1 general.png|thumb|x700px|700px|centre|Figure 1: Formation of Cyclohaxadiene]]

Also known as the Diels-Alder reaction, this exercise investigates the well-known [4+2] cycloaddition between a conjugated diene (butadiene) and a dienophile (ethylene). The electrophilic reaction involves 4 pi-electrons from the diene and 2 pi-electrons from the alkene, and is a popular method to form regio- and stereochemically controlled 6-membered rings.

Method 2 was used to compute the transition state (TS) for this exercise. All steps are optimised to the PM6 level. First, the reactants are optimised to a minimum. The carbons at the reacting termini were then frozen at around 2.20 Å before optimised to a minimum to give a frozen-guess TS. Then finally, the molecule was optimised as a TS and an IRC was performed in order to confirm and locate the transition state.

=== Analysis of the Molecular Orbitals (MO) ===

The Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) for the reactants and the TS are shown below and its energies were recorded in order to produce the MO diagram as shown in figure 2.

{| class="wikitable"
! Ethene - HOMO
! Ethene - LUMO
! Butadiene - HOMO
! Butadiene - LUMO
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Cc5115 exer1finalMO.png|thumb|x800px|800px|left|Figure 2: MO Diagram for the formation of Transition State of the Diels-Alder Reaction]]

The symmetric TS HOMO and LUMO are formed through the interactions between the HOMO of ethylene and the LUMO of butadiene, both of which are symmetric. On the other hand, the LUMO of ethylene and the HOMO of butadiene, both of which are asymmetric, interacts to give an asymmetric HOMO-1 and LUMO+1. What can be concluded about the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed, and that the reaction is forbidden when the symmetry of the molecular orbitals aren't the same. The orbital overlap integral, S<sub>AB</sub>, is a quantitative measure of orbital overlap of two different atoms. Orbitals of the same symmetry will lead to constructive overlap and gives a non-zero value while orbitals of different symmetry will lead to destructive overlap and an orbital overlap integral of zero. Thus the overlap integral are:

- Non-zero for symmetric-symmetric interaction

- Non-zero for asymmetric-asymmetric interaction

- Zero for symmetric-asymmetric interaction

As observed in the MO diagram, the energy gap between the HOMO and LUMO for butadiene is smaller that those for ethylene due to butadiene being more electron rich than ethylene. Furthermore, in a normal MO diagram, the bonding MO formed should have a lower energy compared to both atomic orbitals (AO) whilst the anti-bonding MO formed should have a higher energy than both AOs. The reason why figure 3 goes against the tide is because the MOs formed corresponds to the transition state where the electrons are very delocalised within the chemical environment of the molecule.

==== LOG Files ====

[[:File:Cc5115_ETHENE_MO.LOG]]

[[:File:Cc5115_BUTADIENE_MO.LOG]]

[[:File:Cc5115_OPT_MO.LOG]]

=== Analysis of the C-C bond lengths ===

{| class="wikitable"
! Bond Lengths (Å)
! C1-C2
! C2-C3
! C3-C4
! C4-C5
! C5-C6
! C6-C1
|-
| Ethylene
|
|
|
|
| 1.36
|
|-
| Butadiene
| 1.36
| 1.54
| 1.36
|
|
|
|-
| Transition State
| 1.38
| 1.41
| 1.38
| 2.11
| 1.38
| 2.12
|-
| Cyclohexadiene
| 1.49
| 1.33
| 1.49
| 1.54
| 1.54
| 1.54
|}

The numbering of the carbon bonds are according to the labels on figure 1. The typical C-C bond lengths are as follows:

{| class="wikitable"
! Bond Type
! Bond Length (Å)
|-
| sp<sup>3</sup>-sp<sup>3</sup> C-C bond
| 1.54
|-
| sp<sup>3</sup>-sp<sup>2</sup> C-C bond
| 1.50
|-
| sp<sup>2</sup>-sp<sup>2</sup> C-C bond
| 1.47
|-
| sp<sup>2</sup>-sp<sup>2</sup> C=C bond
| 1.34
|}

When the reaction proceeds to the transition state, the sp<sup>2</sup>-sp<sup>2</sup> C5-C6 bond (originally ethylene) becomes longer as the carbons starts to change from sp<sup>2</sup> hybridised to sp<sup>3</sup> hybridised.
This trait is also apparent with C1-C2 and C3-C4 bonds where it once was the double bonds on butadiene, however, the increase in length of these bonds is less than that of C5-C6 due to the formation of a new double bond between C2 and C3, thus these carbons still remain sp<sup>2</sup> hybridised. This also leads to the next observation, where the C2-C3 bond decreases in length as it moves from the reactants to the transition state then the product, cyclohexadiene. This is because it is changing from a sp<sup>3</sup>-sp<sup>3</sup> C-C bond to a sp<sup>2</sup>-sp<sup>2</sup> C=C bond where the increase in s character shortens the bond lengths. This reaction also leads to the formation of 2 new bonds, namely C4-C5 and C6-C1. The Van der Waals radius of a carbon atom is 1.7 Å, and so the distance between 2 carbon atoms should be 3.4 Å, which is relatively longer than the bonds C4-C5 and C6-C1 which has a length of 2.11 and 2.12 Å respectively. This shows that the bonds are already partially formed in the transition state and they are beginning to interact together. This bond then settled at 1.54 Å in the product which matches with the typical bond length for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond.

=== Analysis of the vibrations ===

The animation for the first vibration is shown below. As observed, the formation of the 2 new bonds are synchronous as the reacting termini of butadiene and ethylene approaches each other at the same rate.

{| class="wikitable"
! <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 2;rotate x -20; </script>
<uploadedFileContents>Cc5115 OPT MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| The vibrations
|}

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

[[File:Cc5115 Exercise 2 generl.png|thumb|x700px|700px|centre|Figure 3: Reaction Scheme]]

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via either the endo or exo pathways to form 2 products with different stereochemistry. Method 3 was employed in order to compute the TS for this exercise. This time, the structures were further optimised with B3LYP/6-31G method and the results are shown and discussed below.

=== Analysis of Molecular Orbitals ===

[[File:Cc5115 Endo MO Exercise 2.png|thumb|x500px|500px|left|Figure 4: MO Diagram for the Endo TS]]

[[File:Cc5115 Exo MO Exercise 2.png|thumb|x500px|500px|right|Figure 5: MO Diagram for the Exo TS]]

There are two types of Diels-Alder (DA) reactions: one is with a normal electron demand where the dienophile is electron deficient and the diene is electron rich, and the other is with an inverse electron demand where the dienophile is electron rich and the diene is electron deficient.

For a normal electron demand DA reaction, the dienophile low-lying LUMO interacts with the diene HOMO which has a high energy. However, observing the energies of the reactants and the transition states, the MO diagram shows that this particular DA reaction has an inverse electron demand where the dienophile (1,3-dioxole) is electron rich (higher in energy) and the diene (cyclohexadiene) is electron poor (lower in energy). The interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene thus leads to the HOMO and LUMO of the transition state. Although opposing that of a normal electron demand DA, this reaction still follows the Woodword-Hoffman rule and is thermally allowed.

Similar to exercise 1, MOs of the same symmetry interact; the symmetrical dienophile HOMO and the diene LUMO interacts to give a symmetrical TS HOMO and LUMO, while the asymmetrical dienophile LUMO and diene HOMO gives the asymmetrical TS HOMO-1 and LUMO+1. It is also observable that the endo TS HOMO has a lower energy than the exo TS HOMO which suggests that the endo reaction is favoured. This will be discussed further in the Thermochemistry section of this exercise.

{| class="wikitable"
! ENDO TS - HOMO -1
! ENDO TS - HOMO
! ENDO TS - LUMO
! ENDO TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Log Files ====

[[File:Cc5115 ENDO B3.LOG]]

[[File:Cc5115 PLEASE WORK B3.LOG]]

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +149.70
| -77.52
|-
| Exo
| +157.52
| -73.92
|}

As discussed briefly in the introduction, the reactants need to pass the activation barrier (transition state) in order to reach to the products. The table regarding the reaction barriers and energies shows that the activation barrier for the endo reaction is less than that of the exo reaction, more-so confirming that the endo reaction is kinetically favoured. This links to the lower energy that the endo TS HOMO has compared to the exo TS. This observance can be explained by secondary orbital interation (SOI). The 2 non-bonding oxygen p-orbitals containing electron lone pairs can overlap with the LUMO of the diene through space thus stabilising the TS and consequentially lowering reaction barrier. However, the more negative reaction energy of the endo reaction can be explained with sterics; in the exo transition state, the steric interaction between the sp<sup>3</sup> bridging carbons and the rest of the 1,3-dioxole structure results in the exo product being higher in energy.

{| class="wikitable"
! Exo Secondary MO
! Endo Secondary MO
|-
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

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

=== IRC ===

{| class="wikitable"
! [[File:Cc5115 Exo IRC gif.gif|thumb|x500px|500px|left|IRC for Exo Product]]
! [[File:Cc5115 Endo IRC gif.gif|thumb|x500px|500px|left|IRC for Endo Product]]
! [[File:Chelatropic IRC gif.gif|thumb|x500px|500px|left|IRC for Chelatropic Product]]
|}

IRC (intrinsic reaction coordinate) show how reactions move in space during its reaction to form products. From the IRC animations, it can be seen that the formation of the new bonds differ to that of exercise 1. Here, in the exo and endo pathways, the formation of the 2 new bonds are asynchronous as one bond forms before the other. However, the bonds form synchronously in the chelatropic reaction leading to the symmetrical product.

The IRC reaction pathways also show a smaller activation barrier compared to that of exercise 1. This is because xylylene is highly unstable. Xylylene can exist with 4π electrons making it anti-aromatic, or either with 6π electrons an a diradical which is very unstable. On the flipside, the product formed is aromatic making the DA reaction extremely favourable. Naphthalene forces the diene to be rigid in its positions easing the overlap capabilities of the diene with the dienophile. This can be observed in the animation as naphthalene doesn't have to go through major rearrangements in order to form the products.

In the reaction, naphthalene initially has a C=C bond length of 1.35 Å and a C-C bond length averaging around 1.51 Å. This changes as the product is formed where all the carbon-carbon bonds on the 6 membered rings become 1.47 Å in length suggesting the formation of an aromatic 6-membered ring where the π electrons are delocalised throughout the ring. The change in bond length can also be seen with careful observation of the animations.

=== Thermochemistry ===

[[File:Cc5115 Energy Diagram Ex3.png|thumb|x500px|600px|right|Figure 6: Reaction profile for the 3 different pathways]]

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +79.85
| -100.95
|-
| Exo
| +83.82
| -101.59
|-
| Chelatropic
| +102.16
| -157.93
|}

Significantly resembling to exercise 2, exercise 3 features the endo pathway being kinetically favoured as its activation energy has the least energy compared to the other pathway. Again, this is due to the overlap between the oxygen p-orbitals overlapping with the π-orbitals of the xylylene ring. However, the difference in activation and reaction energies between the exo and endo pathways do not differ that much due to the SOI not contributing significantly in the TS and there are little steric difference between the two products. For the chelatropic product, there is a hugh drop in reaction energy. Observing the product, the large sulfur atom forming a 5-membered ring decreases the ring-strain making the product relatively stable compared to the products from the DA reaction.

=== Cyclisation at the other reaction site ===

{| class="wikitable"
! [[File:Cc5115 IRC exo reaction site b.gif|thumb|x500px|500px|left|IRC for Exo Product at reaction site B]]
! [[File:Cc5115 IRC endo reaction site b.gif|thumb|x500px|500px|left|IRC for Endo Product at reaction site B]]
|}

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +110.06
| -14.33
|-
| Exo
| +117.90
| -18.78
|}

For this exercise, the Diels-Alder reaction can also take place at the other reaction site as illustrated in the animations.

== Conclusion ==

Gaussian was used to calculate the geometries of the transition states using the PM6 and the B3LYP methods. The TS was validated by a correct imaginary frequency from frequency calculations as well as the correct pathways along the reaction coordinate from IRC.

Rep:Mod:cc5115TS

2018-02-14T10:53:31Z

Cc5115: /* Thermochemistry */

= Y3C Transition states and Reactivity =

== Introduction ==

This section aims to illustrate the 3 different computational techniques that can be utilised in order to analyse the transition state (TS) of a reaction. The TS is the state which has the highest energy along a reaction coordinate, as a result it is the least stable state. In the reaction, the reactants needs to have a certain amount of energy in order to surpass the activation barrier, also known as the transition state energy, and reach the product state. This computational lab allows for calculations leading to the location of the TS. The structure of the TS is crucial in determining the mechanism of a reaction.

A potential energy surface (PES) has a 3N-6 dimension, which coincides to the degrees of freedom that the molecule has, where N is the number of atoms that the molecule possesses. In a 3-D PES, the saddle point (also called the TS), is a local mixami amidst 2 minima, and can be sometimes identified through secondary derivatives as it would be negative in one direction and positive in all other directions.

There are 3 calculation methods available in order to determine the structure of the TS.

1. The first and fastest method requires only one step where a guessed structure of the TS is optimised to give an optimised TS. This means that one will need of the TS to quite an extent, furthermore this method is rather unreliable as there is a high chance that the guessed TS is incorrectly drawn.

2. The second method works from a pre-frozen guess structure of the TS where the reacting termini of the reactants are frozen in space before the remaining structure is optimised to a minima. After that, the molecules are optimised as a transition state. This allows for a more reliable representation of the TS. This method is sufficient for Exercise 1.

3. The third method is the longest and most reliable method. Here, one starts by either optimising from the reactants or the products to a minima. For the reactant case, each reactants are optimised to a minima, arranged to resemble the TS and the reacting termini are frozen and the rest of the method 2 is repeated. A similar case occurs with the product; when the product is optimised to a minima, the bonds formed in the reactions are removed, the 2 fragments are arranged to resemble the TS and the reacting termini are frozen and method 2 was used once more. This method allows for the most reliable representation of the TS and is used for Exercise 2 & 3.

In this computational lab, two methods of calculation were used on Gaussian in order to find the TS. During the optimisation, the position of the molecule is decided as it is built in Gaussian. The time-independent Schrödinger equation was solved whilst utilising the Born-Oppenheimer approximation in order to find the energy and the wavefunction φ which represents the electronic states for the fixed nuclear positions and is dependent on on frozen nuclei positions. This is also known as the self-consistent field method (SCF). The two methods employed are the semi-empirical method PM6, which is usually performed first and sometimes followed by the Density Functional Theory (DFT) method B3LYP. The semi-empirical method PM6, although based on the Hartree-Fock formalism, this method uses many approximations based on experimental data in order to solve the Schrodinger equations. This method is usually fast and reliable, but can be easily countered if the environment of the molecule that is being computed is not similar enough to the approximated parameters of this method. The other method is B3LYP, a hydrid functional which utilises the DFT in order to calculate the majority of the Hamiltonian while a small portion still utilises the Hartree-Fock theory to calculate the exchange integral term. B3LYP stands for Becke, 3-parameter, Lee-Yang-Parr and uses a 6-31G basis set as the electronic wavefunction in order to produce more accurate results at the cost of increased calculation time.

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

[[File:Ex1 general.png|thumb|x700px|700px|centre|Figure 1: Formation of Cyclohaxadiene]]

Also known as the Diels-Alder reaction, this exercise investigates the well-known [4+2] cycloaddition between a conjugated diene (butadiene) and a dienophile (ethylene). The electrophilic reaction involves 4 pi-electrons from the diene and 2 pi-electrons from the alkene, and is a popular method to form regio- and stereochemically controlled 6-membered rings.

Method 2 was used to compute the transition state (TS) for this exercise. All steps are optimised to the PM6 level. First, the reactants are optimised to a minimum. The carbons at the reacting termini were then frozen at around 2.20 Å before optimised to a minimum to give a frozen-guess TS. Then finally, the molecule was optimised as a TS and an IRC was performed in order to confirm and locate the transition state.

=== Analysis of the Molecular Orbitals (MO) ===

The Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) for the reactants and the TS are shown below and its energies were recorded in order to produce the MO diagram as shown in figure 2.

{| class="wikitable"
! Ethene - HOMO
! Ethene - LUMO
! Butadiene - HOMO
! Butadiene - LUMO
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Cc5115 exer1finalMO.png|thumb|x800px|800px|left|Figure 2: MO Diagram for the formation of Transition State of the Diels-Alder Reaction]]

The symmetric TS HOMO and LUMO are formed through the interactions between the HOMO of ethylene and the LUMO of butadiene, both of which are symmetric. On the other hand, the LUMO of ethylene and the HOMO of butadiene, both of which are asymmetric, interacts to give an asymmetric HOMO-1 and LUMO+1. What can be concluded about the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed, and that the reaction is forbidden when the symmetry of the molecular orbitals aren't the same. The orbital overlap integral, S<sub>AB</sub>, is a quantitative measure of orbital overlap of two different atoms. Orbitals of the same symmetry will lead to constructive overlap and gives a non-zero value while orbitals of different symmetry will lead to destructive overlap and an orbital overlap integral of zero. Thus the overlap integral are:

- Non-zero for symmetric-symmetric interaction

- Non-zero for asymmetric-asymmetric interaction

- Zero for symmetric-asymmetric interaction

As observed in the MO diagram, the energy gap between the HOMO and LUMO for butadiene is smaller that those for ethylene due to butadiene being more electron rich than ethylene. Furthermore, in a normal MO diagram, the bonding MO formed should have a lower energy compared to both atomic orbitals (AO) whilst the anti-bonding MO formed should have a higher energy than both AOs. The reason why figure 3 goes against the tide is because the MOs formed corresponds to the transition state where the electrons are very delocalised within the chemical environment of the molecule.

==== LOG Files ====

[[:File:Cc5115_ETHENE_MO.LOG]]

[[:File:Cc5115_BUTADIENE_MO.LOG]]

[[:File:Cc5115_OPT_MO.LOG]]

=== Analysis of the C-C bond lengths ===

{| class="wikitable"
! Bond Lengths (Å)
! C1-C2
! C2-C3
! C3-C4
! C4-C5
! C5-C6
! C6-C1
|-
| Ethylene
|
|
|
|
| 1.36
|
|-
| Butadiene
| 1.36
| 1.54
| 1.36
|
|
|
|-
| Transition State
| 1.38
| 1.41
| 1.38
| 2.11
| 1.38
| 2.12
|-
| Cyclohexadiene
| 1.49
| 1.33
| 1.49
| 1.54
| 1.54
| 1.54
|}

The numbering of the carbon bonds are according to the labels on figure 1. The typical C-C bond lengths are as follows:

{| class="wikitable"
! Bond Type
! Bond Length (Å)
|-
| sp<sup>3</sup>-sp<sup>3</sup> C-C bond
| 1.54
|-
| sp<sup>3</sup>-sp<sup>2</sup> C-C bond
| 1.50
|-
| sp<sup>2</sup>-sp<sup>2</sup> C-C bond
| 1.47
|-
| sp<sup>2</sup>-sp<sup>2</sup> C=C bond
| 1.34
|}

When the reaction proceeds to the transition state, the sp<sup>2</sup>-sp<sup>2</sup> C5-C6 bond (originally ethylene) becomes longer as the carbons starts to change from sp<sup>2</sup> hybridised to sp<sup>3</sup> hybridised.
This trait is also apparent with C1-C2 and C3-C4 bonds where it once was the double bonds on butadiene, however, the increase in length of these bonds is less than that of C5-C6 due to the formation of a new double bond between C2 and C3, thus these carbons still remain sp<sup>2</sup> hybridised. This also leads to the next observation, where the C2-C3 bond decreases in length as it moves from the reactants to the transition state then the product, cyclohexadiene. This is because it is changing from a sp<sup>3</sup>-sp<sup>3</sup> C-C bond to a sp<sup>2</sup>-sp<sup>2</sup> C=C bond where the increase in s character shortens the bond lengths. This reaction also leads to the formation of 2 new bonds, namely C4-C5 and C6-C1. The Van der Waals radius of a carbon atom is 1.7 Å, and so the distance between 2 carbon atoms should be 3.4 Å, which is relatively longer than the bonds C4-C5 and C6-C1 which has a length of 2.11 and 2.12 Å respectively. This shows that the bonds are already partially formed in the transition state and they are beginning to interact together. This bond then settled at 1.54 Å in the product which matches with the typical bond length for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond.

=== Analysis of the vibrations ===

The animation for the first vibration is shown below. As observed, the formation of the 2 new bonds are synchronous as the reacting termini of butadiene and ethylene approaches each other at the same rate.

{| class="wikitable"
! <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 2;rotate x -20; </script>
<uploadedFileContents>Cc5115 OPT MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| The vibrations
|}

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

[[File:Cc5115 Exercise 2 generl.png|thumb|x700px|700px|centre|Figure 3: Reaction Scheme]]

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via either the endo or exo pathways to form 2 products with different stereochemistry. Method 3 was employed in order to compute the TS for this exercise. This time, the structures were further optimised with B3LYP/6-31G method and the results are shown and discussed below.

=== Analysis of Molecular Orbitals ===

[[File:Cc5115 Endo MO Exercise 2.png|thumb|x500px|500px|left|Figure 4: MO Diagram for the Endo TS]]

[[File:Cc5115 Exo MO Exercise 2.png|thumb|x500px|500px|right|Figure 5: MO Diagram for the Exo TS]]

There are two types of Diels-Alder (DA) reactions: one is with a normal electron demand where the dienophile is electron deficient and the diene is electron rich, and the other is with an inverse electron demand where the dienophile is electron rich and the diene is electron deficient.

For a normal electron demand DA reaction, the dienophile low-lying LUMO interacts with the diene HOMO which has a high energy. However, observing the energies of the reactants and the transition states, the MO diagram shows that this particular DA reaction has an inverse electron demand where the dienophile (1,3-dioxole) is electron rich (higher in energy) and the diene (cyclohexadiene) is electron poor (lower in energy). The interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene thus leads to the HOMO and LUMO of the transition state. Although opposing that of a normal electron demand DA, this reaction still follows the Woodword-Hoffman rule and is thermally allowed.

Similar to exercise 1, MOs of the same symmetry interact; the symmetrical dienophile HOMO and the diene LUMO interacts to give a symmetrical TS HOMO and LUMO, while the asymmetrical dienophile LUMO and diene HOMO gives the asymmetrical TS HOMO-1 and LUMO+1. It is also observable that the endo TS HOMO has a lower energy than the exo TS HOMO which suggests that the endo reaction is favoured. This will be discussed further in the Thermochemistry section of this exercise.

{| class="wikitable"
! ENDO TS - HOMO -1
! ENDO TS - HOMO
! ENDO TS - LUMO
! ENDO TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Log Files ====

[[File:Cc5115 ENDO B3.LOG]]

[[File:Cc5115 PLEASE WORK B3.LOG]]

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +149.70
| -77.52
|-
| Exo
| +157.52
| -73.92
|}

As discussed briefly in the introduction, the reactants need to pass the activation barrier (transition state) in order to reach to the products. The table regarding the reaction barriers and energies shows that the activation barrier for the endo reaction is less than that of the exo reaction, more-so confirming that the endo reaction is kinetically favoured. This links to the lower energy that the endo TS HOMO has compared to the exo TS. This observance can be explained by secondary orbital interation (SOI). The 2 non-bonding oxygen p-orbitals containing electron lone pairs can overlap with the LUMO of the diene through space thus stabilising the TS and consequentially lowering reaction barrier. However, the more negative reaction energy of the endo reaction can be explained with sterics; in the exo transition state, the steric interaction between the sp<sup>3</sup> bridging carbons and the rest of the 1,3-dioxole structure results in the exo product being higher in energy.

{| class="wikitable"
! Exo Secondary MO
! Endo Secondary MO
|-
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

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

=== IRC ===

{| class="wikitable"
! [[File:Cc5115 Exo IRC gif.gif|thumb|x500px|500px|left|IRC for Exo Product]]
! [[File:Cc5115 Endo IRC gif.gif|thumb|x500px|500px|left|IRC for Endo Product]]
! [[File:Chelatropic IRC gif.gif|thumb|x500px|500px|left|IRC for Chelatropic Product]]
|}

IRC (intrinsic reaction coordinate) show how reactions move in space during its reaction to form products. From the IRC animations, it can be seen that the formation of the new bonds differ to that of exercise 1. Here, in the exo and endo pathways, the formation of the 2 new bonds are asynchronous as one bond forms before the other. However, the bonds form synchronously in the chelatropic reaction leading to the symmetrical product.

The IRC reaction pathways also show a smaller activation barrier compared to that of exercise 1. This is because xylylene is highly unstable. Xylylene can exist with 4π electrons making it anti-aromatic, or either with 6π electrons an a diradical which is very unstable. On the flipside, the product formed is aromatic making the DA reaction extremely favourable. Naphthalene forces the diene to be rigid in its positions easing the overlap capabilities of the diene with the dienophile. This can be observed in the animation as naphthalene doesn't have to go through major rearrangements in order to form the products.

In the reaction, naphthalene initially has a C=C bond length of 1.35 Å and a C-C bond length averaging around 1.51 Å. This changes as the product is formed where all the carbon-carbon bonds on the 6 membered rings become 1.47 Å in length suggesting the formation of an aromatic 6-membered ring where the π electrons are delocalised throughout the ring. The change in bond length can also be seen with careful observation of the animations.

=== Thermochemistry ===

[[File:Cc5115 Energy Diagram Ex3.png]]

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +79.85
| -100.95
|-
| Exo
| +83.82
| -101.59
|-
| Chelatropic
| +102.16
| -157.93
|}

Significantly resembling to exercise 2, exercise 3 features the endo pathway being kinetically favoured as its activation energy has the least energy compared to the other pathway. Again, this is due to the overlap between the oxygen p-orbitals overlapping with the π-orbitals of the xylylene ring. However, the difference in activation and reaction energies between the exo and endo pathways do not differ that much due to the SOI not contributing significantly in the TS and there are little steric difference between the two products. For the chelatropic product, there is a hugh drop in reaction energy. Observing the product, the large sulfur atom forming a 5-membered ring decreases the ring-strain making the product relatively stable compared to the products from the DA reaction.

=== Cyclisation at the other reaction site ===

{| class="wikitable"
! [[File:Cc5115 IRC exo reaction site b.gif|thumb|x500px|500px|left|IRC for Exo Product at reaction site B]]
! [[File:Cc5115 IRC endo reaction site b.gif|thumb|x500px|500px|left|IRC for Endo Product at reaction site B]]
|}

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +110.06
| -14.33
|-
| Exo
| +117.90
| -18.78
|}

For this exercise, the Diels-Alder reaction can also take place at the other reaction site as illustrated in the animations.

== Conclusion ==

Gaussian was used to calculate the geometries of the transition states using the PM6 and the B3LYP methods. The TS was validated by a correct imaginary frequency from frequency calculations as well as the correct pathways along the reaction coordinate from IRC.

File:Cc5115 Energy Diagram Ex3.png

2018-02-14T10:53:13Z

Cc5115:

Rep:Mod:cc5115TS

2018-02-14T10:44:14Z

Cc5115: /* Thermochemistry */

= Y3C Transition states and Reactivity =

== Introduction ==

This section aims to illustrate the 3 different computational techniques that can be utilised in order to analyse the transition state (TS) of a reaction. The TS is the state which has the highest energy along a reaction coordinate, as a result it is the least stable state. In the reaction, the reactants needs to have a certain amount of energy in order to surpass the activation barrier, also known as the transition state energy, and reach the product state. This computational lab allows for calculations leading to the location of the TS. The structure of the TS is crucial in determining the mechanism of a reaction.

A potential energy surface (PES) has a 3N-6 dimension, which coincides to the degrees of freedom that the molecule has, where N is the number of atoms that the molecule possesses. In a 3-D PES, the saddle point (also called the TS), is a local mixami amidst 2 minima, and can be sometimes identified through secondary derivatives as it would be negative in one direction and positive in all other directions.

There are 3 calculation methods available in order to determine the structure of the TS.

1. The first and fastest method requires only one step where a guessed structure of the TS is optimised to give an optimised TS. This means that one will need of the TS to quite an extent, furthermore this method is rather unreliable as there is a high chance that the guessed TS is incorrectly drawn.

2. The second method works from a pre-frozen guess structure of the TS where the reacting termini of the reactants are frozen in space before the remaining structure is optimised to a minima. After that, the molecules are optimised as a transition state. This allows for a more reliable representation of the TS. This method is sufficient for Exercise 1.

3. The third method is the longest and most reliable method. Here, one starts by either optimising from the reactants or the products to a minima. For the reactant case, each reactants are optimised to a minima, arranged to resemble the TS and the reacting termini are frozen and the rest of the method 2 is repeated. A similar case occurs with the product; when the product is optimised to a minima, the bonds formed in the reactions are removed, the 2 fragments are arranged to resemble the TS and the reacting termini are frozen and method 2 was used once more. This method allows for the most reliable representation of the TS and is used for Exercise 2 & 3.

In this computational lab, two methods of calculation were used on Gaussian in order to find the TS. During the optimisation, the position of the molecule is decided as it is built in Gaussian. The time-independent Schrödinger equation was solved whilst utilising the Born-Oppenheimer approximation in order to find the energy and the wavefunction φ which represents the electronic states for the fixed nuclear positions and is dependent on on frozen nuclei positions. This is also known as the self-consistent field method (SCF). The two methods employed are the semi-empirical method PM6, which is usually performed first and sometimes followed by the Density Functional Theory (DFT) method B3LYP. The semi-empirical method PM6, although based on the Hartree-Fock formalism, this method uses many approximations based on experimental data in order to solve the Schrodinger equations. This method is usually fast and reliable, but can be easily countered if the environment of the molecule that is being computed is not similar enough to the approximated parameters of this method. The other method is B3LYP, a hydrid functional which utilises the DFT in order to calculate the majority of the Hamiltonian while a small portion still utilises the Hartree-Fock theory to calculate the exchange integral term. B3LYP stands for Becke, 3-parameter, Lee-Yang-Parr and uses a 6-31G basis set as the electronic wavefunction in order to produce more accurate results at the cost of increased calculation time.

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

[[File:Ex1 general.png|thumb|x700px|700px|centre|Figure 1: Formation of Cyclohaxadiene]]

Also known as the Diels-Alder reaction, this exercise investigates the well-known [4+2] cycloaddition between a conjugated diene (butadiene) and a dienophile (ethylene). The electrophilic reaction involves 4 pi-electrons from the diene and 2 pi-electrons from the alkene, and is a popular method to form regio- and stereochemically controlled 6-membered rings.

Method 2 was used to compute the transition state (TS) for this exercise. All steps are optimised to the PM6 level. First, the reactants are optimised to a minimum. The carbons at the reacting termini were then frozen at around 2.20 Å before optimised to a minimum to give a frozen-guess TS. Then finally, the molecule was optimised as a TS and an IRC was performed in order to confirm and locate the transition state.

=== Analysis of the Molecular Orbitals (MO) ===

The Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) for the reactants and the TS are shown below and its energies were recorded in order to produce the MO diagram as shown in figure 2.

{| class="wikitable"
! Ethene - HOMO
! Ethene - LUMO
! Butadiene - HOMO
! Butadiene - LUMO
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Cc5115 exer1finalMO.png|thumb|x800px|800px|left|Figure 2: MO Diagram for the formation of Transition State of the Diels-Alder Reaction]]

The symmetric TS HOMO and LUMO are formed through the interactions between the HOMO of ethylene and the LUMO of butadiene, both of which are symmetric. On the other hand, the LUMO of ethylene and the HOMO of butadiene, both of which are asymmetric, interacts to give an asymmetric HOMO-1 and LUMO+1. What can be concluded about the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed, and that the reaction is forbidden when the symmetry of the molecular orbitals aren't the same. The orbital overlap integral, S<sub>AB</sub>, is a quantitative measure of orbital overlap of two different atoms. Orbitals of the same symmetry will lead to constructive overlap and gives a non-zero value while orbitals of different symmetry will lead to destructive overlap and an orbital overlap integral of zero. Thus the overlap integral are:

- Non-zero for symmetric-symmetric interaction

- Non-zero for asymmetric-asymmetric interaction

- Zero for symmetric-asymmetric interaction

As observed in the MO diagram, the energy gap between the HOMO and LUMO for butadiene is smaller that those for ethylene due to butadiene being more electron rich than ethylene. Furthermore, in a normal MO diagram, the bonding MO formed should have a lower energy compared to both atomic orbitals (AO) whilst the anti-bonding MO formed should have a higher energy than both AOs. The reason why figure 3 goes against the tide is because the MOs formed corresponds to the transition state where the electrons are very delocalised within the chemical environment of the molecule.

==== LOG Files ====

[[:File:Cc5115_ETHENE_MO.LOG]]

[[:File:Cc5115_BUTADIENE_MO.LOG]]

[[:File:Cc5115_OPT_MO.LOG]]

=== Analysis of the C-C bond lengths ===

{| class="wikitable"
! Bond Lengths (Å)
! C1-C2
! C2-C3
! C3-C4
! C4-C5
! C5-C6
! C6-C1
|-
| Ethylene
|
|
|
|
| 1.36
|
|-
| Butadiene
| 1.36
| 1.54
| 1.36
|
|
|
|-
| Transition State
| 1.38
| 1.41
| 1.38
| 2.11
| 1.38
| 2.12
|-
| Cyclohexadiene
| 1.49
| 1.33
| 1.49
| 1.54
| 1.54
| 1.54
|}

The numbering of the carbon bonds are according to the labels on figure 1. The typical C-C bond lengths are as follows:

{| class="wikitable"
! Bond Type
! Bond Length (Å)
|-
| sp<sup>3</sup>-sp<sup>3</sup> C-C bond
| 1.54
|-
| sp<sup>3</sup>-sp<sup>2</sup> C-C bond
| 1.50
|-
| sp<sup>2</sup>-sp<sup>2</sup> C-C bond
| 1.47
|-
| sp<sup>2</sup>-sp<sup>2</sup> C=C bond
| 1.34
|}

When the reaction proceeds to the transition state, the sp<sup>2</sup>-sp<sup>2</sup> C5-C6 bond (originally ethylene) becomes longer as the carbons starts to change from sp<sup>2</sup> hybridised to sp<sup>3</sup> hybridised.
This trait is also apparent with C1-C2 and C3-C4 bonds where it once was the double bonds on butadiene, however, the increase in length of these bonds is less than that of C5-C6 due to the formation of a new double bond between C2 and C3, thus these carbons still remain sp<sup>2</sup> hybridised. This also leads to the next observation, where the C2-C3 bond decreases in length as it moves from the reactants to the transition state then the product, cyclohexadiene. This is because it is changing from a sp<sup>3</sup>-sp<sup>3</sup> C-C bond to a sp<sup>2</sup>-sp<sup>2</sup> C=C bond where the increase in s character shortens the bond lengths. This reaction also leads to the formation of 2 new bonds, namely C4-C5 and C6-C1. The Van der Waals radius of a carbon atom is 1.7 Å, and so the distance between 2 carbon atoms should be 3.4 Å, which is relatively longer than the bonds C4-C5 and C6-C1 which has a length of 2.11 and 2.12 Å respectively. This shows that the bonds are already partially formed in the transition state and they are beginning to interact together. This bond then settled at 1.54 Å in the product which matches with the typical bond length for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond.

=== Analysis of the vibrations ===

The animation for the first vibration is shown below. As observed, the formation of the 2 new bonds are synchronous as the reacting termini of butadiene and ethylene approaches each other at the same rate.

{| class="wikitable"
! <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 2;rotate x -20; </script>
<uploadedFileContents>Cc5115 OPT MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| The vibrations
|}

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

[[File:Cc5115 Exercise 2 generl.png|thumb|x700px|700px|centre|Figure 3: Reaction Scheme]]

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via either the endo or exo pathways to form 2 products with different stereochemistry. Method 3 was employed in order to compute the TS for this exercise. This time, the structures were further optimised with B3LYP/6-31G method and the results are shown and discussed below.

=== Analysis of Molecular Orbitals ===

[[File:Cc5115 Endo MO Exercise 2.png|thumb|x500px|500px|left|Figure 4: MO Diagram for the Endo TS]]

[[File:Cc5115 Exo MO Exercise 2.png|thumb|x500px|500px|right|Figure 5: MO Diagram for the Exo TS]]

There are two types of Diels-Alder (DA) reactions: one is with a normal electron demand where the dienophile is electron deficient and the diene is electron rich, and the other is with an inverse electron demand where the dienophile is electron rich and the diene is electron deficient.

For a normal electron demand DA reaction, the dienophile low-lying LUMO interacts with the diene HOMO which has a high energy. However, observing the energies of the reactants and the transition states, the MO diagram shows that this particular DA reaction has an inverse electron demand where the dienophile (1,3-dioxole) is electron rich (higher in energy) and the diene (cyclohexadiene) is electron poor (lower in energy). The interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene thus leads to the HOMO and LUMO of the transition state. Although opposing that of a normal electron demand DA, this reaction still follows the Woodword-Hoffman rule and is thermally allowed.

Similar to exercise 1, MOs of the same symmetry interact; the symmetrical dienophile HOMO and the diene LUMO interacts to give a symmetrical TS HOMO and LUMO, while the asymmetrical dienophile LUMO and diene HOMO gives the asymmetrical TS HOMO-1 and LUMO+1. It is also observable that the endo TS HOMO has a lower energy than the exo TS HOMO which suggests that the endo reaction is favoured. This will be discussed further in the Thermochemistry section of this exercise.

{| class="wikitable"
! ENDO TS - HOMO -1
! ENDO TS - HOMO
! ENDO TS - LUMO
! ENDO TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Log Files ====

[[File:Cc5115 ENDO B3.LOG]]

[[File:Cc5115 PLEASE WORK B3.LOG]]

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +149.70
| -77.52
|-
| Exo
| +157.52
| -73.92
|}

As discussed briefly in the introduction, the reactants need to pass the activation barrier (transition state) in order to reach to the products. The table regarding the reaction barriers and energies shows that the activation barrier for the endo reaction is less than that of the exo reaction, more-so confirming that the endo reaction is kinetically favoured. This links to the lower energy that the endo TS HOMO has compared to the exo TS. This observance can be explained by secondary orbital interation (SOI). The 2 non-bonding oxygen p-orbitals containing electron lone pairs can overlap with the LUMO of the diene through space thus stabilising the TS and consequentially lowering reaction barrier. However, the more negative reaction energy of the endo reaction can be explained with sterics; in the exo transition state, the steric interaction between the sp<sup>3</sup> bridging carbons and the rest of the 1,3-dioxole structure results in the exo product being higher in energy.

{| class="wikitable"
! Exo Secondary MO
! Endo Secondary MO
|-
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

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

=== IRC ===

{| class="wikitable"
! [[File:Cc5115 Exo IRC gif.gif|thumb|x500px|500px|left|IRC for Exo Product]]
! [[File:Cc5115 Endo IRC gif.gif|thumb|x500px|500px|left|IRC for Endo Product]]
! [[File:Chelatropic IRC gif.gif|thumb|x500px|500px|left|IRC for Chelatropic Product]]
|}

IRC (intrinsic reaction coordinate) show how reactions move in space during its reaction to form products. From the IRC animations, it can be seen that the formation of the new bonds differ to that of exercise 1. Here, in the exo and endo pathways, the formation of the 2 new bonds are asynchronous as one bond forms before the other. However, the bonds form synchronously in the chelatropic reaction leading to the symmetrical product.

The IRC reaction pathways also show a smaller activation barrier compared to that of exercise 1. This is because xylylene is highly unstable. Xylylene can exist with 4π electrons making it anti-aromatic, or either with 6π electrons an a diradical which is very unstable. On the flipside, the product formed is aromatic making the DA reaction extremely favourable. Naphthalene forces the diene to be rigid in its positions easing the overlap capabilities of the diene with the dienophile. This can be observed in the animation as naphthalene doesn't have to go through major rearrangements in order to form the products.

In the reaction, naphthalene initially has a C=C bond length of 1.35 Å and a C-C bond length averaging around 1.51 Å. This changes as the product is formed where all the carbon-carbon bonds on the 6 membered rings become 1.47 Å in length suggesting the formation of an aromatic 6-membered ring where the π electrons are delocalised throughout the ring. The change in bond length can also be seen with careful observation of the animations.

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +79.85
| -100.95
|-
| Exo
| +83.82
| -101.59
|-
| Chelatropic
| +102.16
| -157.93
|}

Significantly resembling to exercise 2, exercise 3 features the endo pathway being kinetically favoured as its activation energy has the least energy compared to the other pathway. Again, this is due to the overlap between the oxygen p-orbitals overlapping with the π-orbitals of the xylylene ring. However, the difference in activation and reaction energies between the exo and endo pathways do not differ that much due to the SOI not contributing significantly in the TS and there are little steric difference between the two products. For the chelatropic product, there is a hugh drop in reaction energy. Observing the product, the large sulfur atom forming a 5-membered ring decreases the ring-strain making the product relatively stable compared to the products from the DA reaction.

=== Cyclisation at the other reaction site ===

{| class="wikitable"
! [[File:Cc5115 IRC exo reaction site b.gif|thumb|x500px|500px|left|IRC for Exo Product at reaction site B]]
! [[File:Cc5115 IRC endo reaction site b.gif|thumb|x500px|500px|left|IRC for Endo Product at reaction site B]]
|}

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +110.06
| -14.33
|-
| Exo
| +117.90
| -18.78
|}

For this exercise, the Diels-Alder reaction can also take place at the other reaction site as illustrated in the animations.

== Conclusion ==

Gaussian was used to calculate the geometries of the transition states using the PM6 and the B3LYP methods. The TS was validated by a correct imaginary frequency from frequency calculations as well as the correct pathways along the reaction coordinate from IRC.

Rep:Mod:cc5115TS

2018-02-14T10:43:38Z

Cc5115: /* Cyclisation at the other reaction site */

= Y3C Transition states and Reactivity =

== Introduction ==

This section aims to illustrate the 3 different computational techniques that can be utilised in order to analyse the transition state (TS) of a reaction. The TS is the state which has the highest energy along a reaction coordinate, as a result it is the least stable state. In the reaction, the reactants needs to have a certain amount of energy in order to surpass the activation barrier, also known as the transition state energy, and reach the product state. This computational lab allows for calculations leading to the location of the TS. The structure of the TS is crucial in determining the mechanism of a reaction.

A potential energy surface (PES) has a 3N-6 dimension, which coincides to the degrees of freedom that the molecule has, where N is the number of atoms that the molecule possesses. In a 3-D PES, the saddle point (also called the TS), is a local mixami amidst 2 minima, and can be sometimes identified through secondary derivatives as it would be negative in one direction and positive in all other directions.

There are 3 calculation methods available in order to determine the structure of the TS.

1. The first and fastest method requires only one step where a guessed structure of the TS is optimised to give an optimised TS. This means that one will need of the TS to quite an extent, furthermore this method is rather unreliable as there is a high chance that the guessed TS is incorrectly drawn.

2. The second method works from a pre-frozen guess structure of the TS where the reacting termini of the reactants are frozen in space before the remaining structure is optimised to a minima. After that, the molecules are optimised as a transition state. This allows for a more reliable representation of the TS. This method is sufficient for Exercise 1.

3. The third method is the longest and most reliable method. Here, one starts by either optimising from the reactants or the products to a minima. For the reactant case, each reactants are optimised to a minima, arranged to resemble the TS and the reacting termini are frozen and the rest of the method 2 is repeated. A similar case occurs with the product; when the product is optimised to a minima, the bonds formed in the reactions are removed, the 2 fragments are arranged to resemble the TS and the reacting termini are frozen and method 2 was used once more. This method allows for the most reliable representation of the TS and is used for Exercise 2 & 3.

In this computational lab, two methods of calculation were used on Gaussian in order to find the TS. During the optimisation, the position of the molecule is decided as it is built in Gaussian. The time-independent Schrödinger equation was solved whilst utilising the Born-Oppenheimer approximation in order to find the energy and the wavefunction φ which represents the electronic states for the fixed nuclear positions and is dependent on on frozen nuclei positions. This is also known as the self-consistent field method (SCF). The two methods employed are the semi-empirical method PM6, which is usually performed first and sometimes followed by the Density Functional Theory (DFT) method B3LYP. The semi-empirical method PM6, although based on the Hartree-Fock formalism, this method uses many approximations based on experimental data in order to solve the Schrodinger equations. This method is usually fast and reliable, but can be easily countered if the environment of the molecule that is being computed is not similar enough to the approximated parameters of this method. The other method is B3LYP, a hydrid functional which utilises the DFT in order to calculate the majority of the Hamiltonian while a small portion still utilises the Hartree-Fock theory to calculate the exchange integral term. B3LYP stands for Becke, 3-parameter, Lee-Yang-Parr and uses a 6-31G basis set as the electronic wavefunction in order to produce more accurate results at the cost of increased calculation time.

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

[[File:Ex1 general.png|thumb|x700px|700px|centre|Figure 1: Formation of Cyclohaxadiene]]

Also known as the Diels-Alder reaction, this exercise investigates the well-known [4+2] cycloaddition between a conjugated diene (butadiene) and a dienophile (ethylene). The electrophilic reaction involves 4 pi-electrons from the diene and 2 pi-electrons from the alkene, and is a popular method to form regio- and stereochemically controlled 6-membered rings.

Method 2 was used to compute the transition state (TS) for this exercise. All steps are optimised to the PM6 level. First, the reactants are optimised to a minimum. The carbons at the reacting termini were then frozen at around 2.20 Å before optimised to a minimum to give a frozen-guess TS. Then finally, the molecule was optimised as a TS and an IRC was performed in order to confirm and locate the transition state.

=== Analysis of the Molecular Orbitals (MO) ===

The Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) for the reactants and the TS are shown below and its energies were recorded in order to produce the MO diagram as shown in figure 2.

{| class="wikitable"
! Ethene - HOMO
! Ethene - LUMO
! Butadiene - HOMO
! Butadiene - LUMO
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Cc5115 exer1finalMO.png|thumb|x800px|800px|left|Figure 2: MO Diagram for the formation of Transition State of the Diels-Alder Reaction]]

The symmetric TS HOMO and LUMO are formed through the interactions between the HOMO of ethylene and the LUMO of butadiene, both of which are symmetric. On the other hand, the LUMO of ethylene and the HOMO of butadiene, both of which are asymmetric, interacts to give an asymmetric HOMO-1 and LUMO+1. What can be concluded about the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed, and that the reaction is forbidden when the symmetry of the molecular orbitals aren't the same. The orbital overlap integral, S<sub>AB</sub>, is a quantitative measure of orbital overlap of two different atoms. Orbitals of the same symmetry will lead to constructive overlap and gives a non-zero value while orbitals of different symmetry will lead to destructive overlap and an orbital overlap integral of zero. Thus the overlap integral are:

- Non-zero for symmetric-symmetric interaction

- Non-zero for asymmetric-asymmetric interaction

- Zero for symmetric-asymmetric interaction

As observed in the MO diagram, the energy gap between the HOMO and LUMO for butadiene is smaller that those for ethylene due to butadiene being more electron rich than ethylene. Furthermore, in a normal MO diagram, the bonding MO formed should have a lower energy compared to both atomic orbitals (AO) whilst the anti-bonding MO formed should have a higher energy than both AOs. The reason why figure 3 goes against the tide is because the MOs formed corresponds to the transition state where the electrons are very delocalised within the chemical environment of the molecule.

==== LOG Files ====

[[:File:Cc5115_ETHENE_MO.LOG]]

[[:File:Cc5115_BUTADIENE_MO.LOG]]

[[:File:Cc5115_OPT_MO.LOG]]

=== Analysis of the C-C bond lengths ===

{| class="wikitable"
! Bond Lengths (Å)
! C1-C2
! C2-C3
! C3-C4
! C4-C5
! C5-C6
! C6-C1
|-
| Ethylene
|
|
|
|
| 1.36
|
|-
| Butadiene
| 1.36
| 1.54
| 1.36
|
|
|
|-
| Transition State
| 1.38
| 1.41
| 1.38
| 2.11
| 1.38
| 2.12
|-
| Cyclohexadiene
| 1.49
| 1.33
| 1.49
| 1.54
| 1.54
| 1.54
|}

The numbering of the carbon bonds are according to the labels on figure 1. The typical C-C bond lengths are as follows:

{| class="wikitable"
! Bond Type
! Bond Length (Å)
|-
| sp<sup>3</sup>-sp<sup>3</sup> C-C bond
| 1.54
|-
| sp<sup>3</sup>-sp<sup>2</sup> C-C bond
| 1.50
|-
| sp<sup>2</sup>-sp<sup>2</sup> C-C bond
| 1.47
|-
| sp<sup>2</sup>-sp<sup>2</sup> C=C bond
| 1.34
|}

When the reaction proceeds to the transition state, the sp<sup>2</sup>-sp<sup>2</sup> C5-C6 bond (originally ethylene) becomes longer as the carbons starts to change from sp<sup>2</sup> hybridised to sp<sup>3</sup> hybridised.
This trait is also apparent with C1-C2 and C3-C4 bonds where it once was the double bonds on butadiene, however, the increase in length of these bonds is less than that of C5-C6 due to the formation of a new double bond between C2 and C3, thus these carbons still remain sp<sup>2</sup> hybridised. This also leads to the next observation, where the C2-C3 bond decreases in length as it moves from the reactants to the transition state then the product, cyclohexadiene. This is because it is changing from a sp<sup>3</sup>-sp<sup>3</sup> C-C bond to a sp<sup>2</sup>-sp<sup>2</sup> C=C bond where the increase in s character shortens the bond lengths. This reaction also leads to the formation of 2 new bonds, namely C4-C5 and C6-C1. The Van der Waals radius of a carbon atom is 1.7 Å, and so the distance between 2 carbon atoms should be 3.4 Å, which is relatively longer than the bonds C4-C5 and C6-C1 which has a length of 2.11 and 2.12 Å respectively. This shows that the bonds are already partially formed in the transition state and they are beginning to interact together. This bond then settled at 1.54 Å in the product which matches with the typical bond length for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond.

=== Analysis of the vibrations ===

The animation for the first vibration is shown below. As observed, the formation of the 2 new bonds are synchronous as the reacting termini of butadiene and ethylene approaches each other at the same rate.

{| class="wikitable"
! <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 2;rotate x -20; </script>
<uploadedFileContents>Cc5115 OPT MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| The vibrations
|}

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

[[File:Cc5115 Exercise 2 generl.png|thumb|x700px|700px|centre|Figure 3: Reaction Scheme]]

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via either the endo or exo pathways to form 2 products with different stereochemistry. Method 3 was employed in order to compute the TS for this exercise. This time, the structures were further optimised with B3LYP/6-31G method and the results are shown and discussed below.

=== Analysis of Molecular Orbitals ===

[[File:Cc5115 Endo MO Exercise 2.png|thumb|x500px|500px|left|Figure 4: MO Diagram for the Endo TS]]

[[File:Cc5115 Exo MO Exercise 2.png|thumb|x500px|500px|right|Figure 5: MO Diagram for the Exo TS]]

There are two types of Diels-Alder (DA) reactions: one is with a normal electron demand where the dienophile is electron deficient and the diene is electron rich, and the other is with an inverse electron demand where the dienophile is electron rich and the diene is electron deficient.

For a normal electron demand DA reaction, the dienophile low-lying LUMO interacts with the diene HOMO which has a high energy. However, observing the energies of the reactants and the transition states, the MO diagram shows that this particular DA reaction has an inverse electron demand where the dienophile (1,3-dioxole) is electron rich (higher in energy) and the diene (cyclohexadiene) is electron poor (lower in energy). The interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene thus leads to the HOMO and LUMO of the transition state. Although opposing that of a normal electron demand DA, this reaction still follows the Woodword-Hoffman rule and is thermally allowed.

Similar to exercise 1, MOs of the same symmetry interact; the symmetrical dienophile HOMO and the diene LUMO interacts to give a symmetrical TS HOMO and LUMO, while the asymmetrical dienophile LUMO and diene HOMO gives the asymmetrical TS HOMO-1 and LUMO+1. It is also observable that the endo TS HOMO has a lower energy than the exo TS HOMO which suggests that the endo reaction is favoured. This will be discussed further in the Thermochemistry section of this exercise.

{| class="wikitable"
! ENDO TS - HOMO -1
! ENDO TS - HOMO
! ENDO TS - LUMO
! ENDO TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Log Files ====

[[File:Cc5115 ENDO B3.LOG]]

[[File:Cc5115 PLEASE WORK B3.LOG]]

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +149.70
| -77.52
|-
| Exo
| +157.52
| -73.92
|}

As discussed briefly in the introduction, the reactants need to pass the activation barrier (transition state) in order to reach to the products. The table regarding the reaction barriers and energies shows that the activation barrier for the endo reaction is less than that of the exo reaction, more-so confirming that the endo reaction is kinetically favoured. This links to the lower energy that the endo TS HOMO has compared to the exo TS. This observance can be explained by secondary orbital interation (SOI). The 2 non-bonding oxygen p-orbitals containing electron lone pairs can overlap with the LUMO of the diene through space thus stabilising the TS and consequentially lowering reaction barrier. However, the more negative reaction energy of the endo reaction can be explained with sterics; in the exo transition state, the steric interaction between the sp<sup>3</sup> bridging carbons and the rest of the 1,3-dioxole structure results in the exo product being higher in energy.

{| class="wikitable"
! Exo Secondary MO
! Endo Secondary MO
|-
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

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

=== IRC ===

{| class="wikitable"
! [[File:Cc5115 Exo IRC gif.gif|thumb|x500px|500px|left|IRC for Exo Product]]
! [[File:Cc5115 Endo IRC gif.gif|thumb|x500px|500px|left|IRC for Endo Product]]
! [[File:Chelatropic IRC gif.gif|thumb|x500px|500px|left|IRC for Chelatropic Product]]
|}

IRC (intrinsic reaction coordinate) show how reactions move in space during its reaction to form products. From the IRC animations, it can be seen that the formation of the new bonds differ to that of exercise 1. Here, in the exo and endo pathways, the formation of the 2 new bonds are asynchronous as one bond forms before the other. However, the bonds form synchronously in the chelatropic reaction leading to the symmetrical product.

The IRC reaction pathways also show a smaller activation barrier compared to that of exercise 1. This is because xylylene is highly unstable. Xylylene can exist with 4π electrons making it anti-aromatic, or either with 6π electrons an a diradical which is very unstable. On the flipside, the product formed is aromatic making the DA reaction extremely favourable. Naphthalene forces the diene to be rigid in its positions easing the overlap capabilities of the diene with the dienophile. This can be observed in the animation as naphthalene doesn't have to go through major rearrangements in order to form the products.

In the reaction, naphthalene initially has a C=C bond length of 1.35 Å and a C-C bond length averaging around 1.51 Å. This changes as the product is formed where all the carbon-carbon bonds on the 6 membered rings become 1.47 Å in length suggesting the formation of an aromatic 6-membered ring where the π electrons are delocalised throughout the ring. The change in bond length can also be seen with careful observation of the animations.

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +79.85
|
|-
| Exo
| +83.82
|
|-
| Chelatropic
| +102.16
|
|}

Significantly resembling to exercise 2, exercise 3 features the endo pathway being kinetically favoured as its activation energy has the least energy compared to the other pathway. Again, this is due to the overlap between the oxygen p-orbitals overlapping with the π-orbitals of the xylylene ring. However, the difference in activation and reaction energies between the exo and endo pathways do not differ that much due to the SOI not contributing significantly in the TS and there are little steric difference between the two products. For the chelatropic product, there is a hugh drop in reaction energy. Observing the product, the large sulfur atom forming a 5-membered ring decreases the ring-strain making the product relatively stable compared to the products from the DA reaction.

=== Cyclisation at the other reaction site ===

{| class="wikitable"
! [[File:Cc5115 IRC exo reaction site b.gif|thumb|x500px|500px|left|IRC for Exo Product at reaction site B]]
! [[File:Cc5115 IRC endo reaction site b.gif|thumb|x500px|500px|left|IRC for Endo Product at reaction site B]]
|}

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +110.06
| -14.33
|-
| Exo
| +117.90
| -18.78
|}

For this exercise, the Diels-Alder reaction can also take place at the other reaction site as illustrated in the animations.

== Conclusion ==

Gaussian was used to calculate the geometries of the transition states using the PM6 and the B3LYP methods. The TS was validated by a correct imaginary frequency from frequency calculations as well as the correct pathways along the reaction coordinate from IRC.

Rep:Mod:cc5115TS

2018-02-14T10:42:09Z

Cc5115: /* Thermochemistry */

= Y3C Transition states and Reactivity =

== Introduction ==

This section aims to illustrate the 3 different computational techniques that can be utilised in order to analyse the transition state (TS) of a reaction. The TS is the state which has the highest energy along a reaction coordinate, as a result it is the least stable state. In the reaction, the reactants needs to have a certain amount of energy in order to surpass the activation barrier, also known as the transition state energy, and reach the product state. This computational lab allows for calculations leading to the location of the TS. The structure of the TS is crucial in determining the mechanism of a reaction.

A potential energy surface (PES) has a 3N-6 dimension, which coincides to the degrees of freedom that the molecule has, where N is the number of atoms that the molecule possesses. In a 3-D PES, the saddle point (also called the TS), is a local mixami amidst 2 minima, and can be sometimes identified through secondary derivatives as it would be negative in one direction and positive in all other directions.

There are 3 calculation methods available in order to determine the structure of the TS.

1. The first and fastest method requires only one step where a guessed structure of the TS is optimised to give an optimised TS. This means that one will need of the TS to quite an extent, furthermore this method is rather unreliable as there is a high chance that the guessed TS is incorrectly drawn.

2. The second method works from a pre-frozen guess structure of the TS where the reacting termini of the reactants are frozen in space before the remaining structure is optimised to a minima. After that, the molecules are optimised as a transition state. This allows for a more reliable representation of the TS. This method is sufficient for Exercise 1.

3. The third method is the longest and most reliable method. Here, one starts by either optimising from the reactants or the products to a minima. For the reactant case, each reactants are optimised to a minima, arranged to resemble the TS and the reacting termini are frozen and the rest of the method 2 is repeated. A similar case occurs with the product; when the product is optimised to a minima, the bonds formed in the reactions are removed, the 2 fragments are arranged to resemble the TS and the reacting termini are frozen and method 2 was used once more. This method allows for the most reliable representation of the TS and is used for Exercise 2 & 3.

In this computational lab, two methods of calculation were used on Gaussian in order to find the TS. During the optimisation, the position of the molecule is decided as it is built in Gaussian. The time-independent Schrödinger equation was solved whilst utilising the Born-Oppenheimer approximation in order to find the energy and the wavefunction φ which represents the electronic states for the fixed nuclear positions and is dependent on on frozen nuclei positions. This is also known as the self-consistent field method (SCF). The two methods employed are the semi-empirical method PM6, which is usually performed first and sometimes followed by the Density Functional Theory (DFT) method B3LYP. The semi-empirical method PM6, although based on the Hartree-Fock formalism, this method uses many approximations based on experimental data in order to solve the Schrodinger equations. This method is usually fast and reliable, but can be easily countered if the environment of the molecule that is being computed is not similar enough to the approximated parameters of this method. The other method is B3LYP, a hydrid functional which utilises the DFT in order to calculate the majority of the Hamiltonian while a small portion still utilises the Hartree-Fock theory to calculate the exchange integral term. B3LYP stands for Becke, 3-parameter, Lee-Yang-Parr and uses a 6-31G basis set as the electronic wavefunction in order to produce more accurate results at the cost of increased calculation time.

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

[[File:Ex1 general.png|thumb|x700px|700px|centre|Figure 1: Formation of Cyclohaxadiene]]

Also known as the Diels-Alder reaction, this exercise investigates the well-known [4+2] cycloaddition between a conjugated diene (butadiene) and a dienophile (ethylene). The electrophilic reaction involves 4 pi-electrons from the diene and 2 pi-electrons from the alkene, and is a popular method to form regio- and stereochemically controlled 6-membered rings.

Method 2 was used to compute the transition state (TS) for this exercise. All steps are optimised to the PM6 level. First, the reactants are optimised to a minimum. The carbons at the reacting termini were then frozen at around 2.20 Å before optimised to a minimum to give a frozen-guess TS. Then finally, the molecule was optimised as a TS and an IRC was performed in order to confirm and locate the transition state.

=== Analysis of the Molecular Orbitals (MO) ===

The Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) for the reactants and the TS are shown below and its energies were recorded in order to produce the MO diagram as shown in figure 2.

{| class="wikitable"
! Ethene - HOMO
! Ethene - LUMO
! Butadiene - HOMO
! Butadiene - LUMO
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Cc5115 exer1finalMO.png|thumb|x800px|800px|left|Figure 2: MO Diagram for the formation of Transition State of the Diels-Alder Reaction]]

The symmetric TS HOMO and LUMO are formed through the interactions between the HOMO of ethylene and the LUMO of butadiene, both of which are symmetric. On the other hand, the LUMO of ethylene and the HOMO of butadiene, both of which are asymmetric, interacts to give an asymmetric HOMO-1 and LUMO+1. What can be concluded about the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed, and that the reaction is forbidden when the symmetry of the molecular orbitals aren't the same. The orbital overlap integral, S<sub>AB</sub>, is a quantitative measure of orbital overlap of two different atoms. Orbitals of the same symmetry will lead to constructive overlap and gives a non-zero value while orbitals of different symmetry will lead to destructive overlap and an orbital overlap integral of zero. Thus the overlap integral are:

- Non-zero for symmetric-symmetric interaction

- Non-zero for asymmetric-asymmetric interaction

- Zero for symmetric-asymmetric interaction

As observed in the MO diagram, the energy gap between the HOMO and LUMO for butadiene is smaller that those for ethylene due to butadiene being more electron rich than ethylene. Furthermore, in a normal MO diagram, the bonding MO formed should have a lower energy compared to both atomic orbitals (AO) whilst the anti-bonding MO formed should have a higher energy than both AOs. The reason why figure 3 goes against the tide is because the MOs formed corresponds to the transition state where the electrons are very delocalised within the chemical environment of the molecule.

==== LOG Files ====

[[:File:Cc5115_ETHENE_MO.LOG]]

[[:File:Cc5115_BUTADIENE_MO.LOG]]

[[:File:Cc5115_OPT_MO.LOG]]

=== Analysis of the C-C bond lengths ===

{| class="wikitable"
! Bond Lengths (Å)
! C1-C2
! C2-C3
! C3-C4
! C4-C5
! C5-C6
! C6-C1
|-
| Ethylene
|
|
|
|
| 1.36
|
|-
| Butadiene
| 1.36
| 1.54
| 1.36
|
|
|
|-
| Transition State
| 1.38
| 1.41
| 1.38
| 2.11
| 1.38
| 2.12
|-
| Cyclohexadiene
| 1.49
| 1.33
| 1.49
| 1.54
| 1.54
| 1.54
|}

The numbering of the carbon bonds are according to the labels on figure 1. The typical C-C bond lengths are as follows:

{| class="wikitable"
! Bond Type
! Bond Length (Å)
|-
| sp<sup>3</sup>-sp<sup>3</sup> C-C bond
| 1.54
|-
| sp<sup>3</sup>-sp<sup>2</sup> C-C bond
| 1.50
|-
| sp<sup>2</sup>-sp<sup>2</sup> C-C bond
| 1.47
|-
| sp<sup>2</sup>-sp<sup>2</sup> C=C bond
| 1.34
|}

When the reaction proceeds to the transition state, the sp<sup>2</sup>-sp<sup>2</sup> C5-C6 bond (originally ethylene) becomes longer as the carbons starts to change from sp<sup>2</sup> hybridised to sp<sup>3</sup> hybridised.
This trait is also apparent with C1-C2 and C3-C4 bonds where it once was the double bonds on butadiene, however, the increase in length of these bonds is less than that of C5-C6 due to the formation of a new double bond between C2 and C3, thus these carbons still remain sp<sup>2</sup> hybridised. This also leads to the next observation, where the C2-C3 bond decreases in length as it moves from the reactants to the transition state then the product, cyclohexadiene. This is because it is changing from a sp<sup>3</sup>-sp<sup>3</sup> C-C bond to a sp<sup>2</sup>-sp<sup>2</sup> C=C bond where the increase in s character shortens the bond lengths. This reaction also leads to the formation of 2 new bonds, namely C4-C5 and C6-C1. The Van der Waals radius of a carbon atom is 1.7 Å, and so the distance between 2 carbon atoms should be 3.4 Å, which is relatively longer than the bonds C4-C5 and C6-C1 which has a length of 2.11 and 2.12 Å respectively. This shows that the bonds are already partially formed in the transition state and they are beginning to interact together. This bond then settled at 1.54 Å in the product which matches with the typical bond length for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond.

=== Analysis of the vibrations ===

The animation for the first vibration is shown below. As observed, the formation of the 2 new bonds are synchronous as the reacting termini of butadiene and ethylene approaches each other at the same rate.

{| class="wikitable"
! <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 2;rotate x -20; </script>
<uploadedFileContents>Cc5115 OPT MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| The vibrations
|}

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

[[File:Cc5115 Exercise 2 generl.png|thumb|x700px|700px|centre|Figure 3: Reaction Scheme]]

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via either the endo or exo pathways to form 2 products with different stereochemistry. Method 3 was employed in order to compute the TS for this exercise. This time, the structures were further optimised with B3LYP/6-31G method and the results are shown and discussed below.

=== Analysis of Molecular Orbitals ===

[[File:Cc5115 Endo MO Exercise 2.png|thumb|x500px|500px|left|Figure 4: MO Diagram for the Endo TS]]

[[File:Cc5115 Exo MO Exercise 2.png|thumb|x500px|500px|right|Figure 5: MO Diagram for the Exo TS]]

There are two types of Diels-Alder (DA) reactions: one is with a normal electron demand where the dienophile is electron deficient and the diene is electron rich, and the other is with an inverse electron demand where the dienophile is electron rich and the diene is electron deficient.

For a normal electron demand DA reaction, the dienophile low-lying LUMO interacts with the diene HOMO which has a high energy. However, observing the energies of the reactants and the transition states, the MO diagram shows that this particular DA reaction has an inverse electron demand where the dienophile (1,3-dioxole) is electron rich (higher in energy) and the diene (cyclohexadiene) is electron poor (lower in energy). The interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene thus leads to the HOMO and LUMO of the transition state. Although opposing that of a normal electron demand DA, this reaction still follows the Woodword-Hoffman rule and is thermally allowed.

Similar to exercise 1, MOs of the same symmetry interact; the symmetrical dienophile HOMO and the diene LUMO interacts to give a symmetrical TS HOMO and LUMO, while the asymmetrical dienophile LUMO and diene HOMO gives the asymmetrical TS HOMO-1 and LUMO+1. It is also observable that the endo TS HOMO has a lower energy than the exo TS HOMO which suggests that the endo reaction is favoured. This will be discussed further in the Thermochemistry section of this exercise.

{| class="wikitable"
! ENDO TS - HOMO -1
! ENDO TS - HOMO
! ENDO TS - LUMO
! ENDO TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Log Files ====

[[File:Cc5115 ENDO B3.LOG]]

[[File:Cc5115 PLEASE WORK B3.LOG]]

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +149.70
| -77.52
|-
| Exo
| +157.52
| -73.92
|}

As discussed briefly in the introduction, the reactants need to pass the activation barrier (transition state) in order to reach to the products. The table regarding the reaction barriers and energies shows that the activation barrier for the endo reaction is less than that of the exo reaction, more-so confirming that the endo reaction is kinetically favoured. This links to the lower energy that the endo TS HOMO has compared to the exo TS. This observance can be explained by secondary orbital interation (SOI). The 2 non-bonding oxygen p-orbitals containing electron lone pairs can overlap with the LUMO of the diene through space thus stabilising the TS and consequentially lowering reaction barrier. However, the more negative reaction energy of the endo reaction can be explained with sterics; in the exo transition state, the steric interaction between the sp<sup>3</sup> bridging carbons and the rest of the 1,3-dioxole structure results in the exo product being higher in energy.

{| class="wikitable"
! Exo Secondary MO
! Endo Secondary MO
|-
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

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

=== IRC ===

{| class="wikitable"
! [[File:Cc5115 Exo IRC gif.gif|thumb|x500px|500px|left|IRC for Exo Product]]
! [[File:Cc5115 Endo IRC gif.gif|thumb|x500px|500px|left|IRC for Endo Product]]
! [[File:Chelatropic IRC gif.gif|thumb|x500px|500px|left|IRC for Chelatropic Product]]
|}

IRC (intrinsic reaction coordinate) show how reactions move in space during its reaction to form products. From the IRC animations, it can be seen that the formation of the new bonds differ to that of exercise 1. Here, in the exo and endo pathways, the formation of the 2 new bonds are asynchronous as one bond forms before the other. However, the bonds form synchronously in the chelatropic reaction leading to the symmetrical product.

The IRC reaction pathways also show a smaller activation barrier compared to that of exercise 1. This is because xylylene is highly unstable. Xylylene can exist with 4π electrons making it anti-aromatic, or either with 6π electrons an a diradical which is very unstable. On the flipside, the product formed is aromatic making the DA reaction extremely favourable. Naphthalene forces the diene to be rigid in its positions easing the overlap capabilities of the diene with the dienophile. This can be observed in the animation as naphthalene doesn't have to go through major rearrangements in order to form the products.

In the reaction, naphthalene initially has a C=C bond length of 1.35 Å and a C-C bond length averaging around 1.51 Å. This changes as the product is formed where all the carbon-carbon bonds on the 6 membered rings become 1.47 Å in length suggesting the formation of an aromatic 6-membered ring where the π electrons are delocalised throughout the ring. The change in bond length can also be seen with careful observation of the animations.

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +79.85
|
|-
| Exo
| +83.82
|
|-
| Chelatropic
| +102.16
|
|}

Significantly resembling to exercise 2, exercise 3 features the endo pathway being kinetically favoured as its activation energy has the least energy compared to the other pathway. Again, this is due to the overlap between the oxygen p-orbitals overlapping with the π-orbitals of the xylylene ring. However, the difference in activation and reaction energies between the exo and endo pathways do not differ that much due to the SOI not contributing significantly in the TS and there are little steric difference between the two products. For the chelatropic product, there is a hugh drop in reaction energy. Observing the product, the large sulfur atom forming a 5-membered ring decreases the ring-strain making the product relatively stable compared to the products from the DA reaction.

=== Cyclisation at the other reaction site ===

{| class="wikitable"
! [[File:Cc5115 IRC exo reaction site b.gif|thumb|x500px|500px|left|IRC for Exo Product at reaction site B]]
! [[File:Cc5115 IRC endo reaction site b.gif|thumb|x500px|500px|left|IRC for Endo Product at reaction site B]]
|}

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +110.06
|
|-
| Exo
| +117.90
|
|}

For this exercise, the Diels-Alder reaction can also take place at the other reaction site as illustrated in the animations.

== Conclusion ==

Gaussian was used to calculate the geometries of the transition states using the PM6 and the B3LYP methods. The TS was validated by a correct imaginary frequency from frequency calculations as well as the correct pathways along the reaction coordinate from IRC.

Rep:Mod:cc5115TS

2018-02-14T10:29:17Z

Cc5115: /* Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole */

= Y3C Transition states and Reactivity =

== Introduction ==

This section aims to illustrate the 3 different computational techniques that can be utilised in order to analyse the transition state (TS) of a reaction. The TS is the state which has the highest energy along a reaction coordinate, as a result it is the least stable state. In the reaction, the reactants needs to have a certain amount of energy in order to surpass the activation barrier, also known as the transition state energy, and reach the product state. This computational lab allows for calculations leading to the location of the TS. The structure of the TS is crucial in determining the mechanism of a reaction.

A potential energy surface (PES) has a 3N-6 dimension, which coincides to the degrees of freedom that the molecule has, where N is the number of atoms that the molecule possesses. In a 3-D PES, the saddle point (also called the TS), is a local mixami amidst 2 minima, and can be sometimes identified through secondary derivatives as it would be negative in one direction and positive in all other directions.

There are 3 calculation methods available in order to determine the structure of the TS.

1. The first and fastest method requires only one step where a guessed structure of the TS is optimised to give an optimised TS. This means that one will need of the TS to quite an extent, furthermore this method is rather unreliable as there is a high chance that the guessed TS is incorrectly drawn.

2. The second method works from a pre-frozen guess structure of the TS where the reacting termini of the reactants are frozen in space before the remaining structure is optimised to a minima. After that, the molecules are optimised as a transition state. This allows for a more reliable representation of the TS. This method is sufficient for Exercise 1.

3. The third method is the longest and most reliable method. Here, one starts by either optimising from the reactants or the products to a minima. For the reactant case, each reactants are optimised to a minima, arranged to resemble the TS and the reacting termini are frozen and the rest of the method 2 is repeated. A similar case occurs with the product; when the product is optimised to a minima, the bonds formed in the reactions are removed, the 2 fragments are arranged to resemble the TS and the reacting termini are frozen and method 2 was used once more. This method allows for the most reliable representation of the TS and is used for Exercise 2 & 3.

In this computational lab, two methods of calculation were used on Gaussian in order to find the TS. During the optimisation, the position of the molecule is decided as it is built in Gaussian. The time-independent Schrödinger equation was solved whilst utilising the Born-Oppenheimer approximation in order to find the energy and the wavefunction φ which represents the electronic states for the fixed nuclear positions and is dependent on on frozen nuclei positions. This is also known as the self-consistent field method (SCF). The two methods employed are the semi-empirical method PM6, which is usually performed first and sometimes followed by the Density Functional Theory (DFT) method B3LYP. The semi-empirical method PM6, although based on the Hartree-Fock formalism, this method uses many approximations based on experimental data in order to solve the Schrodinger equations. This method is usually fast and reliable, but can be easily countered if the environment of the molecule that is being computed is not similar enough to the approximated parameters of this method. The other method is B3LYP, a hydrid functional which utilises the DFT in order to calculate the majority of the Hamiltonian while a small portion still utilises the Hartree-Fock theory to calculate the exchange integral term. B3LYP stands for Becke, 3-parameter, Lee-Yang-Parr and uses a 6-31G basis set as the electronic wavefunction in order to produce more accurate results at the cost of increased calculation time.

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

[[File:Ex1 general.png|thumb|x700px|700px|centre|Figure 1: Formation of Cyclohaxadiene]]

Also known as the Diels-Alder reaction, this exercise investigates the well-known [4+2] cycloaddition between a conjugated diene (butadiene) and a dienophile (ethylene). The electrophilic reaction involves 4 pi-electrons from the diene and 2 pi-electrons from the alkene, and is a popular method to form regio- and stereochemically controlled 6-membered rings.

Method 2 was used to compute the transition state (TS) for this exercise. All steps are optimised to the PM6 level. First, the reactants are optimised to a minimum. The carbons at the reacting termini were then frozen at around 2.20 Å before optimised to a minimum to give a frozen-guess TS. Then finally, the molecule was optimised as a TS and an IRC was performed in order to confirm and locate the transition state.

=== Analysis of the Molecular Orbitals (MO) ===

The Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) for the reactants and the TS are shown below and its energies were recorded in order to produce the MO diagram as shown in figure 2.

{| class="wikitable"
! Ethene - HOMO
! Ethene - LUMO
! Butadiene - HOMO
! Butadiene - LUMO
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Cc5115 exer1finalMO.png|thumb|x800px|800px|left|Figure 2: MO Diagram for the formation of Transition State of the Diels-Alder Reaction]]

The symmetric TS HOMO and LUMO are formed through the interactions between the HOMO of ethylene and the LUMO of butadiene, both of which are symmetric. On the other hand, the LUMO of ethylene and the HOMO of butadiene, both of which are asymmetric, interacts to give an asymmetric HOMO-1 and LUMO+1. What can be concluded about the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed, and that the reaction is forbidden when the symmetry of the molecular orbitals aren't the same. The orbital overlap integral, S<sub>AB</sub>, is a quantitative measure of orbital overlap of two different atoms. Orbitals of the same symmetry will lead to constructive overlap and gives a non-zero value while orbitals of different symmetry will lead to destructive overlap and an orbital overlap integral of zero. Thus the overlap integral are:

- Non-zero for symmetric-symmetric interaction

- Non-zero for asymmetric-asymmetric interaction

- Zero for symmetric-asymmetric interaction

As observed in the MO diagram, the energy gap between the HOMO and LUMO for butadiene is smaller that those for ethylene due to butadiene being more electron rich than ethylene. Furthermore, in a normal MO diagram, the bonding MO formed should have a lower energy compared to both atomic orbitals (AO) whilst the anti-bonding MO formed should have a higher energy than both AOs. The reason why figure 3 goes against the tide is because the MOs formed corresponds to the transition state where the electrons are very delocalised within the chemical environment of the molecule.

==== LOG Files ====

[[:File:Cc5115_ETHENE_MO.LOG]]

[[:File:Cc5115_BUTADIENE_MO.LOG]]

[[:File:Cc5115_OPT_MO.LOG]]

=== Analysis of the C-C bond lengths ===

{| class="wikitable"
! Bond Lengths (Å)
! C1-C2
! C2-C3
! C3-C4
! C4-C5
! C5-C6
! C6-C1
|-
| Ethylene
|
|
|
|
| 1.36
|
|-
| Butadiene
| 1.36
| 1.54
| 1.36
|
|
|
|-
| Transition State
| 1.38
| 1.41
| 1.38
| 2.11
| 1.38
| 2.12
|-
| Cyclohexadiene
| 1.49
| 1.33
| 1.49
| 1.54
| 1.54
| 1.54
|}

The numbering of the carbon bonds are according to the labels on figure 1. The typical C-C bond lengths are as follows:

{| class="wikitable"
! Bond Type
! Bond Length (Å)
|-
| sp<sup>3</sup>-sp<sup>3</sup> C-C bond
| 1.54
|-
| sp<sup>3</sup>-sp<sup>2</sup> C-C bond
| 1.50
|-
| sp<sup>2</sup>-sp<sup>2</sup> C-C bond
| 1.47
|-
| sp<sup>2</sup>-sp<sup>2</sup> C=C bond
| 1.34
|}

When the reaction proceeds to the transition state, the sp<sup>2</sup>-sp<sup>2</sup> C5-C6 bond (originally ethylene) becomes longer as the carbons starts to change from sp<sup>2</sup> hybridised to sp<sup>3</sup> hybridised.
This trait is also apparent with C1-C2 and C3-C4 bonds where it once was the double bonds on butadiene, however, the increase in length of these bonds is less than that of C5-C6 due to the formation of a new double bond between C2 and C3, thus these carbons still remain sp<sup>2</sup> hybridised. This also leads to the next observation, where the C2-C3 bond decreases in length as it moves from the reactants to the transition state then the product, cyclohexadiene. This is because it is changing from a sp<sup>3</sup>-sp<sup>3</sup> C-C bond to a sp<sup>2</sup>-sp<sup>2</sup> C=C bond where the increase in s character shortens the bond lengths. This reaction also leads to the formation of 2 new bonds, namely C4-C5 and C6-C1. The Van der Waals radius of a carbon atom is 1.7 Å, and so the distance between 2 carbon atoms should be 3.4 Å, which is relatively longer than the bonds C4-C5 and C6-C1 which has a length of 2.11 and 2.12 Å respectively. This shows that the bonds are already partially formed in the transition state and they are beginning to interact together. This bond then settled at 1.54 Å in the product which matches with the typical bond length for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond.

=== Analysis of the vibrations ===

The animation for the first vibration is shown below. As observed, the formation of the 2 new bonds are synchronous as the reacting termini of butadiene and ethylene approaches each other at the same rate.

{| class="wikitable"
! <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 2;rotate x -20; </script>
<uploadedFileContents>Cc5115 OPT MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| The vibrations
|}

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

[[File:Cc5115 Exercise 2 generl.png|thumb|x700px|700px|centre|Figure 3: Reaction Scheme]]

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via either the endo or exo pathways to form 2 products with different stereochemistry. Method 3 was employed in order to compute the TS for this exercise. This time, the structures were further optimised with B3LYP/6-31G method and the results are shown and discussed below.

=== Analysis of Molecular Orbitals ===

[[File:Cc5115 Endo MO Exercise 2.png|thumb|x500px|500px|left|Figure 4: MO Diagram for the Endo TS]]

[[File:Cc5115 Exo MO Exercise 2.png|thumb|x500px|500px|right|Figure 5: MO Diagram for the Exo TS]]

There are two types of Diels-Alder (DA) reactions: one is with a normal electron demand where the dienophile is electron deficient and the diene is electron rich, and the other is with an inverse electron demand where the dienophile is electron rich and the diene is electron deficient.

For a normal electron demand DA reaction, the dienophile low-lying LUMO interacts with the diene HOMO which has a high energy. However, observing the energies of the reactants and the transition states, the MO diagram shows that this particular DA reaction has an inverse electron demand where the dienophile (1,3-dioxole) is electron rich (higher in energy) and the diene (cyclohexadiene) is electron poor (lower in energy). The interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene thus leads to the HOMO and LUMO of the transition state. Although opposing that of a normal electron demand DA, this reaction still follows the Woodword-Hoffman rule and is thermally allowed.

Similar to exercise 1, MOs of the same symmetry interact; the symmetrical dienophile HOMO and the diene LUMO interacts to give a symmetrical TS HOMO and LUMO, while the asymmetrical dienophile LUMO and diene HOMO gives the asymmetrical TS HOMO-1 and LUMO+1. It is also observable that the endo TS HOMO has a lower energy than the exo TS HOMO which suggests that the endo reaction is favoured. This will be discussed further in the Thermochemistry section of this exercise.

{| class="wikitable"
! ENDO TS - HOMO -1
! ENDO TS - HOMO
! ENDO TS - LUMO
! ENDO TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Log Files ====

[[File:Cc5115 ENDO B3.LOG]]

[[File:Cc5115 PLEASE WORK B3.LOG]]

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +149.70
| -77.52
|-
| Exo
| +157.52
| -73.92
|}

As discussed briefly in the introduction, the reactants need to pass the activation barrier (transition state) in order to reach to the products. The table regarding the reaction barriers and energies shows that the activation barrier for the endo reaction is less than that of the exo reaction, more-so confirming that the endo reaction is kinetically favoured. This links to the lower energy that the endo TS HOMO has compared to the exo TS. This observance can be explained by secondary orbital interation (SOI). The 2 non-bonding oxygen p-orbitals containing electron lone pairs can overlap with the LUMO of the diene through space thus stabilising the TS and consequentially lowering reaction barrier. However, the more negative reaction energy of the endo reaction can be explained with sterics; in the exo transition state, the steric interaction between the sp<sup>3</sup> bridging carbons and the rest of the 1,3-dioxole structure results in the exo product being higher in energy.

{| class="wikitable"
! Exo Secondary MO
! Endo Secondary MO
|-
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

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

=== IRC ===

{| class="wikitable"
! [[File:Cc5115 Exo IRC gif.gif|thumb|x500px|500px|left|IRC for Exo Product]]
! [[File:Cc5115 Endo IRC gif.gif|thumb|x500px|500px|left|IRC for Endo Product]]
! [[File:Chelatropic IRC gif.gif|thumb|x500px|500px|left|IRC for Chelatropic Product]]
|}

IRC (intrinsic reaction coordinate) show how reactions move in space during its reaction to form products. From the IRC animations, it can be seen that the formation of the new bonds differ to that of exercise 1. Here, in the exo and endo pathways, the formation of the 2 new bonds are asynchronous as one bond forms before the other. However, the bonds form synchronously in the chelatropic reaction leading to the symmetrical product.

The IRC reaction pathways also show a smaller activation barrier compared to that of exercise 1. This is because xylylene is highly unstable. Xylylene can exist with 4π electrons making it anti-aromatic, or either with 6π electrons an a diradical which is very unstable. On the flipside, the product formed is aromatic making the DA reaction extremely favourable. Naphthalene forces the diene to be rigid in its positions easing the overlap capabilities of the diene with the dienophile. This can be observed in the animation as naphthalene doesn't have to go through major rearrangements in order to form the products.

In the reaction, naphthalene initially has a C=C bond length of 1.35 Å and a C-C bond length averaging around 1.51 Å. This changes as the product is formed where all the carbon-carbon bonds on the 6 membered rings become 1.47 Å in length suggesting the formation of an aromatic 6-membered ring where the π electrons are delocalised throughout the ring. The change in bond length can also be seen with careful observation of the animations.

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +79.85
|
|-
| Exo
| +83.82
|
|-
| Chelatropic
| +102.16
|
|}

Significantly resembling to exercise 2, exercise 3 features the endo pathway being kinetically favoured as its activation energy has the least energy compared to the other pathway. Again, this is due to the overlap between the oxygen p-orbitals overlapping with the π-orbitals of the xylylene ring. However, the difference in activation and reaction energies between the exo and endo pathways do not differ that much due to the SOI not contributing significantly in the TS and there are little steric difference between the two products. For the chelatropic product, there is a hugh drop in reaction energy. Observing the product, the large sulfur atom forming a 5-membered ring decreases the ring-strain making the product relatively stable compared to the products from the DA reaction.

=== Cyclisation at the other reaction site ===

{| class="wikitable"
! [[File:Cc5115 IRC exo reaction site b.gif|thumb|x500px|500px|left|IRC for Exo Product at reaction site B]]
! [[File:Cc5115 IRC endo reaction site b.gif|thumb|x500px|500px|left|IRC for Endo Product at reaction site B]]
|}

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +110.06
|
|-
| Exo
| +117.90
|
|}

For this exercise, the Diels-Alder reaction can also take place at the other reaction site as illustrated in the animations.

== Conclusion ==

Gaussian was used to calculate the geometries of the transition states using the PM6 and the B3LYP methods. The TS was validated by a correct imaginary frequency from frequency calculations as well as the correct pathways along the reaction coordinate from IRC.

Rep:Mod:cc5115TS

2018-02-14T10:28:49Z

Cc5115: /* Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole */

= Y3C Transition states and Reactivity =

== Introduction ==

This section aims to illustrate the 3 different computational techniques that can be utilised in order to analyse the transition state (TS) of a reaction. The TS is the state which has the highest energy along a reaction coordinate, as a result it is the least stable state. In the reaction, the reactants needs to have a certain amount of energy in order to surpass the activation barrier, also known as the transition state energy, and reach the product state. This computational lab allows for calculations leading to the location of the TS. The structure of the TS is crucial in determining the mechanism of a reaction.

A potential energy surface (PES) has a 3N-6 dimension, which coincides to the degrees of freedom that the molecule has, where N is the number of atoms that the molecule possesses. In a 3-D PES, the saddle point (also called the TS), is a local mixami amidst 2 minima, and can be sometimes identified through secondary derivatives as it would be negative in one direction and positive in all other directions.

There are 3 calculation methods available in order to determine the structure of the TS.

1. The first and fastest method requires only one step where a guessed structure of the TS is optimised to give an optimised TS. This means that one will need of the TS to quite an extent, furthermore this method is rather unreliable as there is a high chance that the guessed TS is incorrectly drawn.

2. The second method works from a pre-frozen guess structure of the TS where the reacting termini of the reactants are frozen in space before the remaining structure is optimised to a minima. After that, the molecules are optimised as a transition state. This allows for a more reliable representation of the TS. This method is sufficient for Exercise 1.

3. The third method is the longest and most reliable method. Here, one starts by either optimising from the reactants or the products to a minima. For the reactant case, each reactants are optimised to a minima, arranged to resemble the TS and the reacting termini are frozen and the rest of the method 2 is repeated. A similar case occurs with the product; when the product is optimised to a minima, the bonds formed in the reactions are removed, the 2 fragments are arranged to resemble the TS and the reacting termini are frozen and method 2 was used once more. This method allows for the most reliable representation of the TS and is used for Exercise 2 & 3.

In this computational lab, two methods of calculation were used on Gaussian in order to find the TS. During the optimisation, the position of the molecule is decided as it is built in Gaussian. The time-independent Schrödinger equation was solved whilst utilising the Born-Oppenheimer approximation in order to find the energy and the wavefunction φ which represents the electronic states for the fixed nuclear positions and is dependent on on frozen nuclei positions. This is also known as the self-consistent field method (SCF). The two methods employed are the semi-empirical method PM6, which is usually performed first and sometimes followed by the Density Functional Theory (DFT) method B3LYP. The semi-empirical method PM6, although based on the Hartree-Fock formalism, this method uses many approximations based on experimental data in order to solve the Schrodinger equations. This method is usually fast and reliable, but can be easily countered if the environment of the molecule that is being computed is not similar enough to the approximated parameters of this method. The other method is B3LYP, a hydrid functional which utilises the DFT in order to calculate the majority of the Hamiltonian while a small portion still utilises the Hartree-Fock theory to calculate the exchange integral term. B3LYP stands for Becke, 3-parameter, Lee-Yang-Parr and uses a 6-31G basis set as the electronic wavefunction in order to produce more accurate results at the cost of increased calculation time.

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

[[File:Ex1 general.png|thumb|x700px|700px|centre|Figure 1: Formation of Cyclohaxadiene]]

Also known as the Diels-Alder reaction, this exercise investigates the well-known [4+2] cycloaddition between a conjugated diene (butadiene) and a dienophile (ethylene). The electrophilic reaction involves 4 pi-electrons from the diene and 2 pi-electrons from the alkene, and is a popular method to form regio- and stereochemically controlled 6-membered rings.

Method 2 was used to compute the transition state (TS) for this exercise. All steps are optimised to the PM6 level. First, the reactants are optimised to a minimum. The carbons at the reacting termini were then frozen at around 2.20 Å before optimised to a minimum to give a frozen-guess TS. Then finally, the molecule was optimised as a TS and an IRC was performed in order to confirm and locate the transition state.

=== Analysis of the Molecular Orbitals (MO) ===

The Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) for the reactants and the TS are shown below and its energies were recorded in order to produce the MO diagram as shown in figure 2.

{| class="wikitable"
! Ethene - HOMO
! Ethene - LUMO
! Butadiene - HOMO
! Butadiene - LUMO
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Cc5115 exer1finalMO.png|thumb|x800px|800px|left|Figure 2: MO Diagram for the formation of Transition State of the Diels-Alder Reaction]]

The symmetric TS HOMO and LUMO are formed through the interactions between the HOMO of ethylene and the LUMO of butadiene, both of which are symmetric. On the other hand, the LUMO of ethylene and the HOMO of butadiene, both of which are asymmetric, interacts to give an asymmetric HOMO-1 and LUMO+1. What can be concluded about the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed, and that the reaction is forbidden when the symmetry of the molecular orbitals aren't the same. The orbital overlap integral, S<sub>AB</sub>, is a quantitative measure of orbital overlap of two different atoms. Orbitals of the same symmetry will lead to constructive overlap and gives a non-zero value while orbitals of different symmetry will lead to destructive overlap and an orbital overlap integral of zero. Thus the overlap integral are:

- Non-zero for symmetric-symmetric interaction

- Non-zero for asymmetric-asymmetric interaction

- Zero for symmetric-asymmetric interaction

As observed in the MO diagram, the energy gap between the HOMO and LUMO for butadiene is smaller that those for ethylene due to butadiene being more electron rich than ethylene. Furthermore, in a normal MO diagram, the bonding MO formed should have a lower energy compared to both atomic orbitals (AO) whilst the anti-bonding MO formed should have a higher energy than both AOs. The reason why figure 3 goes against the tide is because the MOs formed corresponds to the transition state where the electrons are very delocalised within the chemical environment of the molecule.

==== LOG Files ====

[[:File:Cc5115_ETHENE_MO.LOG]]

[[:File:Cc5115_BUTADIENE_MO.LOG]]

[[:File:Cc5115_OPT_MO.LOG]]

=== Analysis of the C-C bond lengths ===

{| class="wikitable"
! Bond Lengths (Å)
! C1-C2
! C2-C3
! C3-C4
! C4-C5
! C5-C6
! C6-C1
|-
| Ethylene
|
|
|
|
| 1.36
|
|-
| Butadiene
| 1.36
| 1.54
| 1.36
|
|
|
|-
| Transition State
| 1.38
| 1.41
| 1.38
| 2.11
| 1.38
| 2.12
|-
| Cyclohexadiene
| 1.49
| 1.33
| 1.49
| 1.54
| 1.54
| 1.54
|}

The numbering of the carbon bonds are according to the labels on figure 1. The typical C-C bond lengths are as follows:

{| class="wikitable"
! Bond Type
! Bond Length (Å)
|-
| sp<sup>3</sup>-sp<sup>3</sup> C-C bond
| 1.54
|-
| sp<sup>3</sup>-sp<sup>2</sup> C-C bond
| 1.50
|-
| sp<sup>2</sup>-sp<sup>2</sup> C-C bond
| 1.47
|-
| sp<sup>2</sup>-sp<sup>2</sup> C=C bond
| 1.34
|}

When the reaction proceeds to the transition state, the sp<sup>2</sup>-sp<sup>2</sup> C5-C6 bond (originally ethylene) becomes longer as the carbons starts to change from sp<sup>2</sup> hybridised to sp<sup>3</sup> hybridised.
This trait is also apparent with C1-C2 and C3-C4 bonds where it once was the double bonds on butadiene, however, the increase in length of these bonds is less than that of C5-C6 due to the formation of a new double bond between C2 and C3, thus these carbons still remain sp<sup>2</sup> hybridised. This also leads to the next observation, where the C2-C3 bond decreases in length as it moves from the reactants to the transition state then the product, cyclohexadiene. This is because it is changing from a sp<sup>3</sup>-sp<sup>3</sup> C-C bond to a sp<sup>2</sup>-sp<sup>2</sup> C=C bond where the increase in s character shortens the bond lengths. This reaction also leads to the formation of 2 new bonds, namely C4-C5 and C6-C1. The Van der Waals radius of a carbon atom is 1.7 Å, and so the distance between 2 carbon atoms should be 3.4 Å, which is relatively longer than the bonds C4-C5 and C6-C1 which has a length of 2.11 and 2.12 Å respectively. This shows that the bonds are already partially formed in the transition state and they are beginning to interact together. This bond then settled at 1.54 Å in the product which matches with the typical bond length for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond.

=== Analysis of the vibrations ===

The animation for the first vibration is shown below. As observed, the formation of the 2 new bonds are synchronous as the reacting termini of butadiene and ethylene approaches each other at the same rate.

{| class="wikitable"
! <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 2;rotate x -20; </script>
<uploadedFileContents>Cc5115 OPT MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| The vibrations
|}

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

[[File:Cc5115 Exercise 2 generl.png|thumb|x700px|700px|centre|Figure 3: Reaction Scheme]]

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via either the endo or exo pathways to form 2 products with different stereochemistry. Method 3 was employed in order to compute the TS for this exercise. This time, the structures were further optimised with B3LYP/6-31G method and the results are shown and discussed below.

=== Analysis of Molecular Orbitals ===

[[File:Cc5115 Endo MO Exercise 2.png|thumb|x500px|500px|left|Figure 4: MO Diagram for the Endo TS]]

[[File:Cc5115 Exo MO Exercise 2.png|thumb|x500px|500px|right|Figure 4: MO Diagram for the Exo TS]]

There are two types of Diels-Alder (DA) reactions: one is with a normal electron demand where the dienophile is electron deficient and the diene is electron rich, and the other is with an inverse electron demand where the dienophile is electron rich and the diene is electron deficient.

For a normal electron demand DA reaction, the dienophile low-lying LUMO interacts with the diene HOMO which has a high energy. However, observing the energies of the reactants and the transition states, the MO diagram shows that this particular DA reaction has an inverse electron demand where the dienophile (1,3-dioxole) is electron rich (higher in energy) and the diene (cyclohexadiene) is electron poor (lower in energy). The interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene thus leads to the HOMO and LUMO of the transition state. Although opposing that of a normal electron demand DA, this reaction still follows the Woodword-Hoffman rule and is thermally allowed.

Similar to exercise 1, MOs of the same symmetry interact; the symmetrical dienophile HOMO and the diene LUMO interacts to give a symmetrical TS HOMO and LUMO, while the asymmetrical dienophile LUMO and diene HOMO gives the asymmetrical TS HOMO-1 and LUMO+1. It is also observable that the endo TS HOMO has a lower energy than the exo TS HOMO which suggests that the endo reaction is favoured. This will be discussed further in the Thermochemistry section of this exercise.

{| class="wikitable"
! ENDO TS - HOMO -1
! ENDO TS - HOMO
! ENDO TS - LUMO
! ENDO TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Log Files ====

[[File:Cc5115 ENDO B3.LOG]]

[[File:Cc5115 PLEASE WORK B3.LOG]]

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +149.70
| -77.52
|-
| Exo
| +157.52
| -73.92
|}

As discussed briefly in the introduction, the reactants need to pass the activation barrier (transition state) in order to reach to the products. The table regarding the reaction barriers and energies shows that the activation barrier for the endo reaction is less than that of the exo reaction, more-so confirming that the endo reaction is kinetically favoured. This links to the lower energy that the endo TS HOMO has compared to the exo TS. This observance can be explained by secondary orbital interation (SOI). The 2 non-bonding oxygen p-orbitals containing electron lone pairs can overlap with the LUMO of the diene through space thus stabilising the TS and consequentially lowering reaction barrier. However, the more negative reaction energy of the endo reaction can be explained with sterics; in the exo transition state, the steric interaction between the sp<sup>3</sup> bridging carbons and the rest of the 1,3-dioxole structure results in the exo product being higher in energy.

{| class="wikitable"
! Exo Secondary MO
! Endo Secondary MO
|-
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

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

=== IRC ===

{| class="wikitable"
! [[File:Cc5115 Exo IRC gif.gif|thumb|x500px|500px|left|IRC for Exo Product]]
! [[File:Cc5115 Endo IRC gif.gif|thumb|x500px|500px|left|IRC for Endo Product]]
! [[File:Chelatropic IRC gif.gif|thumb|x500px|500px|left|IRC for Chelatropic Product]]
|}

IRC (intrinsic reaction coordinate) show how reactions move in space during its reaction to form products. From the IRC animations, it can be seen that the formation of the new bonds differ to that of exercise 1. Here, in the exo and endo pathways, the formation of the 2 new bonds are asynchronous as one bond forms before the other. However, the bonds form synchronously in the chelatropic reaction leading to the symmetrical product.

The IRC reaction pathways also show a smaller activation barrier compared to that of exercise 1. This is because xylylene is highly unstable. Xylylene can exist with 4π electrons making it anti-aromatic, or either with 6π electrons an a diradical which is very unstable. On the flipside, the product formed is aromatic making the DA reaction extremely favourable. Naphthalene forces the diene to be rigid in its positions easing the overlap capabilities of the diene with the dienophile. This can be observed in the animation as naphthalene doesn't have to go through major rearrangements in order to form the products.

In the reaction, naphthalene initially has a C=C bond length of 1.35 Å and a C-C bond length averaging around 1.51 Å. This changes as the product is formed where all the carbon-carbon bonds on the 6 membered rings become 1.47 Å in length suggesting the formation of an aromatic 6-membered ring where the π electrons are delocalised throughout the ring. The change in bond length can also be seen with careful observation of the animations.

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +79.85
|
|-
| Exo
| +83.82
|
|-
| Chelatropic
| +102.16
|
|}

Significantly resembling to exercise 2, exercise 3 features the endo pathway being kinetically favoured as its activation energy has the least energy compared to the other pathway. Again, this is due to the overlap between the oxygen p-orbitals overlapping with the π-orbitals of the xylylene ring. However, the difference in activation and reaction energies between the exo and endo pathways do not differ that much due to the SOI not contributing significantly in the TS and there are little steric difference between the two products. For the chelatropic product, there is a hugh drop in reaction energy. Observing the product, the large sulfur atom forming a 5-membered ring decreases the ring-strain making the product relatively stable compared to the products from the DA reaction.

=== Cyclisation at the other reaction site ===

{| class="wikitable"
! [[File:Cc5115 IRC exo reaction site b.gif|thumb|x500px|500px|left|IRC for Exo Product at reaction site B]]
! [[File:Cc5115 IRC endo reaction site b.gif|thumb|x500px|500px|left|IRC for Endo Product at reaction site B]]
|}

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +110.06
|
|-
| Exo
| +117.90
|
|}

For this exercise, the Diels-Alder reaction can also take place at the other reaction site as illustrated in the animations.

== Conclusion ==

Gaussian was used to calculate the geometries of the transition states using the PM6 and the B3LYP methods. The TS was validated by a correct imaginary frequency from frequency calculations as well as the correct pathways along the reaction coordinate from IRC.

File:Cc5115 Exo MO Exercise 2.png

2018-02-14T10:28:05Z

Cc5115:

File:Cc5115 Endo MO Exercise 2.png

2018-02-14T10:26:36Z

Cc5115:

Rep:Mod:cc5115TS

2018-02-14T10:26:18Z

Cc5115: /* Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole */

= Y3C Transition states and Reactivity =

== Introduction ==

This section aims to illustrate the 3 different computational techniques that can be utilised in order to analyse the transition state (TS) of a reaction. The TS is the state which has the highest energy along a reaction coordinate, as a result it is the least stable state. In the reaction, the reactants needs to have a certain amount of energy in order to surpass the activation barrier, also known as the transition state energy, and reach the product state. This computational lab allows for calculations leading to the location of the TS. The structure of the TS is crucial in determining the mechanism of a reaction.

A potential energy surface (PES) has a 3N-6 dimension, which coincides to the degrees of freedom that the molecule has, where N is the number of atoms that the molecule possesses. In a 3-D PES, the saddle point (also called the TS), is a local mixami amidst 2 minima, and can be sometimes identified through secondary derivatives as it would be negative in one direction and positive in all other directions.

There are 3 calculation methods available in order to determine the structure of the TS.

1. The first and fastest method requires only one step where a guessed structure of the TS is optimised to give an optimised TS. This means that one will need of the TS to quite an extent, furthermore this method is rather unreliable as there is a high chance that the guessed TS is incorrectly drawn.

2. The second method works from a pre-frozen guess structure of the TS where the reacting termini of the reactants are frozen in space before the remaining structure is optimised to a minima. After that, the molecules are optimised as a transition state. This allows for a more reliable representation of the TS. This method is sufficient for Exercise 1.

3. The third method is the longest and most reliable method. Here, one starts by either optimising from the reactants or the products to a minima. For the reactant case, each reactants are optimised to a minima, arranged to resemble the TS and the reacting termini are frozen and the rest of the method 2 is repeated. A similar case occurs with the product; when the product is optimised to a minima, the bonds formed in the reactions are removed, the 2 fragments are arranged to resemble the TS and the reacting termini are frozen and method 2 was used once more. This method allows for the most reliable representation of the TS and is used for Exercise 2 & 3.

In this computational lab, two methods of calculation were used on Gaussian in order to find the TS. During the optimisation, the position of the molecule is decided as it is built in Gaussian. The time-independent Schrödinger equation was solved whilst utilising the Born-Oppenheimer approximation in order to find the energy and the wavefunction φ which represents the electronic states for the fixed nuclear positions and is dependent on on frozen nuclei positions. This is also known as the self-consistent field method (SCF). The two methods employed are the semi-empirical method PM6, which is usually performed first and sometimes followed by the Density Functional Theory (DFT) method B3LYP. The semi-empirical method PM6, although based on the Hartree-Fock formalism, this method uses many approximations based on experimental data in order to solve the Schrodinger equations. This method is usually fast and reliable, but can be easily countered if the environment of the molecule that is being computed is not similar enough to the approximated parameters of this method. The other method is B3LYP, a hydrid functional which utilises the DFT in order to calculate the majority of the Hamiltonian while a small portion still utilises the Hartree-Fock theory to calculate the exchange integral term. B3LYP stands for Becke, 3-parameter, Lee-Yang-Parr and uses a 6-31G basis set as the electronic wavefunction in order to produce more accurate results at the cost of increased calculation time.

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

[[File:Ex1 general.png|thumb|x700px|700px|centre|Figure 1: Formation of Cyclohaxadiene]]

Also known as the Diels-Alder reaction, this exercise investigates the well-known [4+2] cycloaddition between a conjugated diene (butadiene) and a dienophile (ethylene). The electrophilic reaction involves 4 pi-electrons from the diene and 2 pi-electrons from the alkene, and is a popular method to form regio- and stereochemically controlled 6-membered rings.

Method 2 was used to compute the transition state (TS) for this exercise. All steps are optimised to the PM6 level. First, the reactants are optimised to a minimum. The carbons at the reacting termini were then frozen at around 2.20 Å before optimised to a minimum to give a frozen-guess TS. Then finally, the molecule was optimised as a TS and an IRC was performed in order to confirm and locate the transition state.

=== Analysis of the Molecular Orbitals (MO) ===

The Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) for the reactants and the TS are shown below and its energies were recorded in order to produce the MO diagram as shown in figure 2.

{| class="wikitable"
! Ethene - HOMO
! Ethene - LUMO
! Butadiene - HOMO
! Butadiene - LUMO
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Cc5115 exer1finalMO.png|thumb|x800px|800px|left|Figure 2: MO Diagram for the formation of Transition State of the Diels-Alder Reaction]]

The symmetric TS HOMO and LUMO are formed through the interactions between the HOMO of ethylene and the LUMO of butadiene, both of which are symmetric. On the other hand, the LUMO of ethylene and the HOMO of butadiene, both of which are asymmetric, interacts to give an asymmetric HOMO-1 and LUMO+1. What can be concluded about the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed, and that the reaction is forbidden when the symmetry of the molecular orbitals aren't the same. The orbital overlap integral, S<sub>AB</sub>, is a quantitative measure of orbital overlap of two different atoms. Orbitals of the same symmetry will lead to constructive overlap and gives a non-zero value while orbitals of different symmetry will lead to destructive overlap and an orbital overlap integral of zero. Thus the overlap integral are:

- Non-zero for symmetric-symmetric interaction

- Non-zero for asymmetric-asymmetric interaction

- Zero for symmetric-asymmetric interaction

As observed in the MO diagram, the energy gap between the HOMO and LUMO for butadiene is smaller that those for ethylene due to butadiene being more electron rich than ethylene. Furthermore, in a normal MO diagram, the bonding MO formed should have a lower energy compared to both atomic orbitals (AO) whilst the anti-bonding MO formed should have a higher energy than both AOs. The reason why figure 3 goes against the tide is because the MOs formed corresponds to the transition state where the electrons are very delocalised within the chemical environment of the molecule.

==== LOG Files ====

[[:File:Cc5115_ETHENE_MO.LOG]]

[[:File:Cc5115_BUTADIENE_MO.LOG]]

[[:File:Cc5115_OPT_MO.LOG]]

=== Analysis of the C-C bond lengths ===

{| class="wikitable"
! Bond Lengths (Å)
! C1-C2
! C2-C3
! C3-C4
! C4-C5
! C5-C6
! C6-C1
|-
| Ethylene
|
|
|
|
| 1.36
|
|-
| Butadiene
| 1.36
| 1.54
| 1.36
|
|
|
|-
| Transition State
| 1.38
| 1.41
| 1.38
| 2.11
| 1.38
| 2.12
|-
| Cyclohexadiene
| 1.49
| 1.33
| 1.49
| 1.54
| 1.54
| 1.54
|}

The numbering of the carbon bonds are according to the labels on figure 1. The typical C-C bond lengths are as follows:

{| class="wikitable"
! Bond Type
! Bond Length (Å)
|-
| sp<sup>3</sup>-sp<sup>3</sup> C-C bond
| 1.54
|-
| sp<sup>3</sup>-sp<sup>2</sup> C-C bond
| 1.50
|-
| sp<sup>2</sup>-sp<sup>2</sup> C-C bond
| 1.47
|-
| sp<sup>2</sup>-sp<sup>2</sup> C=C bond
| 1.34
|}

When the reaction proceeds to the transition state, the sp<sup>2</sup>-sp<sup>2</sup> C5-C6 bond (originally ethylene) becomes longer as the carbons starts to change from sp<sup>2</sup> hybridised to sp<sup>3</sup> hybridised.
This trait is also apparent with C1-C2 and C3-C4 bonds where it once was the double bonds on butadiene, however, the increase in length of these bonds is less than that of C5-C6 due to the formation of a new double bond between C2 and C3, thus these carbons still remain sp<sup>2</sup> hybridised. This also leads to the next observation, where the C2-C3 bond decreases in length as it moves from the reactants to the transition state then the product, cyclohexadiene. This is because it is changing from a sp<sup>3</sup>-sp<sup>3</sup> C-C bond to a sp<sup>2</sup>-sp<sup>2</sup> C=C bond where the increase in s character shortens the bond lengths. This reaction also leads to the formation of 2 new bonds, namely C4-C5 and C6-C1. The Van der Waals radius of a carbon atom is 1.7 Å, and so the distance between 2 carbon atoms should be 3.4 Å, which is relatively longer than the bonds C4-C5 and C6-C1 which has a length of 2.11 and 2.12 Å respectively. This shows that the bonds are already partially formed in the transition state and they are beginning to interact together. This bond then settled at 1.54 Å in the product which matches with the typical bond length for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond.

=== Analysis of the vibrations ===

The animation for the first vibration is shown below. As observed, the formation of the 2 new bonds are synchronous as the reacting termini of butadiene and ethylene approaches each other at the same rate.

{| class="wikitable"
! <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 2;rotate x -20; </script>
<uploadedFileContents>Cc5115 OPT MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| The vibrations
|}

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

[[File:Cc5115 Exercise 2 generl.png|thumb|x700px|700px|centre|Figure 1: Formation of Cyclohaxadiene]]

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via either the endo or exo pathways to form 2 products with different stereochemistry. Method 3 was employed in order to compute the TS for this exercise. This time, the structures were further optimised with B3LYP/6-31G method and the results are shown and discussed below.

=== Analysis of Molecular Orbitals ===

There are two types of Diels-Alder (DA) reactions: one is with a normal electron demand where the dienophile is electron deficient and the diene is electron rich, and the other is with an inverse electron demand where the dienophile is electron rich and the diene is electron deficient.

For a normal electron demand DA reaction, the dienophile low-lying LUMO interacts with the diene HOMO which has a high energy. However, observing the energies of the reactants and the transition states, the MO diagram shows that this particular DA reaction has an inverse electron demand where the dienophile (1,3-dioxole) is electron rich (higher in energy) and the diene (cyclohexadiene) is electron poor (lower in energy). The interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene thus leads to the HOMO and LUMO of the transition state. Although opposing that of a normal electron demand DA, this reaction still follows the Woodword-Hoffman rule and is thermally allowed.

Similar to exercise 1, MOs of the same symmetry interact; the symmetrical dienophile HOMO and the diene LUMO interacts to give a symmetrical TS HOMO and LUMO, while the asymmetrical dienophile LUMO and diene HOMO gives the asymmetrical TS HOMO-1 and LUMO+1. It is also observable that the endo TS HOMO has a lower energy than the exo TS HOMO which suggests that the endo reaction is favoured. This will be discussed further in the Thermochemistry section of this exercise.

{| class="wikitable"
! ENDO TS - HOMO -1
! ENDO TS - HOMO
! ENDO TS - LUMO
! ENDO TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Log Files ====

[[File:Cc5115 ENDO B3.LOG]]

[[File:Cc5115 PLEASE WORK B3.LOG]]

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +149.70
| -77.52
|-
| Exo
| +157.52
| -73.92
|}

As discussed briefly in the introduction, the reactants need to pass the activation barrier (transition state) in order to reach to the products. The table regarding the reaction barriers and energies shows that the activation barrier for the endo reaction is less than that of the exo reaction, more-so confirming that the endo reaction is kinetically favoured. This links to the lower energy that the endo TS HOMO has compared to the exo TS. This observance can be explained by secondary orbital interation (SOI). The 2 non-bonding oxygen p-orbitals containing electron lone pairs can overlap with the LUMO of the diene through space thus stabilising the TS and consequentially lowering reaction barrier. However, the more negative reaction energy of the endo reaction can be explained with sterics; in the exo transition state, the steric interaction between the sp<sup>3</sup> bridging carbons and the rest of the 1,3-dioxole structure results in the exo product being higher in energy.

{| class="wikitable"
! Exo Secondary MO
! Endo Secondary MO
|-
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

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

=== IRC ===

{| class="wikitable"
! [[File:Cc5115 Exo IRC gif.gif|thumb|x500px|500px|left|IRC for Exo Product]]
! [[File:Cc5115 Endo IRC gif.gif|thumb|x500px|500px|left|IRC for Endo Product]]
! [[File:Chelatropic IRC gif.gif|thumb|x500px|500px|left|IRC for Chelatropic Product]]
|}

IRC (intrinsic reaction coordinate) show how reactions move in space during its reaction to form products. From the IRC animations, it can be seen that the formation of the new bonds differ to that of exercise 1. Here, in the exo and endo pathways, the formation of the 2 new bonds are asynchronous as one bond forms before the other. However, the bonds form synchronously in the chelatropic reaction leading to the symmetrical product.

The IRC reaction pathways also show a smaller activation barrier compared to that of exercise 1. This is because xylylene is highly unstable. Xylylene can exist with 4π electrons making it anti-aromatic, or either with 6π electrons an a diradical which is very unstable. On the flipside, the product formed is aromatic making the DA reaction extremely favourable. Naphthalene forces the diene to be rigid in its positions easing the overlap capabilities of the diene with the dienophile. This can be observed in the animation as naphthalene doesn't have to go through major rearrangements in order to form the products.

In the reaction, naphthalene initially has a C=C bond length of 1.35 Å and a C-C bond length averaging around 1.51 Å. This changes as the product is formed where all the carbon-carbon bonds on the 6 membered rings become 1.47 Å in length suggesting the formation of an aromatic 6-membered ring where the π electrons are delocalised throughout the ring. The change in bond length can also be seen with careful observation of the animations.

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +79.85
|
|-
| Exo
| +83.82
|
|-
| Chelatropic
| +102.16
|
|}

Significantly resembling to exercise 2, exercise 3 features the endo pathway being kinetically favoured as its activation energy has the least energy compared to the other pathway. Again, this is due to the overlap between the oxygen p-orbitals overlapping with the π-orbitals of the xylylene ring. However, the difference in activation and reaction energies between the exo and endo pathways do not differ that much due to the SOI not contributing significantly in the TS and there are little steric difference between the two products. For the chelatropic product, there is a hugh drop in reaction energy. Observing the product, the large sulfur atom forming a 5-membered ring decreases the ring-strain making the product relatively stable compared to the products from the DA reaction.

=== Cyclisation at the other reaction site ===

{| class="wikitable"
! [[File:Cc5115 IRC exo reaction site b.gif|thumb|x500px|500px|left|IRC for Exo Product at reaction site B]]
! [[File:Cc5115 IRC endo reaction site b.gif|thumb|x500px|500px|left|IRC for Endo Product at reaction site B]]
|}

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +110.06
|
|-
| Exo
| +117.90
|
|}

For this exercise, the Diels-Alder reaction can also take place at the other reaction site as illustrated in the animations.

== Conclusion ==

Gaussian was used to calculate the geometries of the transition states using the PM6 and the B3LYP methods. The TS was validated by a correct imaginary frequency from frequency calculations as well as the correct pathways along the reaction coordinate from IRC.

Rep:Mod:cc5115TS

2018-02-14T10:25:49Z

Cc5115: /* Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole */

= Y3C Transition states and Reactivity =

== Introduction ==

This section aims to illustrate the 3 different computational techniques that can be utilised in order to analyse the transition state (TS) of a reaction. The TS is the state which has the highest energy along a reaction coordinate, as a result it is the least stable state. In the reaction, the reactants needs to have a certain amount of energy in order to surpass the activation barrier, also known as the transition state energy, and reach the product state. This computational lab allows for calculations leading to the location of the TS. The structure of the TS is crucial in determining the mechanism of a reaction.

A potential energy surface (PES) has a 3N-6 dimension, which coincides to the degrees of freedom that the molecule has, where N is the number of atoms that the molecule possesses. In a 3-D PES, the saddle point (also called the TS), is a local mixami amidst 2 minima, and can be sometimes identified through secondary derivatives as it would be negative in one direction and positive in all other directions.

There are 3 calculation methods available in order to determine the structure of the TS.

1. The first and fastest method requires only one step where a guessed structure of the TS is optimised to give an optimised TS. This means that one will need of the TS to quite an extent, furthermore this method is rather unreliable as there is a high chance that the guessed TS is incorrectly drawn.

2. The second method works from a pre-frozen guess structure of the TS where the reacting termini of the reactants are frozen in space before the remaining structure is optimised to a minima. After that, the molecules are optimised as a transition state. This allows for a more reliable representation of the TS. This method is sufficient for Exercise 1.

3. The third method is the longest and most reliable method. Here, one starts by either optimising from the reactants or the products to a minima. For the reactant case, each reactants are optimised to a minima, arranged to resemble the TS and the reacting termini are frozen and the rest of the method 2 is repeated. A similar case occurs with the product; when the product is optimised to a minima, the bonds formed in the reactions are removed, the 2 fragments are arranged to resemble the TS and the reacting termini are frozen and method 2 was used once more. This method allows for the most reliable representation of the TS and is used for Exercise 2 & 3.

In this computational lab, two methods of calculation were used on Gaussian in order to find the TS. During the optimisation, the position of the molecule is decided as it is built in Gaussian. The time-independent Schrödinger equation was solved whilst utilising the Born-Oppenheimer approximation in order to find the energy and the wavefunction φ which represents the electronic states for the fixed nuclear positions and is dependent on on frozen nuclei positions. This is also known as the self-consistent field method (SCF). The two methods employed are the semi-empirical method PM6, which is usually performed first and sometimes followed by the Density Functional Theory (DFT) method B3LYP. The semi-empirical method PM6, although based on the Hartree-Fock formalism, this method uses many approximations based on experimental data in order to solve the Schrodinger equations. This method is usually fast and reliable, but can be easily countered if the environment of the molecule that is being computed is not similar enough to the approximated parameters of this method. The other method is B3LYP, a hydrid functional which utilises the DFT in order to calculate the majority of the Hamiltonian while a small portion still utilises the Hartree-Fock theory to calculate the exchange integral term. B3LYP stands for Becke, 3-parameter, Lee-Yang-Parr and uses a 6-31G basis set as the electronic wavefunction in order to produce more accurate results at the cost of increased calculation time.

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

[[File:Ex1 general.png|thumb|x700px|700px|centre|Figure 1: Formation of Cyclohaxadiene]]

Also known as the Diels-Alder reaction, this exercise investigates the well-known [4+2] cycloaddition between a conjugated diene (butadiene) and a dienophile (ethylene). The electrophilic reaction involves 4 pi-electrons from the diene and 2 pi-electrons from the alkene, and is a popular method to form regio- and stereochemically controlled 6-membered rings.

Method 2 was used to compute the transition state (TS) for this exercise. All steps are optimised to the PM6 level. First, the reactants are optimised to a minimum. The carbons at the reacting termini were then frozen at around 2.20 Å before optimised to a minimum to give a frozen-guess TS. Then finally, the molecule was optimised as a TS and an IRC was performed in order to confirm and locate the transition state.

=== Analysis of the Molecular Orbitals (MO) ===

The Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) for the reactants and the TS are shown below and its energies were recorded in order to produce the MO diagram as shown in figure 2.

{| class="wikitable"
! Ethene - HOMO
! Ethene - LUMO
! Butadiene - HOMO
! Butadiene - LUMO
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Cc5115 exer1finalMO.png|thumb|x800px|800px|left|Figure 2: MO Diagram for the formation of Transition State of the Diels-Alder Reaction]]

The symmetric TS HOMO and LUMO are formed through the interactions between the HOMO of ethylene and the LUMO of butadiene, both of which are symmetric. On the other hand, the LUMO of ethylene and the HOMO of butadiene, both of which are asymmetric, interacts to give an asymmetric HOMO-1 and LUMO+1. What can be concluded about the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed, and that the reaction is forbidden when the symmetry of the molecular orbitals aren't the same. The orbital overlap integral, S<sub>AB</sub>, is a quantitative measure of orbital overlap of two different atoms. Orbitals of the same symmetry will lead to constructive overlap and gives a non-zero value while orbitals of different symmetry will lead to destructive overlap and an orbital overlap integral of zero. Thus the overlap integral are:

- Non-zero for symmetric-symmetric interaction

- Non-zero for asymmetric-asymmetric interaction

- Zero for symmetric-asymmetric interaction

As observed in the MO diagram, the energy gap between the HOMO and LUMO for butadiene is smaller that those for ethylene due to butadiene being more electron rich than ethylene. Furthermore, in a normal MO diagram, the bonding MO formed should have a lower energy compared to both atomic orbitals (AO) whilst the anti-bonding MO formed should have a higher energy than both AOs. The reason why figure 3 goes against the tide is because the MOs formed corresponds to the transition state where the electrons are very delocalised within the chemical environment of the molecule.

==== LOG Files ====

[[:File:Cc5115_ETHENE_MO.LOG]]

[[:File:Cc5115_BUTADIENE_MO.LOG]]

[[:File:Cc5115_OPT_MO.LOG]]

=== Analysis of the C-C bond lengths ===

{| class="wikitable"
! Bond Lengths (Å)
! C1-C2
! C2-C3
! C3-C4
! C4-C5
! C5-C6
! C6-C1
|-
| Ethylene
|
|
|
|
| 1.36
|
|-
| Butadiene
| 1.36
| 1.54
| 1.36
|
|
|
|-
| Transition State
| 1.38
| 1.41
| 1.38
| 2.11
| 1.38
| 2.12
|-
| Cyclohexadiene
| 1.49
| 1.33
| 1.49
| 1.54
| 1.54
| 1.54
|}

The numbering of the carbon bonds are according to the labels on figure 1. The typical C-C bond lengths are as follows:

{| class="wikitable"
! Bond Type
! Bond Length (Å)
|-
| sp<sup>3</sup>-sp<sup>3</sup> C-C bond
| 1.54
|-
| sp<sup>3</sup>-sp<sup>2</sup> C-C bond
| 1.50
|-
| sp<sup>2</sup>-sp<sup>2</sup> C-C bond
| 1.47
|-
| sp<sup>2</sup>-sp<sup>2</sup> C=C bond
| 1.34
|}

When the reaction proceeds to the transition state, the sp<sup>2</sup>-sp<sup>2</sup> C5-C6 bond (originally ethylene) becomes longer as the carbons starts to change from sp<sup>2</sup> hybridised to sp<sup>3</sup> hybridised.
This trait is also apparent with C1-C2 and C3-C4 bonds where it once was the double bonds on butadiene, however, the increase in length of these bonds is less than that of C5-C6 due to the formation of a new double bond between C2 and C3, thus these carbons still remain sp<sup>2</sup> hybridised. This also leads to the next observation, where the C2-C3 bond decreases in length as it moves from the reactants to the transition state then the product, cyclohexadiene. This is because it is changing from a sp<sup>3</sup>-sp<sup>3</sup> C-C bond to a sp<sup>2</sup>-sp<sup>2</sup> C=C bond where the increase in s character shortens the bond lengths. This reaction also leads to the formation of 2 new bonds, namely C4-C5 and C6-C1. The Van der Waals radius of a carbon atom is 1.7 Å, and so the distance between 2 carbon atoms should be 3.4 Å, which is relatively longer than the bonds C4-C5 and C6-C1 which has a length of 2.11 and 2.12 Å respectively. This shows that the bonds are already partially formed in the transition state and they are beginning to interact together. This bond then settled at 1.54 Å in the product which matches with the typical bond length for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond.

=== Analysis of the vibrations ===

The animation for the first vibration is shown below. As observed, the formation of the 2 new bonds are synchronous as the reacting termini of butadiene and ethylene approaches each other at the same rate.

{| class="wikitable"
! <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 2;rotate x -20; </script>
<uploadedFileContents>Cc5115 OPT MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| The vibrations
|}

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

[[File:Cc5115 Exercise 2 generl.png]]

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via either the endo or exo pathways to form 2 products with different stereochemistry. Method 3 was employed in order to compute the TS for this exercise. This time, the structures were further optimised with B3LYP/6-31G method and the results are shown and discussed below.

=== Analysis of Molecular Orbitals ===

There are two types of Diels-Alder (DA) reactions: one is with a normal electron demand where the dienophile is electron deficient and the diene is electron rich, and the other is with an inverse electron demand where the dienophile is electron rich and the diene is electron deficient.

For a normal electron demand DA reaction, the dienophile low-lying LUMO interacts with the diene HOMO which has a high energy. However, observing the energies of the reactants and the transition states, the MO diagram shows that this particular DA reaction has an inverse electron demand where the dienophile (1,3-dioxole) is electron rich (higher in energy) and the diene (cyclohexadiene) is electron poor (lower in energy). The interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene thus leads to the HOMO and LUMO of the transition state. Although opposing that of a normal electron demand DA, this reaction still follows the Woodword-Hoffman rule and is thermally allowed.

Similar to exercise 1, MOs of the same symmetry interact; the symmetrical dienophile HOMO and the diene LUMO interacts to give a symmetrical TS HOMO and LUMO, while the asymmetrical dienophile LUMO and diene HOMO gives the asymmetrical TS HOMO-1 and LUMO+1. It is also observable that the endo TS HOMO has a lower energy than the exo TS HOMO which suggests that the endo reaction is favoured. This will be discussed further in the Thermochemistry section of this exercise.

{| class="wikitable"
! ENDO TS - HOMO -1
! ENDO TS - HOMO
! ENDO TS - LUMO
! ENDO TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Log Files ====

[[File:Cc5115 ENDO B3.LOG]]

[[File:Cc5115 PLEASE WORK B3.LOG]]

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +149.70
| -77.52
|-
| Exo
| +157.52
| -73.92
|}

As discussed briefly in the introduction, the reactants need to pass the activation barrier (transition state) in order to reach to the products. The table regarding the reaction barriers and energies shows that the activation barrier for the endo reaction is less than that of the exo reaction, more-so confirming that the endo reaction is kinetically favoured. This links to the lower energy that the endo TS HOMO has compared to the exo TS. This observance can be explained by secondary orbital interation (SOI). The 2 non-bonding oxygen p-orbitals containing electron lone pairs can overlap with the LUMO of the diene through space thus stabilising the TS and consequentially lowering reaction barrier. However, the more negative reaction energy of the endo reaction can be explained with sterics; in the exo transition state, the steric interaction between the sp<sup>3</sup> bridging carbons and the rest of the 1,3-dioxole structure results in the exo product being higher in energy.

{| class="wikitable"
! Exo Secondary MO
! Endo Secondary MO
|-
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

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

=== IRC ===

{| class="wikitable"
! [[File:Cc5115 Exo IRC gif.gif|thumb|x500px|500px|left|IRC for Exo Product]]
! [[File:Cc5115 Endo IRC gif.gif|thumb|x500px|500px|left|IRC for Endo Product]]
! [[File:Chelatropic IRC gif.gif|thumb|x500px|500px|left|IRC for Chelatropic Product]]
|}

IRC (intrinsic reaction coordinate) show how reactions move in space during its reaction to form products. From the IRC animations, it can be seen that the formation of the new bonds differ to that of exercise 1. Here, in the exo and endo pathways, the formation of the 2 new bonds are asynchronous as one bond forms before the other. However, the bonds form synchronously in the chelatropic reaction leading to the symmetrical product.

The IRC reaction pathways also show a smaller activation barrier compared to that of exercise 1. This is because xylylene is highly unstable. Xylylene can exist with 4π electrons making it anti-aromatic, or either with 6π electrons an a diradical which is very unstable. On the flipside, the product formed is aromatic making the DA reaction extremely favourable. Naphthalene forces the diene to be rigid in its positions easing the overlap capabilities of the diene with the dienophile. This can be observed in the animation as naphthalene doesn't have to go through major rearrangements in order to form the products.

In the reaction, naphthalene initially has a C=C bond length of 1.35 Å and a C-C bond length averaging around 1.51 Å. This changes as the product is formed where all the carbon-carbon bonds on the 6 membered rings become 1.47 Å in length suggesting the formation of an aromatic 6-membered ring where the π electrons are delocalised throughout the ring. The change in bond length can also be seen with careful observation of the animations.

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +79.85
|
|-
| Exo
| +83.82
|
|-
| Chelatropic
| +102.16
|
|}

Significantly resembling to exercise 2, exercise 3 features the endo pathway being kinetically favoured as its activation energy has the least energy compared to the other pathway. Again, this is due to the overlap between the oxygen p-orbitals overlapping with the π-orbitals of the xylylene ring. However, the difference in activation and reaction energies between the exo and endo pathways do not differ that much due to the SOI not contributing significantly in the TS and there are little steric difference between the two products. For the chelatropic product, there is a hugh drop in reaction energy. Observing the product, the large sulfur atom forming a 5-membered ring decreases the ring-strain making the product relatively stable compared to the products from the DA reaction.

=== Cyclisation at the other reaction site ===

{| class="wikitable"
! [[File:Cc5115 IRC exo reaction site b.gif|thumb|x500px|500px|left|IRC for Exo Product at reaction site B]]
! [[File:Cc5115 IRC endo reaction site b.gif|thumb|x500px|500px|left|IRC for Endo Product at reaction site B]]
|}

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +110.06
|
|-
| Exo
| +117.90
|
|}

For this exercise, the Diels-Alder reaction can also take place at the other reaction site as illustrated in the animations.

== Conclusion ==

Gaussian was used to calculate the geometries of the transition states using the PM6 and the B3LYP methods. The TS was validated by a correct imaginary frequency from frequency calculations as well as the correct pathways along the reaction coordinate from IRC.

File:Cc5115 Exercise 2 generl.png

2018-02-14T10:25:28Z

Cc5115:

File:Cc5115 Exercise 2 generl.cdx

2018-02-14T10:23:59Z

Cc5115:

Rep:Mod:cc5115TS

2018-02-14T03:50:49Z

Cc5115: /* Conclusion */

= Y3C Transition states and Reactivity =

== Introduction ==

This section aims to illustrate the 3 different computational techniques that can be utilised in order to analyse the transition state (TS) of a reaction. The TS is the state which has the highest energy along a reaction coordinate, as a result it is the least stable state. In the reaction, the reactants needs to have a certain amount of energy in order to surpass the activation barrier, also known as the transition state energy, and reach the product state. This computational lab allows for calculations leading to the location of the TS. The structure of the TS is crucial in determining the mechanism of a reaction.

A potential energy surface (PES) has a 3N-6 dimension, which coincides to the degrees of freedom that the molecule has, where N is the number of atoms that the molecule possesses. In a 3-D PES, the saddle point (also called the TS), is a local mixami amidst 2 minima, and can be sometimes identified through secondary derivatives as it would be negative in one direction and positive in all other directions.

There are 3 calculation methods available in order to determine the structure of the TS.

1. The first and fastest method requires only one step where a guessed structure of the TS is optimised to give an optimised TS. This means that one will need of the TS to quite an extent, furthermore this method is rather unreliable as there is a high chance that the guessed TS is incorrectly drawn.

2. The second method works from a pre-frozen guess structure of the TS where the reacting termini of the reactants are frozen in space before the remaining structure is optimised to a minima. After that, the molecules are optimised as a transition state. This allows for a more reliable representation of the TS. This method is sufficient for Exercise 1.

3. The third method is the longest and most reliable method. Here, one starts by either optimising from the reactants or the products to a minima. For the reactant case, each reactants are optimised to a minima, arranged to resemble the TS and the reacting termini are frozen and the rest of the method 2 is repeated. A similar case occurs with the product; when the product is optimised to a minima, the bonds formed in the reactions are removed, the 2 fragments are arranged to resemble the TS and the reacting termini are frozen and method 2 was used once more. This method allows for the most reliable representation of the TS and is used for Exercise 2 & 3.

In this computational lab, two methods of calculation were used on Gaussian in order to find the TS. During the optimisation, the position of the molecule is decided as it is built in Gaussian. The time-independent Schrödinger equation was solved whilst utilising the Born-Oppenheimer approximation in order to find the energy and the wavefunction φ which represents the electronic states for the fixed nuclear positions and is dependent on on frozen nuclei positions. This is also known as the self-consistent field method (SCF). The two methods employed are the semi-empirical method PM6, which is usually performed first and sometimes followed by the Density Functional Theory (DFT) method B3LYP. The semi-empirical method PM6, although based on the Hartree-Fock formalism, this method uses many approximations based on experimental data in order to solve the Schrodinger equations. This method is usually fast and reliable, but can be easily countered if the environment of the molecule that is being computed is not similar enough to the approximated parameters of this method. The other method is B3LYP, a hydrid functional which utilises the DFT in order to calculate the majority of the Hamiltonian while a small portion still utilises the Hartree-Fock theory to calculate the exchange integral term. B3LYP stands for Becke, 3-parameter, Lee-Yang-Parr and uses a 6-31G basis set as the electronic wavefunction in order to produce more accurate results at the cost of increased calculation time.

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

[[File:Ex1 general.png|thumb|x700px|700px|centre|Figure 1: Formation of Cyclohaxadiene]]

Also known as the Diels-Alder reaction, this exercise investigates the well-known [4+2] cycloaddition between a conjugated diene (butadiene) and a dienophile (ethylene). The electrophilic reaction involves 4 pi-electrons from the diene and 2 pi-electrons from the alkene, and is a popular method to form regio- and stereochemically controlled 6-membered rings.

Method 2 was used to compute the transition state (TS) for this exercise. All steps are optimised to the PM6 level. First, the reactants are optimised to a minimum. The carbons at the reacting termini were then frozen at around 2.20 Å before optimised to a minimum to give a frozen-guess TS. Then finally, the molecule was optimised as a TS and an IRC was performed in order to confirm and locate the transition state.

=== Analysis of the Molecular Orbitals (MO) ===

The Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) for the reactants and the TS are shown below and its energies were recorded in order to produce the MO diagram as shown in figure 2.

{| class="wikitable"
! Ethene - HOMO
! Ethene - LUMO
! Butadiene - HOMO
! Butadiene - LUMO
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Cc5115 exer1finalMO.png|thumb|x800px|800px|left|Figure 2: MO Diagram for the formation of Transition State of the Diels-Alder Reaction]]

The symmetric TS HOMO and LUMO are formed through the interactions between the HOMO of ethylene and the LUMO of butadiene, both of which are symmetric. On the other hand, the LUMO of ethylene and the HOMO of butadiene, both of which are asymmetric, interacts to give an asymmetric HOMO-1 and LUMO+1. What can be concluded about the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed, and that the reaction is forbidden when the symmetry of the molecular orbitals aren't the same. The orbital overlap integral, S<sub>AB</sub>, is a quantitative measure of orbital overlap of two different atoms. Orbitals of the same symmetry will lead to constructive overlap and gives a non-zero value while orbitals of different symmetry will lead to destructive overlap and an orbital overlap integral of zero. Thus the overlap integral are:

- Non-zero for symmetric-symmetric interaction

- Non-zero for asymmetric-asymmetric interaction

- Zero for symmetric-asymmetric interaction

As observed in the MO diagram, the energy gap between the HOMO and LUMO for butadiene is smaller that those for ethylene due to butadiene being more electron rich than ethylene. Furthermore, in a normal MO diagram, the bonding MO formed should have a lower energy compared to both atomic orbitals (AO) whilst the anti-bonding MO formed should have a higher energy than both AOs. The reason why figure 3 goes against the tide is because the MOs formed corresponds to the transition state where the electrons are very delocalised within the chemical environment of the molecule.

==== LOG Files ====

[[:File:Cc5115_ETHENE_MO.LOG]]

[[:File:Cc5115_BUTADIENE_MO.LOG]]

[[:File:Cc5115_OPT_MO.LOG]]

=== Analysis of the C-C bond lengths ===

{| class="wikitable"
! Bond Lengths (Å)
! C1-C2
! C2-C3
! C3-C4
! C4-C5
! C5-C6
! C6-C1
|-
| Ethylene
|
|
|
|
| 1.36
|
|-
| Butadiene
| 1.36
| 1.54
| 1.36
|
|
|
|-
| Transition State
| 1.38
| 1.41
| 1.38
| 2.11
| 1.38
| 2.12
|-
| Cyclohexadiene
| 1.49
| 1.33
| 1.49
| 1.54
| 1.54
| 1.54
|}

The numbering of the carbon bonds are according to the labels on figure 1. The typical C-C bond lengths are as follows:

{| class="wikitable"
! Bond Type
! Bond Length (Å)
|-
| sp<sup>3</sup>-sp<sup>3</sup> C-C bond
| 1.54
|-
| sp<sup>3</sup>-sp<sup>2</sup> C-C bond
| 1.50
|-
| sp<sup>2</sup>-sp<sup>2</sup> C-C bond
| 1.47
|-
| sp<sup>2</sup>-sp<sup>2</sup> C=C bond
| 1.34
|}

When the reaction proceeds to the transition state, the sp<sup>2</sup>-sp<sup>2</sup> C5-C6 bond (originally ethylene) becomes longer as the carbons starts to change from sp<sup>2</sup> hybridised to sp<sup>3</sup> hybridised.
This trait is also apparent with C1-C2 and C3-C4 bonds where it once was the double bonds on butadiene, however, the increase in length of these bonds is less than that of C5-C6 due to the formation of a new double bond between C2 and C3, thus these carbons still remain sp<sup>2</sup> hybridised. This also leads to the next observation, where the C2-C3 bond decreases in length as it moves from the reactants to the transition state then the product, cyclohexadiene. This is because it is changing from a sp<sup>3</sup>-sp<sup>3</sup> C-C bond to a sp<sup>2</sup>-sp<sup>2</sup> C=C bond where the increase in s character shortens the bond lengths. This reaction also leads to the formation of 2 new bonds, namely C4-C5 and C6-C1. The Van der Waals radius of a carbon atom is 1.7 Å, and so the distance between 2 carbon atoms should be 3.4 Å, which is relatively longer than the bonds C4-C5 and C6-C1 which has a length of 2.11 and 2.12 Å respectively. This shows that the bonds are already partially formed in the transition state and they are beginning to interact together. This bond then settled at 1.54 Å in the product which matches with the typical bond length for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond.

=== Analysis of the vibrations ===

The animation for the first vibration is shown below. As observed, the formation of the 2 new bonds are synchronous as the reacting termini of butadiene and ethylene approaches each other at the same rate.

{| class="wikitable"
! <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 2;rotate x -20; </script>
<uploadedFileContents>Cc5115 OPT MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| The vibrations
|}

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

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via either the endo or exo pathways to form 2 products with different stereochemistry. Method 3 was employed in order to compute the TS for this exercise. This time, the structures were further optimised with B3LYP/6-31G method and the results are shown and discussed below.

=== Analysis of Molecular Orbitals ===

There are two types of Diels-Alder (DA) reactions: one is with a normal electron demand where the dienophile is electron deficient and the diene is electron rich, and the other is with an inverse electron demand where the dienophile is electron rich and the diene is electron deficient.

For a normal electron demand DA reaction, the dienophile low-lying LUMO interacts with the diene HOMO which has a high energy. However, observing the energies of the reactants and the transition states, the MO diagram shows that this particular DA reaction has an inverse electron demand where the dienophile (1,3-dioxole) is electron rich (higher in energy) and the diene (cyclohexadiene) is electron poor (lower in energy). The interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene thus leads to the HOMO and LUMO of the transition state. Although opposing that of a normal electron demand DA, this reaction still follows the Woodword-Hoffman rule and is thermally allowed.

Similar to exercise 1, MOs of the same symmetry interact; the symmetrical dienophile HOMO and the diene LUMO interacts to give a symmetrical TS HOMO and LUMO, while the asymmetrical dienophile LUMO and diene HOMO gives the asymmetrical TS HOMO-1 and LUMO+1. It is also observable that the endo TS HOMO has a lower energy than the exo TS HOMO which suggests that the endo reaction is favoured. This will be discussed further in the Thermochemistry section of this exercise.

{| class="wikitable"
! ENDO TS - HOMO -1
! ENDO TS - HOMO
! ENDO TS - LUMO
! ENDO TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Log Files ====

[[File:Cc5115 ENDO B3.LOG]]

[[File:Cc5115 PLEASE WORK B3.LOG]]

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +149.70
| -77.52
|-
| Exo
| +157.52
| -73.92
|}

As discussed briefly in the introduction, the reactants need to pass the activation barrier (transition state) in order to reach to the products. The table regarding the reaction barriers and energies shows that the activation barrier for the endo reaction is less than that of the exo reaction, more-so confirming that the endo reaction is kinetically favoured. This links to the lower energy that the endo TS HOMO has compared to the exo TS. This observance can be explained by secondary orbital interation (SOI). The 2 non-bonding oxygen p-orbitals containing electron lone pairs can overlap with the LUMO of the diene through space thus stabilising the TS and consequentially lowering reaction barrier. However, the more negative reaction energy of the endo reaction can be explained with sterics; in the exo transition state, the steric interaction between the sp<sup>3</sup> bridging carbons and the rest of the 1,3-dioxole structure results in the exo product being higher in energy.

{| class="wikitable"
! Exo Secondary MO
! Endo Secondary MO
|-
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

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

=== IRC ===

{| class="wikitable"
! [[File:Cc5115 Exo IRC gif.gif|thumb|x500px|500px|left|IRC for Exo Product]]
! [[File:Cc5115 Endo IRC gif.gif|thumb|x500px|500px|left|IRC for Endo Product]]
! [[File:Chelatropic IRC gif.gif|thumb|x500px|500px|left|IRC for Chelatropic Product]]
|}

IRC (intrinsic reaction coordinate) show how reactions move in space during its reaction to form products. From the IRC animations, it can be seen that the formation of the new bonds differ to that of exercise 1. Here, in the exo and endo pathways, the formation of the 2 new bonds are asynchronous as one bond forms before the other. However, the bonds form synchronously in the chelatropic reaction leading to the symmetrical product.

The IRC reaction pathways also show a smaller activation barrier compared to that of exercise 1. This is because xylylene is highly unstable. Xylylene can exist with 4π electrons making it anti-aromatic, or either with 6π electrons an a diradical which is very unstable. On the flipside, the product formed is aromatic making the DA reaction extremely favourable. Naphthalene forces the diene to be rigid in its positions easing the overlap capabilities of the diene with the dienophile. This can be observed in the animation as naphthalene doesn't have to go through major rearrangements in order to form the products.

In the reaction, naphthalene initially has a C=C bond length of 1.35 Å and a C-C bond length averaging around 1.51 Å. This changes as the product is formed where all the carbon-carbon bonds on the 6 membered rings become 1.47 Å in length suggesting the formation of an aromatic 6-membered ring where the π electrons are delocalised throughout the ring. The change in bond length can also be seen with careful observation of the animations.

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +79.85
|
|-
| Exo
| +83.82
|
|-
| Chelatropic
| +102.16
|
|}

Significantly resembling to exercise 2, exercise 3 features the endo pathway being kinetically favoured as its activation energy has the least energy compared to the other pathway. Again, this is due to the overlap between the oxygen p-orbitals overlapping with the π-orbitals of the xylylene ring. However, the difference in activation and reaction energies between the exo and endo pathways do not differ that much due to the SOI not contributing significantly in the TS and there are little steric difference between the two products. For the chelatropic product, there is a hugh drop in reaction energy. Observing the product, the large sulfur atom forming a 5-membered ring decreases the ring-strain making the product relatively stable compared to the products from the DA reaction.

=== Cyclisation at the other reaction site ===

{| class="wikitable"
! [[File:Cc5115 IRC exo reaction site b.gif|thumb|x500px|500px|left|IRC for Exo Product at reaction site B]]
! [[File:Cc5115 IRC endo reaction site b.gif|thumb|x500px|500px|left|IRC for Endo Product at reaction site B]]
|}

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +110.06
|
|-
| Exo
| +117.90
|
|}

For this exercise, the Diels-Alder reaction can also take place at the other reaction site as illustrated in the animations.

== Conclusion ==

Gaussian was used to calculate the geometries of the transition states using the PM6 and the B3LYP methods. The TS was validated by a correct imaginary frequency from frequency calculations as well as the correct pathways along the reaction coordinate from IRC.

Rep:Mod:cc5115TS

2018-02-14T03:43:03Z

Cc5115: /* Cyclisation at the other reaction site */

= Y3C Transition states and Reactivity =

== Introduction ==

This section aims to illustrate the 3 different computational techniques that can be utilised in order to analyse the transition state (TS) of a reaction. The TS is the state which has the highest energy along a reaction coordinate, as a result it is the least stable state. In the reaction, the reactants needs to have a certain amount of energy in order to surpass the activation barrier, also known as the transition state energy, and reach the product state. This computational lab allows for calculations leading to the location of the TS. The structure of the TS is crucial in determining the mechanism of a reaction.

A potential energy surface (PES) has a 3N-6 dimension, which coincides to the degrees of freedom that the molecule has, where N is the number of atoms that the molecule possesses. In a 3-D PES, the saddle point (also called the TS), is a local mixami amidst 2 minima, and can be sometimes identified through secondary derivatives as it would be negative in one direction and positive in all other directions.

There are 3 calculation methods available in order to determine the structure of the TS.

1. The first and fastest method requires only one step where a guessed structure of the TS is optimised to give an optimised TS. This means that one will need of the TS to quite an extent, furthermore this method is rather unreliable as there is a high chance that the guessed TS is incorrectly drawn.

2. The second method works from a pre-frozen guess structure of the TS where the reacting termini of the reactants are frozen in space before the remaining structure is optimised to a minima. After that, the molecules are optimised as a transition state. This allows for a more reliable representation of the TS. This method is sufficient for Exercise 1.

3. The third method is the longest and most reliable method. Here, one starts by either optimising from the reactants or the products to a minima. For the reactant case, each reactants are optimised to a minima, arranged to resemble the TS and the reacting termini are frozen and the rest of the method 2 is repeated. A similar case occurs with the product; when the product is optimised to a minima, the bonds formed in the reactions are removed, the 2 fragments are arranged to resemble the TS and the reacting termini are frozen and method 2 was used once more. This method allows for the most reliable representation of the TS and is used for Exercise 2 & 3.

In this computational lab, two methods of calculation were used on Gaussian in order to find the TS. During the optimisation, the position of the molecule is decided as it is built in Gaussian. The time-independent Schrödinger equation was solved whilst utilising the Born-Oppenheimer approximation in order to find the energy and the wavefunction φ which represents the electronic states for the fixed nuclear positions and is dependent on on frozen nuclei positions. This is also known as the self-consistent field method (SCF). The two methods employed are the semi-empirical method PM6, which is usually performed first and sometimes followed by the Density Functional Theory (DFT) method B3LYP. The semi-empirical method PM6, although based on the Hartree-Fock formalism, this method uses many approximations based on experimental data in order to solve the Schrodinger equations. This method is usually fast and reliable, but can be easily countered if the environment of the molecule that is being computed is not similar enough to the approximated parameters of this method. The other method is B3LYP, a hydrid functional which utilises the DFT in order to calculate the majority of the Hamiltonian while a small portion still utilises the Hartree-Fock theory to calculate the exchange integral term. B3LYP stands for Becke, 3-parameter, Lee-Yang-Parr and uses a 6-31G basis set as the electronic wavefunction in order to produce more accurate results at the cost of increased calculation time.

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

[[File:Ex1 general.png|thumb|x700px|700px|centre|Figure 1: Formation of Cyclohaxadiene]]

Also known as the Diels-Alder reaction, this exercise investigates the well-known [4+2] cycloaddition between a conjugated diene (butadiene) and a dienophile (ethylene). The electrophilic reaction involves 4 pi-electrons from the diene and 2 pi-electrons from the alkene, and is a popular method to form regio- and stereochemically controlled 6-membered rings.

Method 2 was used to compute the transition state (TS) for this exercise. All steps are optimised to the PM6 level. First, the reactants are optimised to a minimum. The carbons at the reacting termini were then frozen at around 2.20 Å before optimised to a minimum to give a frozen-guess TS. Then finally, the molecule was optimised as a TS and an IRC was performed in order to confirm and locate the transition state.

=== Analysis of the Molecular Orbitals (MO) ===

The Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) for the reactants and the TS are shown below and its energies were recorded in order to produce the MO diagram as shown in figure 2.

{| class="wikitable"
! Ethene - HOMO
! Ethene - LUMO
! Butadiene - HOMO
! Butadiene - LUMO
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Cc5115 exer1finalMO.png|thumb|x800px|800px|left|Figure 2: MO Diagram for the formation of Transition State of the Diels-Alder Reaction]]

The symmetric TS HOMO and LUMO are formed through the interactions between the HOMO of ethylene and the LUMO of butadiene, both of which are symmetric. On the other hand, the LUMO of ethylene and the HOMO of butadiene, both of which are asymmetric, interacts to give an asymmetric HOMO-1 and LUMO+1. What can be concluded about the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed, and that the reaction is forbidden when the symmetry of the molecular orbitals aren't the same. The orbital overlap integral, S<sub>AB</sub>, is a quantitative measure of orbital overlap of two different atoms. Orbitals of the same symmetry will lead to constructive overlap and gives a non-zero value while orbitals of different symmetry will lead to destructive overlap and an orbital overlap integral of zero. Thus the overlap integral are:

- Non-zero for symmetric-symmetric interaction

- Non-zero for asymmetric-asymmetric interaction

- Zero for symmetric-asymmetric interaction

As observed in the MO diagram, the energy gap between the HOMO and LUMO for butadiene is smaller that those for ethylene due to butadiene being more electron rich than ethylene. Furthermore, in a normal MO diagram, the bonding MO formed should have a lower energy compared to both atomic orbitals (AO) whilst the anti-bonding MO formed should have a higher energy than both AOs. The reason why figure 3 goes against the tide is because the MOs formed corresponds to the transition state where the electrons are very delocalised within the chemical environment of the molecule.

==== LOG Files ====

[[:File:Cc5115_ETHENE_MO.LOG]]

[[:File:Cc5115_BUTADIENE_MO.LOG]]

[[:File:Cc5115_OPT_MO.LOG]]

=== Analysis of the C-C bond lengths ===

{| class="wikitable"
! Bond Lengths (Å)
! C1-C2
! C2-C3
! C3-C4
! C4-C5
! C5-C6
! C6-C1
|-
| Ethylene
|
|
|
|
| 1.36
|
|-
| Butadiene
| 1.36
| 1.54
| 1.36
|
|
|
|-
| Transition State
| 1.38
| 1.41
| 1.38
| 2.11
| 1.38
| 2.12
|-
| Cyclohexadiene
| 1.49
| 1.33
| 1.49
| 1.54
| 1.54
| 1.54
|}

The numbering of the carbon bonds are according to the labels on figure 1. The typical C-C bond lengths are as follows:

{| class="wikitable"
! Bond Type
! Bond Length (Å)
|-
| sp<sup>3</sup>-sp<sup>3</sup> C-C bond
| 1.54
|-
| sp<sup>3</sup>-sp<sup>2</sup> C-C bond
| 1.50
|-
| sp<sup>2</sup>-sp<sup>2</sup> C-C bond
| 1.47
|-
| sp<sup>2</sup>-sp<sup>2</sup> C=C bond
| 1.34
|}

When the reaction proceeds to the transition state, the sp<sup>2</sup>-sp<sup>2</sup> C5-C6 bond (originally ethylene) becomes longer as the carbons starts to change from sp<sup>2</sup> hybridised to sp<sup>3</sup> hybridised.
This trait is also apparent with C1-C2 and C3-C4 bonds where it once was the double bonds on butadiene, however, the increase in length of these bonds is less than that of C5-C6 due to the formation of a new double bond between C2 and C3, thus these carbons still remain sp<sup>2</sup> hybridised. This also leads to the next observation, where the C2-C3 bond decreases in length as it moves from the reactants to the transition state then the product, cyclohexadiene. This is because it is changing from a sp<sup>3</sup>-sp<sup>3</sup> C-C bond to a sp<sup>2</sup>-sp<sup>2</sup> C=C bond where the increase in s character shortens the bond lengths. This reaction also leads to the formation of 2 new bonds, namely C4-C5 and C6-C1. The Van der Waals radius of a carbon atom is 1.7 Å, and so the distance between 2 carbon atoms should be 3.4 Å, which is relatively longer than the bonds C4-C5 and C6-C1 which has a length of 2.11 and 2.12 Å respectively. This shows that the bonds are already partially formed in the transition state and they are beginning to interact together. This bond then settled at 1.54 Å in the product which matches with the typical bond length for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond.

=== Analysis of the vibrations ===

The animation for the first vibration is shown below. As observed, the formation of the 2 new bonds are synchronous as the reacting termini of butadiene and ethylene approaches each other at the same rate.

{| class="wikitable"
! <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 2;rotate x -20; </script>
<uploadedFileContents>Cc5115 OPT MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| The vibrations
|}

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

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via either the endo or exo pathways to form 2 products with different stereochemistry. Method 3 was employed in order to compute the TS for this exercise. This time, the structures were further optimised with B3LYP/6-31G method and the results are shown and discussed below.

=== Analysis of Molecular Orbitals ===

There are two types of Diels-Alder (DA) reactions: one is with a normal electron demand where the dienophile is electron deficient and the diene is electron rich, and the other is with an inverse electron demand where the dienophile is electron rich and the diene is electron deficient.

For a normal electron demand DA reaction, the dienophile low-lying LUMO interacts with the diene HOMO which has a high energy. However, observing the energies of the reactants and the transition states, the MO diagram shows that this particular DA reaction has an inverse electron demand where the dienophile (1,3-dioxole) is electron rich (higher in energy) and the diene (cyclohexadiene) is electron poor (lower in energy). The interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene thus leads to the HOMO and LUMO of the transition state. Although opposing that of a normal electron demand DA, this reaction still follows the Woodword-Hoffman rule and is thermally allowed.

Similar to exercise 1, MOs of the same symmetry interact; the symmetrical dienophile HOMO and the diene LUMO interacts to give a symmetrical TS HOMO and LUMO, while the asymmetrical dienophile LUMO and diene HOMO gives the asymmetrical TS HOMO-1 and LUMO+1. It is also observable that the endo TS HOMO has a lower energy than the exo TS HOMO which suggests that the endo reaction is favoured. This will be discussed further in the Thermochemistry section of this exercise.

{| class="wikitable"
! ENDO TS - HOMO -1
! ENDO TS - HOMO
! ENDO TS - LUMO
! ENDO TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Log Files ====

[[File:Cc5115 ENDO B3.LOG]]

[[File:Cc5115 PLEASE WORK B3.LOG]]

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +149.70
| -77.52
|-
| Exo
| +157.52
| -73.92
|}

As discussed briefly in the introduction, the reactants need to pass the activation barrier (transition state) in order to reach to the products. The table regarding the reaction barriers and energies shows that the activation barrier for the endo reaction is less than that of the exo reaction, more-so confirming that the endo reaction is kinetically favoured. This links to the lower energy that the endo TS HOMO has compared to the exo TS. This observance can be explained by secondary orbital interation (SOI). The 2 non-bonding oxygen p-orbitals containing electron lone pairs can overlap with the LUMO of the diene through space thus stabilising the TS and consequentially lowering reaction barrier. However, the more negative reaction energy of the endo reaction can be explained with sterics; in the exo transition state, the steric interaction between the sp<sup>3</sup> bridging carbons and the rest of the 1,3-dioxole structure results in the exo product being higher in energy.

{| class="wikitable"
! Exo Secondary MO
! Endo Secondary MO
|-
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

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

=== IRC ===

{| class="wikitable"
! [[File:Cc5115 Exo IRC gif.gif|thumb|x500px|500px|left|IRC for Exo Product]]
! [[File:Cc5115 Endo IRC gif.gif|thumb|x500px|500px|left|IRC for Endo Product]]
! [[File:Chelatropic IRC gif.gif|thumb|x500px|500px|left|IRC for Chelatropic Product]]
|}

IRC (intrinsic reaction coordinate) show how reactions move in space during its reaction to form products. From the IRC animations, it can be seen that the formation of the new bonds differ to that of exercise 1. Here, in the exo and endo pathways, the formation of the 2 new bonds are asynchronous as one bond forms before the other. However, the bonds form synchronously in the chelatropic reaction leading to the symmetrical product.

The IRC reaction pathways also show a smaller activation barrier compared to that of exercise 1. This is because xylylene is highly unstable. Xylylene can exist with 4π electrons making it anti-aromatic, or either with 6π electrons an a diradical which is very unstable. On the flipside, the product formed is aromatic making the DA reaction extremely favourable. Naphthalene forces the diene to be rigid in its positions easing the overlap capabilities of the diene with the dienophile. This can be observed in the animation as naphthalene doesn't have to go through major rearrangements in order to form the products.

In the reaction, naphthalene initially has a C=C bond length of 1.35 Å and a C-C bond length averaging around 1.51 Å. This changes as the product is formed where all the carbon-carbon bonds on the 6 membered rings become 1.47 Å in length suggesting the formation of an aromatic 6-membered ring where the π electrons are delocalised throughout the ring. The change in bond length can also be seen with careful observation of the animations.

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +79.85
|
|-
| Exo
| +83.82
|
|-
| Chelatropic
| +102.16
|
|}

Significantly resembling to exercise 2, exercise 3 features the endo pathway being kinetically favoured as its activation energy has the least energy compared to the other pathway. Again, this is due to the overlap between the oxygen p-orbitals overlapping with the π-orbitals of the xylylene ring. However, the difference in activation and reaction energies between the exo and endo pathways do not differ that much due to the SOI not contributing significantly in the TS and there are little steric difference between the two products. For the chelatropic product, there is a hugh drop in reaction energy. Observing the product, the large sulfur atom forming a 5-membered ring decreases the ring-strain making the product relatively stable compared to the products from the DA reaction.

=== Cyclisation at the other reaction site ===

{| class="wikitable"
! [[File:Cc5115 IRC exo reaction site b.gif|thumb|x500px|500px|left|IRC for Exo Product at reaction site B]]
! [[File:Cc5115 IRC endo reaction site b.gif|thumb|x500px|500px|left|IRC for Endo Product at reaction site B]]
|}

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +110.06
|
|-
| Exo
| +117.90
|
|}

For this exercise, the Diels-Alder reaction can also take place at the other reaction site as illustrated in the animations.

== Conclusion ==

Rep:Mod:cc5115TS

2018-02-14T03:42:29Z

Cc5115: /* Cyclisation at the other reaction site */

= Y3C Transition states and Reactivity =

== Introduction ==

This section aims to illustrate the 3 different computational techniques that can be utilised in order to analyse the transition state (TS) of a reaction. The TS is the state which has the highest energy along a reaction coordinate, as a result it is the least stable state. In the reaction, the reactants needs to have a certain amount of energy in order to surpass the activation barrier, also known as the transition state energy, and reach the product state. This computational lab allows for calculations leading to the location of the TS. The structure of the TS is crucial in determining the mechanism of a reaction.

A potential energy surface (PES) has a 3N-6 dimension, which coincides to the degrees of freedom that the molecule has, where N is the number of atoms that the molecule possesses. In a 3-D PES, the saddle point (also called the TS), is a local mixami amidst 2 minima, and can be sometimes identified through secondary derivatives as it would be negative in one direction and positive in all other directions.

There are 3 calculation methods available in order to determine the structure of the TS.

1. The first and fastest method requires only one step where a guessed structure of the TS is optimised to give an optimised TS. This means that one will need of the TS to quite an extent, furthermore this method is rather unreliable as there is a high chance that the guessed TS is incorrectly drawn.

2. The second method works from a pre-frozen guess structure of the TS where the reacting termini of the reactants are frozen in space before the remaining structure is optimised to a minima. After that, the molecules are optimised as a transition state. This allows for a more reliable representation of the TS. This method is sufficient for Exercise 1.

3. The third method is the longest and most reliable method. Here, one starts by either optimising from the reactants or the products to a minima. For the reactant case, each reactants are optimised to a minima, arranged to resemble the TS and the reacting termini are frozen and the rest of the method 2 is repeated. A similar case occurs with the product; when the product is optimised to a minima, the bonds formed in the reactions are removed, the 2 fragments are arranged to resemble the TS and the reacting termini are frozen and method 2 was used once more. This method allows for the most reliable representation of the TS and is used for Exercise 2 & 3.

In this computational lab, two methods of calculation were used on Gaussian in order to find the TS. During the optimisation, the position of the molecule is decided as it is built in Gaussian. The time-independent Schrödinger equation was solved whilst utilising the Born-Oppenheimer approximation in order to find the energy and the wavefunction φ which represents the electronic states for the fixed nuclear positions and is dependent on on frozen nuclei positions. This is also known as the self-consistent field method (SCF). The two methods employed are the semi-empirical method PM6, which is usually performed first and sometimes followed by the Density Functional Theory (DFT) method B3LYP. The semi-empirical method PM6, although based on the Hartree-Fock formalism, this method uses many approximations based on experimental data in order to solve the Schrodinger equations. This method is usually fast and reliable, but can be easily countered if the environment of the molecule that is being computed is not similar enough to the approximated parameters of this method. The other method is B3LYP, a hydrid functional which utilises the DFT in order to calculate the majority of the Hamiltonian while a small portion still utilises the Hartree-Fock theory to calculate the exchange integral term. B3LYP stands for Becke, 3-parameter, Lee-Yang-Parr and uses a 6-31G basis set as the electronic wavefunction in order to produce more accurate results at the cost of increased calculation time.

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

[[File:Ex1 general.png|thumb|x700px|700px|centre|Figure 1: Formation of Cyclohaxadiene]]

Also known as the Diels-Alder reaction, this exercise investigates the well-known [4+2] cycloaddition between a conjugated diene (butadiene) and a dienophile (ethylene). The electrophilic reaction involves 4 pi-electrons from the diene and 2 pi-electrons from the alkene, and is a popular method to form regio- and stereochemically controlled 6-membered rings.

Method 2 was used to compute the transition state (TS) for this exercise. All steps are optimised to the PM6 level. First, the reactants are optimised to a minimum. The carbons at the reacting termini were then frozen at around 2.20 Å before optimised to a minimum to give a frozen-guess TS. Then finally, the molecule was optimised as a TS and an IRC was performed in order to confirm and locate the transition state.

=== Analysis of the Molecular Orbitals (MO) ===

The Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) for the reactants and the TS are shown below and its energies were recorded in order to produce the MO diagram as shown in figure 2.

{| class="wikitable"
! Ethene - HOMO
! Ethene - LUMO
! Butadiene - HOMO
! Butadiene - LUMO
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Cc5115 exer1finalMO.png|thumb|x800px|800px|left|Figure 2: MO Diagram for the formation of Transition State of the Diels-Alder Reaction]]

The symmetric TS HOMO and LUMO are formed through the interactions between the HOMO of ethylene and the LUMO of butadiene, both of which are symmetric. On the other hand, the LUMO of ethylene and the HOMO of butadiene, both of which are asymmetric, interacts to give an asymmetric HOMO-1 and LUMO+1. What can be concluded about the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed, and that the reaction is forbidden when the symmetry of the molecular orbitals aren't the same. The orbital overlap integral, S<sub>AB</sub>, is a quantitative measure of orbital overlap of two different atoms. Orbitals of the same symmetry will lead to constructive overlap and gives a non-zero value while orbitals of different symmetry will lead to destructive overlap and an orbital overlap integral of zero. Thus the overlap integral are:

- Non-zero for symmetric-symmetric interaction

- Non-zero for asymmetric-asymmetric interaction

- Zero for symmetric-asymmetric interaction

As observed in the MO diagram, the energy gap between the HOMO and LUMO for butadiene is smaller that those for ethylene due to butadiene being more electron rich than ethylene. Furthermore, in a normal MO diagram, the bonding MO formed should have a lower energy compared to both atomic orbitals (AO) whilst the anti-bonding MO formed should have a higher energy than both AOs. The reason why figure 3 goes against the tide is because the MOs formed corresponds to the transition state where the electrons are very delocalised within the chemical environment of the molecule.

==== LOG Files ====

[[:File:Cc5115_ETHENE_MO.LOG]]

[[:File:Cc5115_BUTADIENE_MO.LOG]]

[[:File:Cc5115_OPT_MO.LOG]]

=== Analysis of the C-C bond lengths ===

{| class="wikitable"
! Bond Lengths (Å)
! C1-C2
! C2-C3
! C3-C4
! C4-C5
! C5-C6
! C6-C1
|-
| Ethylene
|
|
|
|
| 1.36
|
|-
| Butadiene
| 1.36
| 1.54
| 1.36
|
|
|
|-
| Transition State
| 1.38
| 1.41
| 1.38
| 2.11
| 1.38
| 2.12
|-
| Cyclohexadiene
| 1.49
| 1.33
| 1.49
| 1.54
| 1.54
| 1.54
|}

The numbering of the carbon bonds are according to the labels on figure 1. The typical C-C bond lengths are as follows:

{| class="wikitable"
! Bond Type
! Bond Length (Å)
|-
| sp<sup>3</sup>-sp<sup>3</sup> C-C bond
| 1.54
|-
| sp<sup>3</sup>-sp<sup>2</sup> C-C bond
| 1.50
|-
| sp<sup>2</sup>-sp<sup>2</sup> C-C bond
| 1.47
|-
| sp<sup>2</sup>-sp<sup>2</sup> C=C bond
| 1.34
|}

When the reaction proceeds to the transition state, the sp<sup>2</sup>-sp<sup>2</sup> C5-C6 bond (originally ethylene) becomes longer as the carbons starts to change from sp<sup>2</sup> hybridised to sp<sup>3</sup> hybridised.
This trait is also apparent with C1-C2 and C3-C4 bonds where it once was the double bonds on butadiene, however, the increase in length of these bonds is less than that of C5-C6 due to the formation of a new double bond between C2 and C3, thus these carbons still remain sp<sup>2</sup> hybridised. This also leads to the next observation, where the C2-C3 bond decreases in length as it moves from the reactants to the transition state then the product, cyclohexadiene. This is because it is changing from a sp<sup>3</sup>-sp<sup>3</sup> C-C bond to a sp<sup>2</sup>-sp<sup>2</sup> C=C bond where the increase in s character shortens the bond lengths. This reaction also leads to the formation of 2 new bonds, namely C4-C5 and C6-C1. The Van der Waals radius of a carbon atom is 1.7 Å, and so the distance between 2 carbon atoms should be 3.4 Å, which is relatively longer than the bonds C4-C5 and C6-C1 which has a length of 2.11 and 2.12 Å respectively. This shows that the bonds are already partially formed in the transition state and they are beginning to interact together. This bond then settled at 1.54 Å in the product which matches with the typical bond length for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond.

=== Analysis of the vibrations ===

The animation for the first vibration is shown below. As observed, the formation of the 2 new bonds are synchronous as the reacting termini of butadiene and ethylene approaches each other at the same rate.

{| class="wikitable"
! <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 2;rotate x -20; </script>
<uploadedFileContents>Cc5115 OPT MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| The vibrations
|}

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

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via either the endo or exo pathways to form 2 products with different stereochemistry. Method 3 was employed in order to compute the TS for this exercise. This time, the structures were further optimised with B3LYP/6-31G method and the results are shown and discussed below.

=== Analysis of Molecular Orbitals ===

There are two types of Diels-Alder (DA) reactions: one is with a normal electron demand where the dienophile is electron deficient and the diene is electron rich, and the other is with an inverse electron demand where the dienophile is electron rich and the diene is electron deficient.

For a normal electron demand DA reaction, the dienophile low-lying LUMO interacts with the diene HOMO which has a high energy. However, observing the energies of the reactants and the transition states, the MO diagram shows that this particular DA reaction has an inverse electron demand where the dienophile (1,3-dioxole) is electron rich (higher in energy) and the diene (cyclohexadiene) is electron poor (lower in energy). The interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene thus leads to the HOMO and LUMO of the transition state. Although opposing that of a normal electron demand DA, this reaction still follows the Woodword-Hoffman rule and is thermally allowed.

Similar to exercise 1, MOs of the same symmetry interact; the symmetrical dienophile HOMO and the diene LUMO interacts to give a symmetrical TS HOMO and LUMO, while the asymmetrical dienophile LUMO and diene HOMO gives the asymmetrical TS HOMO-1 and LUMO+1. It is also observable that the endo TS HOMO has a lower energy than the exo TS HOMO which suggests that the endo reaction is favoured. This will be discussed further in the Thermochemistry section of this exercise.

{| class="wikitable"
! ENDO TS - HOMO -1
! ENDO TS - HOMO
! ENDO TS - LUMO
! ENDO TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Log Files ====

[[File:Cc5115 ENDO B3.LOG]]

[[File:Cc5115 PLEASE WORK B3.LOG]]

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +149.70
| -77.52
|-
| Exo
| +157.52
| -73.92
|}

As discussed briefly in the introduction, the reactants need to pass the activation barrier (transition state) in order to reach to the products. The table regarding the reaction barriers and energies shows that the activation barrier for the endo reaction is less than that of the exo reaction, more-so confirming that the endo reaction is kinetically favoured. This links to the lower energy that the endo TS HOMO has compared to the exo TS. This observance can be explained by secondary orbital interation (SOI). The 2 non-bonding oxygen p-orbitals containing electron lone pairs can overlap with the LUMO of the diene through space thus stabilising the TS and consequentially lowering reaction barrier. However, the more negative reaction energy of the endo reaction can be explained with sterics; in the exo transition state, the steric interaction between the sp<sup>3</sup> bridging carbons and the rest of the 1,3-dioxole structure results in the exo product being higher in energy.

{| class="wikitable"
! Exo Secondary MO
! Endo Secondary MO
|-
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

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

=== IRC ===

{| class="wikitable"
! [[File:Cc5115 Exo IRC gif.gif|thumb|x500px|500px|left|IRC for Exo Product]]
! [[File:Cc5115 Endo IRC gif.gif|thumb|x500px|500px|left|IRC for Endo Product]]
! [[File:Chelatropic IRC gif.gif|thumb|x500px|500px|left|IRC for Chelatropic Product]]
|}

IRC (intrinsic reaction coordinate) show how reactions move in space during its reaction to form products. From the IRC animations, it can be seen that the formation of the new bonds differ to that of exercise 1. Here, in the exo and endo pathways, the formation of the 2 new bonds are asynchronous as one bond forms before the other. However, the bonds form synchronously in the chelatropic reaction leading to the symmetrical product.

The IRC reaction pathways also show a smaller activation barrier compared to that of exercise 1. This is because xylylene is highly unstable. Xylylene can exist with 4π electrons making it anti-aromatic, or either with 6π electrons an a diradical which is very unstable. On the flipside, the product formed is aromatic making the DA reaction extremely favourable. Naphthalene forces the diene to be rigid in its positions easing the overlap capabilities of the diene with the dienophile. This can be observed in the animation as naphthalene doesn't have to go through major rearrangements in order to form the products.

In the reaction, naphthalene initially has a C=C bond length of 1.35 Å and a C-C bond length averaging around 1.51 Å. This changes as the product is formed where all the carbon-carbon bonds on the 6 membered rings become 1.47 Å in length suggesting the formation of an aromatic 6-membered ring where the π electrons are delocalised throughout the ring. The change in bond length can also be seen with careful observation of the animations.

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +79.85
|
|-
| Exo
| +83.82
|
|-
| Chelatropic
| +102.16
|
|}

Significantly resembling to exercise 2, exercise 3 features the endo pathway being kinetically favoured as its activation energy has the least energy compared to the other pathway. Again, this is due to the overlap between the oxygen p-orbitals overlapping with the π-orbitals of the xylylene ring. However, the difference in activation and reaction energies between the exo and endo pathways do not differ that much due to the SOI not contributing significantly in the TS and there are little steric difference between the two products. For the chelatropic product, there is a hugh drop in reaction energy. Observing the product, the large sulfur atom forming a 5-membered ring decreases the ring-strain making the product relatively stable compared to the products from the DA reaction.

=== Cyclisation at the other reaction site ===

{| class="wikitable"
! [[File:Cc5115 IRC exo reaction site b.gif|thumb|x500px|500px|left|IRC for Exo Product at reaction site B]]
! [[File:Cc5115 IRC endo reaction site b.gif|thumb|x500px|500px|left|IRC for Endo Product at reaction site B]]
|}

For this exercise, the Diels-Alder reaction can also take place at the other reaction site as illustrated in the animations.

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +110.06
|
|-
| Exo
| +117.90
|
|}

== Conclusion ==

Rep:Mod:cc5115TS

2018-02-14T03:40:20Z

Cc5115: /* Exercise 3: Diels-Alder vs Cheletropic */

= Y3C Transition states and Reactivity =

== Introduction ==

This section aims to illustrate the 3 different computational techniques that can be utilised in order to analyse the transition state (TS) of a reaction. The TS is the state which has the highest energy along a reaction coordinate, as a result it is the least stable state. In the reaction, the reactants needs to have a certain amount of energy in order to surpass the activation barrier, also known as the transition state energy, and reach the product state. This computational lab allows for calculations leading to the location of the TS. The structure of the TS is crucial in determining the mechanism of a reaction.

A potential energy surface (PES) has a 3N-6 dimension, which coincides to the degrees of freedom that the molecule has, where N is the number of atoms that the molecule possesses. In a 3-D PES, the saddle point (also called the TS), is a local mixami amidst 2 minima, and can be sometimes identified through secondary derivatives as it would be negative in one direction and positive in all other directions.

There are 3 calculation methods available in order to determine the structure of the TS.

1. The first and fastest method requires only one step where a guessed structure of the TS is optimised to give an optimised TS. This means that one will need of the TS to quite an extent, furthermore this method is rather unreliable as there is a high chance that the guessed TS is incorrectly drawn.

2. The second method works from a pre-frozen guess structure of the TS where the reacting termini of the reactants are frozen in space before the remaining structure is optimised to a minima. After that, the molecules are optimised as a transition state. This allows for a more reliable representation of the TS. This method is sufficient for Exercise 1.

3. The third method is the longest and most reliable method. Here, one starts by either optimising from the reactants or the products to a minima. For the reactant case, each reactants are optimised to a minima, arranged to resemble the TS and the reacting termini are frozen and the rest of the method 2 is repeated. A similar case occurs with the product; when the product is optimised to a minima, the bonds formed in the reactions are removed, the 2 fragments are arranged to resemble the TS and the reacting termini are frozen and method 2 was used once more. This method allows for the most reliable representation of the TS and is used for Exercise 2 & 3.

In this computational lab, two methods of calculation were used on Gaussian in order to find the TS. During the optimisation, the position of the molecule is decided as it is built in Gaussian. The time-independent Schrödinger equation was solved whilst utilising the Born-Oppenheimer approximation in order to find the energy and the wavefunction φ which represents the electronic states for the fixed nuclear positions and is dependent on on frozen nuclei positions. This is also known as the self-consistent field method (SCF). The two methods employed are the semi-empirical method PM6, which is usually performed first and sometimes followed by the Density Functional Theory (DFT) method B3LYP. The semi-empirical method PM6, although based on the Hartree-Fock formalism, this method uses many approximations based on experimental data in order to solve the Schrodinger equations. This method is usually fast and reliable, but can be easily countered if the environment of the molecule that is being computed is not similar enough to the approximated parameters of this method. The other method is B3LYP, a hydrid functional which utilises the DFT in order to calculate the majority of the Hamiltonian while a small portion still utilises the Hartree-Fock theory to calculate the exchange integral term. B3LYP stands for Becke, 3-parameter, Lee-Yang-Parr and uses a 6-31G basis set as the electronic wavefunction in order to produce more accurate results at the cost of increased calculation time.

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

[[File:Ex1 general.png|thumb|x700px|700px|centre|Figure 1: Formation of Cyclohaxadiene]]

Also known as the Diels-Alder reaction, this exercise investigates the well-known [4+2] cycloaddition between a conjugated diene (butadiene) and a dienophile (ethylene). The electrophilic reaction involves 4 pi-electrons from the diene and 2 pi-electrons from the alkene, and is a popular method to form regio- and stereochemically controlled 6-membered rings.

Method 2 was used to compute the transition state (TS) for this exercise. All steps are optimised to the PM6 level. First, the reactants are optimised to a minimum. The carbons at the reacting termini were then frozen at around 2.20 Å before optimised to a minimum to give a frozen-guess TS. Then finally, the molecule was optimised as a TS and an IRC was performed in order to confirm and locate the transition state.

=== Analysis of the Molecular Orbitals (MO) ===

The Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) for the reactants and the TS are shown below and its energies were recorded in order to produce the MO diagram as shown in figure 2.

{| class="wikitable"
! Ethene - HOMO
! Ethene - LUMO
! Butadiene - HOMO
! Butadiene - LUMO
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Cc5115 exer1finalMO.png|thumb|x800px|800px|left|Figure 2: MO Diagram for the formation of Transition State of the Diels-Alder Reaction]]

The symmetric TS HOMO and LUMO are formed through the interactions between the HOMO of ethylene and the LUMO of butadiene, both of which are symmetric. On the other hand, the LUMO of ethylene and the HOMO of butadiene, both of which are asymmetric, interacts to give an asymmetric HOMO-1 and LUMO+1. What can be concluded about the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed, and that the reaction is forbidden when the symmetry of the molecular orbitals aren't the same. The orbital overlap integral, S<sub>AB</sub>, is a quantitative measure of orbital overlap of two different atoms. Orbitals of the same symmetry will lead to constructive overlap and gives a non-zero value while orbitals of different symmetry will lead to destructive overlap and an orbital overlap integral of zero. Thus the overlap integral are:

- Non-zero for symmetric-symmetric interaction

- Non-zero for asymmetric-asymmetric interaction

- Zero for symmetric-asymmetric interaction

As observed in the MO diagram, the energy gap between the HOMO and LUMO for butadiene is smaller that those for ethylene due to butadiene being more electron rich than ethylene. Furthermore, in a normal MO diagram, the bonding MO formed should have a lower energy compared to both atomic orbitals (AO) whilst the anti-bonding MO formed should have a higher energy than both AOs. The reason why figure 3 goes against the tide is because the MOs formed corresponds to the transition state where the electrons are very delocalised within the chemical environment of the molecule.

==== LOG Files ====

[[:File:Cc5115_ETHENE_MO.LOG]]

[[:File:Cc5115_BUTADIENE_MO.LOG]]

[[:File:Cc5115_OPT_MO.LOG]]

=== Analysis of the C-C bond lengths ===

{| class="wikitable"
! Bond Lengths (Å)
! C1-C2
! C2-C3
! C3-C4
! C4-C5
! C5-C6
! C6-C1
|-
| Ethylene
|
|
|
|
| 1.36
|
|-
| Butadiene
| 1.36
| 1.54
| 1.36
|
|
|
|-
| Transition State
| 1.38
| 1.41
| 1.38
| 2.11
| 1.38
| 2.12
|-
| Cyclohexadiene
| 1.49
| 1.33
| 1.49
| 1.54
| 1.54
| 1.54
|}

The numbering of the carbon bonds are according to the labels on figure 1. The typical C-C bond lengths are as follows:

{| class="wikitable"
! Bond Type
! Bond Length (Å)
|-
| sp<sup>3</sup>-sp<sup>3</sup> C-C bond
| 1.54
|-
| sp<sup>3</sup>-sp<sup>2</sup> C-C bond
| 1.50
|-
| sp<sup>2</sup>-sp<sup>2</sup> C-C bond
| 1.47
|-
| sp<sup>2</sup>-sp<sup>2</sup> C=C bond
| 1.34
|}

When the reaction proceeds to the transition state, the sp<sup>2</sup>-sp<sup>2</sup> C5-C6 bond (originally ethylene) becomes longer as the carbons starts to change from sp<sup>2</sup> hybridised to sp<sup>3</sup> hybridised.
This trait is also apparent with C1-C2 and C3-C4 bonds where it once was the double bonds on butadiene, however, the increase in length of these bonds is less than that of C5-C6 due to the formation of a new double bond between C2 and C3, thus these carbons still remain sp<sup>2</sup> hybridised. This also leads to the next observation, where the C2-C3 bond decreases in length as it moves from the reactants to the transition state then the product, cyclohexadiene. This is because it is changing from a sp<sup>3</sup>-sp<sup>3</sup> C-C bond to a sp<sup>2</sup>-sp<sup>2</sup> C=C bond where the increase in s character shortens the bond lengths. This reaction also leads to the formation of 2 new bonds, namely C4-C5 and C6-C1. The Van der Waals radius of a carbon atom is 1.7 Å, and so the distance between 2 carbon atoms should be 3.4 Å, which is relatively longer than the bonds C4-C5 and C6-C1 which has a length of 2.11 and 2.12 Å respectively. This shows that the bonds are already partially formed in the transition state and they are beginning to interact together. This bond then settled at 1.54 Å in the product which matches with the typical bond length for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond.

=== Analysis of the vibrations ===

The animation for the first vibration is shown below. As observed, the formation of the 2 new bonds are synchronous as the reacting termini of butadiene and ethylene approaches each other at the same rate.

{| class="wikitable"
! <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 2;rotate x -20; </script>
<uploadedFileContents>Cc5115 OPT MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| The vibrations
|}

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

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via either the endo or exo pathways to form 2 products with different stereochemistry. Method 3 was employed in order to compute the TS for this exercise. This time, the structures were further optimised with B3LYP/6-31G method and the results are shown and discussed below.

=== Analysis of Molecular Orbitals ===

There are two types of Diels-Alder (DA) reactions: one is with a normal electron demand where the dienophile is electron deficient and the diene is electron rich, and the other is with an inverse electron demand where the dienophile is electron rich and the diene is electron deficient.

For a normal electron demand DA reaction, the dienophile low-lying LUMO interacts with the diene HOMO which has a high energy. However, observing the energies of the reactants and the transition states, the MO diagram shows that this particular DA reaction has an inverse electron demand where the dienophile (1,3-dioxole) is electron rich (higher in energy) and the diene (cyclohexadiene) is electron poor (lower in energy). The interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene thus leads to the HOMO and LUMO of the transition state. Although opposing that of a normal electron demand DA, this reaction still follows the Woodword-Hoffman rule and is thermally allowed.

Similar to exercise 1, MOs of the same symmetry interact; the symmetrical dienophile HOMO and the diene LUMO interacts to give a symmetrical TS HOMO and LUMO, while the asymmetrical dienophile LUMO and diene HOMO gives the asymmetrical TS HOMO-1 and LUMO+1. It is also observable that the endo TS HOMO has a lower energy than the exo TS HOMO which suggests that the endo reaction is favoured. This will be discussed further in the Thermochemistry section of this exercise.

{| class="wikitable"
! ENDO TS - HOMO -1
! ENDO TS - HOMO
! ENDO TS - LUMO
! ENDO TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Log Files ====

[[File:Cc5115 ENDO B3.LOG]]

[[File:Cc5115 PLEASE WORK B3.LOG]]

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +149.70
| -77.52
|-
| Exo
| +157.52
| -73.92
|}

As discussed briefly in the introduction, the reactants need to pass the activation barrier (transition state) in order to reach to the products. The table regarding the reaction barriers and energies shows that the activation barrier for the endo reaction is less than that of the exo reaction, more-so confirming that the endo reaction is kinetically favoured. This links to the lower energy that the endo TS HOMO has compared to the exo TS. This observance can be explained by secondary orbital interation (SOI). The 2 non-bonding oxygen p-orbitals containing electron lone pairs can overlap with the LUMO of the diene through space thus stabilising the TS and consequentially lowering reaction barrier. However, the more negative reaction energy of the endo reaction can be explained with sterics; in the exo transition state, the steric interaction between the sp<sup>3</sup> bridging carbons and the rest of the 1,3-dioxole structure results in the exo product being higher in energy.

{| class="wikitable"
! Exo Secondary MO
! Endo Secondary MO
|-
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

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

=== IRC ===

{| class="wikitable"
! [[File:Cc5115 Exo IRC gif.gif|thumb|x500px|500px|left|IRC for Exo Product]]
! [[File:Cc5115 Endo IRC gif.gif|thumb|x500px|500px|left|IRC for Endo Product]]
! [[File:Chelatropic IRC gif.gif|thumb|x500px|500px|left|IRC for Chelatropic Product]]
|}

IRC (intrinsic reaction coordinate) show how reactions move in space during its reaction to form products. From the IRC animations, it can be seen that the formation of the new bonds differ to that of exercise 1. Here, in the exo and endo pathways, the formation of the 2 new bonds are asynchronous as one bond forms before the other. However, the bonds form synchronously in the chelatropic reaction leading to the symmetrical product.

The IRC reaction pathways also show a smaller activation barrier compared to that of exercise 1. This is because xylylene is highly unstable. Xylylene can exist with 4π electrons making it anti-aromatic, or either with 6π electrons an a diradical which is very unstable. On the flipside, the product formed is aromatic making the DA reaction extremely favourable. Naphthalene forces the diene to be rigid in its positions easing the overlap capabilities of the diene with the dienophile. This can be observed in the animation as naphthalene doesn't have to go through major rearrangements in order to form the products.

In the reaction, naphthalene initially has a C=C bond length of 1.35 Å and a C-C bond length averaging around 1.51 Å. This changes as the product is formed where all the carbon-carbon bonds on the 6 membered rings become 1.47 Å in length suggesting the formation of an aromatic 6-membered ring where the π electrons are delocalised throughout the ring. The change in bond length can also be seen with careful observation of the animations.

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +79.85
|
|-
| Exo
| +83.82
|
|-
| Chelatropic
| +102.16
|
|}

Significantly resembling to exercise 2, exercise 3 features the endo pathway being kinetically favoured as its activation energy has the least energy compared to the other pathway. Again, this is due to the overlap between the oxygen p-orbitals overlapping with the π-orbitals of the xylylene ring. However, the difference in activation and reaction energies between the exo and endo pathways do not differ that much due to the SOI not contributing significantly in the TS and there are little steric difference between the two products. For the chelatropic product, there is a hugh drop in reaction energy. Observing the product, the large sulfur atom forming a 5-membered ring decreases the ring-strain making the product relatively stable compared to the products from the DA reaction.

=== Cyclisation at the other reaction site ===

{| class="wikitable"
! [[File:Cc5115 IRC exo reaction site b.gif|thumb|x500px|500px|left|IRC for Exo Product at reaction site B]]
! [[File:Cc5115 IRC endo reaction site b.gif|thumb|x500px|500px|left|IRC for Endo Product at reaction site B]]
|}

For this exercise, the Diels-Alder reaction can also take place at the other reaction site as illustrated in the animations.

== Conclusion ==

File:Cc5115 IRC endo reaction site b.gif

2018-02-14T03:39:58Z

Cc5115:

File:Cc5115 IRC exo reaction site b.gif

2018-02-14T03:39:20Z

Cc5115:

Rep:Mod:cc5115TS

2018-02-14T03:34:48Z

Cc5115: /* Thermochemistry */

= Y3C Transition states and Reactivity =

== Introduction ==

This section aims to illustrate the 3 different computational techniques that can be utilised in order to analyse the transition state (TS) of a reaction. The TS is the state which has the highest energy along a reaction coordinate, as a result it is the least stable state. In the reaction, the reactants needs to have a certain amount of energy in order to surpass the activation barrier, also known as the transition state energy, and reach the product state. This computational lab allows for calculations leading to the location of the TS. The structure of the TS is crucial in determining the mechanism of a reaction.

A potential energy surface (PES) has a 3N-6 dimension, which coincides to the degrees of freedom that the molecule has, where N is the number of atoms that the molecule possesses. In a 3-D PES, the saddle point (also called the TS), is a local mixami amidst 2 minima, and can be sometimes identified through secondary derivatives as it would be negative in one direction and positive in all other directions.

There are 3 calculation methods available in order to determine the structure of the TS.

1. The first and fastest method requires only one step where a guessed structure of the TS is optimised to give an optimised TS. This means that one will need of the TS to quite an extent, furthermore this method is rather unreliable as there is a high chance that the guessed TS is incorrectly drawn.

2. The second method works from a pre-frozen guess structure of the TS where the reacting termini of the reactants are frozen in space before the remaining structure is optimised to a minima. After that, the molecules are optimised as a transition state. This allows for a more reliable representation of the TS. This method is sufficient for Exercise 1.

3. The third method is the longest and most reliable method. Here, one starts by either optimising from the reactants or the products to a minima. For the reactant case, each reactants are optimised to a minima, arranged to resemble the TS and the reacting termini are frozen and the rest of the method 2 is repeated. A similar case occurs with the product; when the product is optimised to a minima, the bonds formed in the reactions are removed, the 2 fragments are arranged to resemble the TS and the reacting termini are frozen and method 2 was used once more. This method allows for the most reliable representation of the TS and is used for Exercise 2 & 3.

In this computational lab, two methods of calculation were used on Gaussian in order to find the TS. During the optimisation, the position of the molecule is decided as it is built in Gaussian. The time-independent Schrödinger equation was solved whilst utilising the Born-Oppenheimer approximation in order to find the energy and the wavefunction φ which represents the electronic states for the fixed nuclear positions and is dependent on on frozen nuclei positions. This is also known as the self-consistent field method (SCF). The two methods employed are the semi-empirical method PM6, which is usually performed first and sometimes followed by the Density Functional Theory (DFT) method B3LYP. The semi-empirical method PM6, although based on the Hartree-Fock formalism, this method uses many approximations based on experimental data in order to solve the Schrodinger equations. This method is usually fast and reliable, but can be easily countered if the environment of the molecule that is being computed is not similar enough to the approximated parameters of this method. The other method is B3LYP, a hydrid functional which utilises the DFT in order to calculate the majority of the Hamiltonian while a small portion still utilises the Hartree-Fock theory to calculate the exchange integral term. B3LYP stands for Becke, 3-parameter, Lee-Yang-Parr and uses a 6-31G basis set as the electronic wavefunction in order to produce more accurate results at the cost of increased calculation time.

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

[[File:Ex1 general.png|thumb|x700px|700px|centre|Figure 1: Formation of Cyclohaxadiene]]

Also known as the Diels-Alder reaction, this exercise investigates the well-known [4+2] cycloaddition between a conjugated diene (butadiene) and a dienophile (ethylene). The electrophilic reaction involves 4 pi-electrons from the diene and 2 pi-electrons from the alkene, and is a popular method to form regio- and stereochemically controlled 6-membered rings.

Method 2 was used to compute the transition state (TS) for this exercise. All steps are optimised to the PM6 level. First, the reactants are optimised to a minimum. The carbons at the reacting termini were then frozen at around 2.20 Å before optimised to a minimum to give a frozen-guess TS. Then finally, the molecule was optimised as a TS and an IRC was performed in order to confirm and locate the transition state.

=== Analysis of the Molecular Orbitals (MO) ===

The Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) for the reactants and the TS are shown below and its energies were recorded in order to produce the MO diagram as shown in figure 2.

{| class="wikitable"
! Ethene - HOMO
! Ethene - LUMO
! Butadiene - HOMO
! Butadiene - LUMO
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Cc5115 exer1finalMO.png|thumb|x800px|800px|left|Figure 2: MO Diagram for the formation of Transition State of the Diels-Alder Reaction]]

The symmetric TS HOMO and LUMO are formed through the interactions between the HOMO of ethylene and the LUMO of butadiene, both of which are symmetric. On the other hand, the LUMO of ethylene and the HOMO of butadiene, both of which are asymmetric, interacts to give an asymmetric HOMO-1 and LUMO+1. What can be concluded about the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed, and that the reaction is forbidden when the symmetry of the molecular orbitals aren't the same. The orbital overlap integral, S<sub>AB</sub>, is a quantitative measure of orbital overlap of two different atoms. Orbitals of the same symmetry will lead to constructive overlap and gives a non-zero value while orbitals of different symmetry will lead to destructive overlap and an orbital overlap integral of zero. Thus the overlap integral are:

- Non-zero for symmetric-symmetric interaction

- Non-zero for asymmetric-asymmetric interaction

- Zero for symmetric-asymmetric interaction

As observed in the MO diagram, the energy gap between the HOMO and LUMO for butadiene is smaller that those for ethylene due to butadiene being more electron rich than ethylene. Furthermore, in a normal MO diagram, the bonding MO formed should have a lower energy compared to both atomic orbitals (AO) whilst the anti-bonding MO formed should have a higher energy than both AOs. The reason why figure 3 goes against the tide is because the MOs formed corresponds to the transition state where the electrons are very delocalised within the chemical environment of the molecule.

==== LOG Files ====

[[:File:Cc5115_ETHENE_MO.LOG]]

[[:File:Cc5115_BUTADIENE_MO.LOG]]

[[:File:Cc5115_OPT_MO.LOG]]

=== Analysis of the C-C bond lengths ===

{| class="wikitable"
! Bond Lengths (Å)
! C1-C2
! C2-C3
! C3-C4
! C4-C5
! C5-C6
! C6-C1
|-
| Ethylene
|
|
|
|
| 1.36
|
|-
| Butadiene
| 1.36
| 1.54
| 1.36
|
|
|
|-
| Transition State
| 1.38
| 1.41
| 1.38
| 2.11
| 1.38
| 2.12
|-
| Cyclohexadiene
| 1.49
| 1.33
| 1.49
| 1.54
| 1.54
| 1.54
|}

The numbering of the carbon bonds are according to the labels on figure 1. The typical C-C bond lengths are as follows:

{| class="wikitable"
! Bond Type
! Bond Length (Å)
|-
| sp<sup>3</sup>-sp<sup>3</sup> C-C bond
| 1.54
|-
| sp<sup>3</sup>-sp<sup>2</sup> C-C bond
| 1.50
|-
| sp<sup>2</sup>-sp<sup>2</sup> C-C bond
| 1.47
|-
| sp<sup>2</sup>-sp<sup>2</sup> C=C bond
| 1.34
|}

When the reaction proceeds to the transition state, the sp<sup>2</sup>-sp<sup>2</sup> C5-C6 bond (originally ethylene) becomes longer as the carbons starts to change from sp<sup>2</sup> hybridised to sp<sup>3</sup> hybridised.
This trait is also apparent with C1-C2 and C3-C4 bonds where it once was the double bonds on butadiene, however, the increase in length of these bonds is less than that of C5-C6 due to the formation of a new double bond between C2 and C3, thus these carbons still remain sp<sup>2</sup> hybridised. This also leads to the next observation, where the C2-C3 bond decreases in length as it moves from the reactants to the transition state then the product, cyclohexadiene. This is because it is changing from a sp<sup>3</sup>-sp<sup>3</sup> C-C bond to a sp<sup>2</sup>-sp<sup>2</sup> C=C bond where the increase in s character shortens the bond lengths. This reaction also leads to the formation of 2 new bonds, namely C4-C5 and C6-C1. The Van der Waals radius of a carbon atom is 1.7 Å, and so the distance between 2 carbon atoms should be 3.4 Å, which is relatively longer than the bonds C4-C5 and C6-C1 which has a length of 2.11 and 2.12 Å respectively. This shows that the bonds are already partially formed in the transition state and they are beginning to interact together. This bond then settled at 1.54 Å in the product which matches with the typical bond length for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond.

=== Analysis of the vibrations ===

The animation for the first vibration is shown below. As observed, the formation of the 2 new bonds are synchronous as the reacting termini of butadiene and ethylene approaches each other at the same rate.

{| class="wikitable"
! <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 2;rotate x -20; </script>
<uploadedFileContents>Cc5115 OPT MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| The vibrations
|}

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

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via either the endo or exo pathways to form 2 products with different stereochemistry. Method 3 was employed in order to compute the TS for this exercise. This time, the structures were further optimised with B3LYP/6-31G method and the results are shown and discussed below.

=== Analysis of Molecular Orbitals ===

There are two types of Diels-Alder (DA) reactions: one is with a normal electron demand where the dienophile is electron deficient and the diene is electron rich, and the other is with an inverse electron demand where the dienophile is electron rich and the diene is electron deficient.

For a normal electron demand DA reaction, the dienophile low-lying LUMO interacts with the diene HOMO which has a high energy. However, observing the energies of the reactants and the transition states, the MO diagram shows that this particular DA reaction has an inverse electron demand where the dienophile (1,3-dioxole) is electron rich (higher in energy) and the diene (cyclohexadiene) is electron poor (lower in energy). The interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene thus leads to the HOMO and LUMO of the transition state. Although opposing that of a normal electron demand DA, this reaction still follows the Woodword-Hoffman rule and is thermally allowed.

Similar to exercise 1, MOs of the same symmetry interact; the symmetrical dienophile HOMO and the diene LUMO interacts to give a symmetrical TS HOMO and LUMO, while the asymmetrical dienophile LUMO and diene HOMO gives the asymmetrical TS HOMO-1 and LUMO+1. It is also observable that the endo TS HOMO has a lower energy than the exo TS HOMO which suggests that the endo reaction is favoured. This will be discussed further in the Thermochemistry section of this exercise.

{| class="wikitable"
! ENDO TS - HOMO -1
! ENDO TS - HOMO
! ENDO TS - LUMO
! ENDO TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Log Files ====

[[File:Cc5115 ENDO B3.LOG]]

[[File:Cc5115 PLEASE WORK B3.LOG]]

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +149.70
| -77.52
|-
| Exo
| +157.52
| -73.92
|}

As discussed briefly in the introduction, the reactants need to pass the activation barrier (transition state) in order to reach to the products. The table regarding the reaction barriers and energies shows that the activation barrier for the endo reaction is less than that of the exo reaction, more-so confirming that the endo reaction is kinetically favoured. This links to the lower energy that the endo TS HOMO has compared to the exo TS. This observance can be explained by secondary orbital interation (SOI). The 2 non-bonding oxygen p-orbitals containing electron lone pairs can overlap with the LUMO of the diene through space thus stabilising the TS and consequentially lowering reaction barrier. However, the more negative reaction energy of the endo reaction can be explained with sterics; in the exo transition state, the steric interaction between the sp<sup>3</sup> bridging carbons and the rest of the 1,3-dioxole structure results in the exo product being higher in energy.

{| class="wikitable"
! Exo Secondary MO
! Endo Secondary MO
|-
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

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

=== IRC ===

{| class="wikitable"
! [[File:Cc5115 Exo IRC gif.gif|thumb|x500px|500px|left|IRC for Exo Product]]
! [[File:Cc5115 Endo IRC gif.gif|thumb|x500px|500px|left|IRC for Endo Product]]
! [[File:Chelatropic IRC gif.gif|thumb|x500px|500px|left|IRC for Chelatropic Product]]
|}

IRC (intrinsic reaction coordinate) show how reactions move in space during its reaction to form products. From the IRC animations, it can be seen that the formation of the new bonds differ to that of exercise 1. Here, in the exo and endo pathways, the formation of the 2 new bonds are asynchronous as one bond forms before the other. However, the bonds form synchronously in the chelatropic reaction leading to the symmetrical product.

The IRC reaction pathways also show a smaller activation barrier compared to that of exercise 1. This is because xylylene is highly unstable. Xylylene can exist with 4π electrons making it anti-aromatic, or either with 6π electrons an a diradical which is very unstable. On the flipside, the product formed is aromatic making the DA reaction extremely favourable. Naphthalene forces the diene to be rigid in its positions easing the overlap capabilities of the diene with the dienophile. This can be observed in the animation as naphthalene doesn't have to go through major rearrangements in order to form the products.

In the reaction, naphthalene initially has a C=C bond length of 1.35 Å and a C-C bond length averaging around 1.51 Å. This changes as the product is formed where all the carbon-carbon bonds on the 6 membered rings become 1.47 Å in length suggesting the formation of an aromatic 6-membered ring where the π electrons are delocalised throughout the ring. The change in bond length can also be seen with careful observation of the animations.

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +79.85
|
|-
| Exo
| +83.82
|
|-
| Chelatropic
| +102.16
|
|}

Significantly resembling to exercise 2, exercise 3 features the endo pathway being kinetically favoured as its activation energy has the least energy compared to the other pathway. Again, this is due to the overlap between the oxygen p-orbitals overlapping with the π-orbitals of the xylylene ring. However, the difference in activation and reaction energies between the exo and endo pathways do not differ that much due to the SOI not contributing significantly in the TS and there are little steric difference between the two products. For the chelatropic product, there is a hugh drop in reaction energy. Observing the product, the large sulfur atom forming a 5-membered ring decreases the ring-strain making the product relatively stable compared to the products from the DA reaction.

Rep:Mod:cc5115TS

2018-02-14T03:22:10Z

Cc5115: /* Thermochemistry */

= Y3C Transition states and Reactivity =

== Introduction ==

This section aims to illustrate the 3 different computational techniques that can be utilised in order to analyse the transition state (TS) of a reaction. The TS is the state which has the highest energy along a reaction coordinate, as a result it is the least stable state. In the reaction, the reactants needs to have a certain amount of energy in order to surpass the activation barrier, also known as the transition state energy, and reach the product state. This computational lab allows for calculations leading to the location of the TS. The structure of the TS is crucial in determining the mechanism of a reaction.

A potential energy surface (PES) has a 3N-6 dimension, which coincides to the degrees of freedom that the molecule has, where N is the number of atoms that the molecule possesses. In a 3-D PES, the saddle point (also called the TS), is a local mixami amidst 2 minima, and can be sometimes identified through secondary derivatives as it would be negative in one direction and positive in all other directions.

There are 3 calculation methods available in order to determine the structure of the TS.

1. The first and fastest method requires only one step where a guessed structure of the TS is optimised to give an optimised TS. This means that one will need of the TS to quite an extent, furthermore this method is rather unreliable as there is a high chance that the guessed TS is incorrectly drawn.

2. The second method works from a pre-frozen guess structure of the TS where the reacting termini of the reactants are frozen in space before the remaining structure is optimised to a minima. After that, the molecules are optimised as a transition state. This allows for a more reliable representation of the TS. This method is sufficient for Exercise 1.

3. The third method is the longest and most reliable method. Here, one starts by either optimising from the reactants or the products to a minima. For the reactant case, each reactants are optimised to a minima, arranged to resemble the TS and the reacting termini are frozen and the rest of the method 2 is repeated. A similar case occurs with the product; when the product is optimised to a minima, the bonds formed in the reactions are removed, the 2 fragments are arranged to resemble the TS and the reacting termini are frozen and method 2 was used once more. This method allows for the most reliable representation of the TS and is used for Exercise 2 & 3.

In this computational lab, two methods of calculation were used on Gaussian in order to find the TS. During the optimisation, the position of the molecule is decided as it is built in Gaussian. The time-independent Schrödinger equation was solved whilst utilising the Born-Oppenheimer approximation in order to find the energy and the wavefunction φ which represents the electronic states for the fixed nuclear positions and is dependent on on frozen nuclei positions. This is also known as the self-consistent field method (SCF). The two methods employed are the semi-empirical method PM6, which is usually performed first and sometimes followed by the Density Functional Theory (DFT) method B3LYP. The semi-empirical method PM6, although based on the Hartree-Fock formalism, this method uses many approximations based on experimental data in order to solve the Schrodinger equations. This method is usually fast and reliable, but can be easily countered if the environment of the molecule that is being computed is not similar enough to the approximated parameters of this method. The other method is B3LYP, a hydrid functional which utilises the DFT in order to calculate the majority of the Hamiltonian while a small portion still utilises the Hartree-Fock theory to calculate the exchange integral term. B3LYP stands for Becke, 3-parameter, Lee-Yang-Parr and uses a 6-31G basis set as the electronic wavefunction in order to produce more accurate results at the cost of increased calculation time.

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

[[File:Ex1 general.png|thumb|x700px|700px|centre|Figure 1: Formation of Cyclohaxadiene]]

Also known as the Diels-Alder reaction, this exercise investigates the well-known [4+2] cycloaddition between a conjugated diene (butadiene) and a dienophile (ethylene). The electrophilic reaction involves 4 pi-electrons from the diene and 2 pi-electrons from the alkene, and is a popular method to form regio- and stereochemically controlled 6-membered rings.

Method 2 was used to compute the transition state (TS) for this exercise. All steps are optimised to the PM6 level. First, the reactants are optimised to a minimum. The carbons at the reacting termini were then frozen at around 2.20 Å before optimised to a minimum to give a frozen-guess TS. Then finally, the molecule was optimised as a TS and an IRC was performed in order to confirm and locate the transition state.

=== Analysis of the Molecular Orbitals (MO) ===

The Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) for the reactants and the TS are shown below and its energies were recorded in order to produce the MO diagram as shown in figure 2.

{| class="wikitable"
! Ethene - HOMO
! Ethene - LUMO
! Butadiene - HOMO
! Butadiene - LUMO
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Cc5115 exer1finalMO.png|thumb|x800px|800px|left|Figure 2: MO Diagram for the formation of Transition State of the Diels-Alder Reaction]]

The symmetric TS HOMO and LUMO are formed through the interactions between the HOMO of ethylene and the LUMO of butadiene, both of which are symmetric. On the other hand, the LUMO of ethylene and the HOMO of butadiene, both of which are asymmetric, interacts to give an asymmetric HOMO-1 and LUMO+1. What can be concluded about the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed, and that the reaction is forbidden when the symmetry of the molecular orbitals aren't the same. The orbital overlap integral, S<sub>AB</sub>, is a quantitative measure of orbital overlap of two different atoms. Orbitals of the same symmetry will lead to constructive overlap and gives a non-zero value while orbitals of different symmetry will lead to destructive overlap and an orbital overlap integral of zero. Thus the overlap integral are:

- Non-zero for symmetric-symmetric interaction

- Non-zero for asymmetric-asymmetric interaction

- Zero for symmetric-asymmetric interaction

As observed in the MO diagram, the energy gap between the HOMO and LUMO for butadiene is smaller that those for ethylene due to butadiene being more electron rich than ethylene. Furthermore, in a normal MO diagram, the bonding MO formed should have a lower energy compared to both atomic orbitals (AO) whilst the anti-bonding MO formed should have a higher energy than both AOs. The reason why figure 3 goes against the tide is because the MOs formed corresponds to the transition state where the electrons are very delocalised within the chemical environment of the molecule.

==== LOG Files ====

[[:File:Cc5115_ETHENE_MO.LOG]]

[[:File:Cc5115_BUTADIENE_MO.LOG]]

[[:File:Cc5115_OPT_MO.LOG]]

=== Analysis of the C-C bond lengths ===

{| class="wikitable"
! Bond Lengths (Å)
! C1-C2
! C2-C3
! C3-C4
! C4-C5
! C5-C6
! C6-C1
|-
| Ethylene
|
|
|
|
| 1.36
|
|-
| Butadiene
| 1.36
| 1.54
| 1.36
|
|
|
|-
| Transition State
| 1.38
| 1.41
| 1.38
| 2.11
| 1.38
| 2.12
|-
| Cyclohexadiene
| 1.49
| 1.33
| 1.49
| 1.54
| 1.54
| 1.54
|}

The numbering of the carbon bonds are according to the labels on figure 1. The typical C-C bond lengths are as follows:

{| class="wikitable"
! Bond Type
! Bond Length (Å)
|-
| sp<sup>3</sup>-sp<sup>3</sup> C-C bond
| 1.54
|-
| sp<sup>3</sup>-sp<sup>2</sup> C-C bond
| 1.50
|-
| sp<sup>2</sup>-sp<sup>2</sup> C-C bond
| 1.47
|-
| sp<sup>2</sup>-sp<sup>2</sup> C=C bond
| 1.34
|}

When the reaction proceeds to the transition state, the sp<sup>2</sup>-sp<sup>2</sup> C5-C6 bond (originally ethylene) becomes longer as the carbons starts to change from sp<sup>2</sup> hybridised to sp<sup>3</sup> hybridised.
This trait is also apparent with C1-C2 and C3-C4 bonds where it once was the double bonds on butadiene, however, the increase in length of these bonds is less than that of C5-C6 due to the formation of a new double bond between C2 and C3, thus these carbons still remain sp<sup>2</sup> hybridised. This also leads to the next observation, where the C2-C3 bond decreases in length as it moves from the reactants to the transition state then the product, cyclohexadiene. This is because it is changing from a sp<sup>3</sup>-sp<sup>3</sup> C-C bond to a sp<sup>2</sup>-sp<sup>2</sup> C=C bond where the increase in s character shortens the bond lengths. This reaction also leads to the formation of 2 new bonds, namely C4-C5 and C6-C1. The Van der Waals radius of a carbon atom is 1.7 Å, and so the distance between 2 carbon atoms should be 3.4 Å, which is relatively longer than the bonds C4-C5 and C6-C1 which has a length of 2.11 and 2.12 Å respectively. This shows that the bonds are already partially formed in the transition state and they are beginning to interact together. This bond then settled at 1.54 Å in the product which matches with the typical bond length for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond.

=== Analysis of the vibrations ===

The animation for the first vibration is shown below. As observed, the formation of the 2 new bonds are synchronous as the reacting termini of butadiene and ethylene approaches each other at the same rate.

{| class="wikitable"
! <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 2;rotate x -20; </script>
<uploadedFileContents>Cc5115 OPT MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| The vibrations
|}

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

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via either the endo or exo pathways to form 2 products with different stereochemistry. Method 3 was employed in order to compute the TS for this exercise. This time, the structures were further optimised with B3LYP/6-31G method and the results are shown and discussed below.

=== Analysis of Molecular Orbitals ===

There are two types of Diels-Alder (DA) reactions: one is with a normal electron demand where the dienophile is electron deficient and the diene is electron rich, and the other is with an inverse electron demand where the dienophile is electron rich and the diene is electron deficient.

For a normal electron demand DA reaction, the dienophile low-lying LUMO interacts with the diene HOMO which has a high energy. However, observing the energies of the reactants and the transition states, the MO diagram shows that this particular DA reaction has an inverse electron demand where the dienophile (1,3-dioxole) is electron rich (higher in energy) and the diene (cyclohexadiene) is electron poor (lower in energy). The interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene thus leads to the HOMO and LUMO of the transition state. Although opposing that of a normal electron demand DA, this reaction still follows the Woodword-Hoffman rule and is thermally allowed.

Similar to exercise 1, MOs of the same symmetry interact; the symmetrical dienophile HOMO and the diene LUMO interacts to give a symmetrical TS HOMO and LUMO, while the asymmetrical dienophile LUMO and diene HOMO gives the asymmetrical TS HOMO-1 and LUMO+1. It is also observable that the endo TS HOMO has a lower energy than the exo TS HOMO which suggests that the endo reaction is favoured. This will be discussed further in the Thermochemistry section of this exercise.

{| class="wikitable"
! ENDO TS - HOMO -1
! ENDO TS - HOMO
! ENDO TS - LUMO
! ENDO TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Log Files ====

[[File:Cc5115 ENDO B3.LOG]]

[[File:Cc5115 PLEASE WORK B3.LOG]]

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +149.70
| -77.52
|-
| Exo
| +157.52
| -73.92
|}

As discussed briefly in the introduction, the reactants need to pass the activation barrier (transition state) in order to reach to the products. The table regarding the reaction barriers and energies shows that the activation barrier for the endo reaction is less than that of the exo reaction, more-so confirming that the endo reaction is kinetically favoured. This links to the lower energy that the endo TS HOMO has compared to the exo TS. This observance can be explained by secondary orbital interation (SOI). The 2 non-bonding oxygen p-orbitals containing electron lone pairs can overlap with the LUMO of the diene through space thus stabilising the TS and consequentially lowering reaction barrier. However, the more negative reaction energy of the endo reaction can be explained with sterics; in the exo transition state, the steric interaction between the sp<sup>3</sup> bridging carbons and the rest of the 1,3-dioxole structure results in the exo product being higher in energy.

{| class="wikitable"
! Exo Secondary MO
! Endo Secondary MO
|-
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

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

=== IRC ===

{| class="wikitable"
! [[File:Cc5115 Exo IRC gif.gif|thumb|x500px|500px|left|IRC for Exo Product]]
! [[File:Cc5115 Endo IRC gif.gif|thumb|x500px|500px|left|IRC for Endo Product]]
! [[File:Chelatropic IRC gif.gif|thumb|x500px|500px|left|IRC for Chelatropic Product]]
|}

IRC (intrinsic reaction coordinate) show how reactions move in space during its reaction to form products. From the IRC animations, it can be seen that the formation of the new bonds differ to that of exercise 1. Here, in the exo and endo pathways, the formation of the 2 new bonds are asynchronous as one bond forms before the other. However, the bonds form synchronously in the chelatropic reaction leading to the symmetrical product.

The IRC reaction pathways also show a smaller activation barrier compared to that of exercise 1. This is because xylylene is highly unstable. Xylylene can exist with 4π electrons making it anti-aromatic, or either with 6π electrons an a diradical which is very unstable. On the flipside, the product formed is aromatic making the DA reaction extremely favourable. Naphthalene forces the diene to be rigid in its positions easing the overlap capabilities of the diene with the dienophile. This can be observed in the animation as naphthalene doesn't have to go through major rearrangements in order to form the products.

In the reaction, naphthalene initially has a C=C bond length of 1.35 Å and a C-C bond length averaging around 1.51 Å. This changes as the product is formed where all the carbon-carbon bonds on the 6 membered rings become 1.47 Å in length suggesting the formation of an aromatic 6-membered ring where the π electrons are delocalised throughout the ring. The change in bond length can also be seen with careful observation of the animations.

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +79.85
|
|-
| Exo
| +83.82
|
|-
| Chelatropic
| +102.16
|
|}

Rep:Mod:cc5115TS

2018-02-14T03:20:17Z

Cc5115: /* Thermochemistry */

= Y3C Transition states and Reactivity =

== Introduction ==

This section aims to illustrate the 3 different computational techniques that can be utilised in order to analyse the transition state (TS) of a reaction. The TS is the state which has the highest energy along a reaction coordinate, as a result it is the least stable state. In the reaction, the reactants needs to have a certain amount of energy in order to surpass the activation barrier, also known as the transition state energy, and reach the product state. This computational lab allows for calculations leading to the location of the TS. The structure of the TS is crucial in determining the mechanism of a reaction.

A potential energy surface (PES) has a 3N-6 dimension, which coincides to the degrees of freedom that the molecule has, where N is the number of atoms that the molecule possesses. In a 3-D PES, the saddle point (also called the TS), is a local mixami amidst 2 minima, and can be sometimes identified through secondary derivatives as it would be negative in one direction and positive in all other directions.

There are 3 calculation methods available in order to determine the structure of the TS.

1. The first and fastest method requires only one step where a guessed structure of the TS is optimised to give an optimised TS. This means that one will need of the TS to quite an extent, furthermore this method is rather unreliable as there is a high chance that the guessed TS is incorrectly drawn.

2. The second method works from a pre-frozen guess structure of the TS where the reacting termini of the reactants are frozen in space before the remaining structure is optimised to a minima. After that, the molecules are optimised as a transition state. This allows for a more reliable representation of the TS. This method is sufficient for Exercise 1.

3. The third method is the longest and most reliable method. Here, one starts by either optimising from the reactants or the products to a minima. For the reactant case, each reactants are optimised to a minima, arranged to resemble the TS and the reacting termini are frozen and the rest of the method 2 is repeated. A similar case occurs with the product; when the product is optimised to a minima, the bonds formed in the reactions are removed, the 2 fragments are arranged to resemble the TS and the reacting termini are frozen and method 2 was used once more. This method allows for the most reliable representation of the TS and is used for Exercise 2 & 3.

In this computational lab, two methods of calculation were used on Gaussian in order to find the TS. During the optimisation, the position of the molecule is decided as it is built in Gaussian. The time-independent Schrödinger equation was solved whilst utilising the Born-Oppenheimer approximation in order to find the energy and the wavefunction φ which represents the electronic states for the fixed nuclear positions and is dependent on on frozen nuclei positions. This is also known as the self-consistent field method (SCF). The two methods employed are the semi-empirical method PM6, which is usually performed first and sometimes followed by the Density Functional Theory (DFT) method B3LYP. The semi-empirical method PM6, although based on the Hartree-Fock formalism, this method uses many approximations based on experimental data in order to solve the Schrodinger equations. This method is usually fast and reliable, but can be easily countered if the environment of the molecule that is being computed is not similar enough to the approximated parameters of this method. The other method is B3LYP, a hydrid functional which utilises the DFT in order to calculate the majority of the Hamiltonian while a small portion still utilises the Hartree-Fock theory to calculate the exchange integral term. B3LYP stands for Becke, 3-parameter, Lee-Yang-Parr and uses a 6-31G basis set as the electronic wavefunction in order to produce more accurate results at the cost of increased calculation time.

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

[[File:Ex1 general.png|thumb|x700px|700px|centre|Figure 1: Formation of Cyclohaxadiene]]

Also known as the Diels-Alder reaction, this exercise investigates the well-known [4+2] cycloaddition between a conjugated diene (butadiene) and a dienophile (ethylene). The electrophilic reaction involves 4 pi-electrons from the diene and 2 pi-electrons from the alkene, and is a popular method to form regio- and stereochemically controlled 6-membered rings.

Method 2 was used to compute the transition state (TS) for this exercise. All steps are optimised to the PM6 level. First, the reactants are optimised to a minimum. The carbons at the reacting termini were then frozen at around 2.20 Å before optimised to a minimum to give a frozen-guess TS. Then finally, the molecule was optimised as a TS and an IRC was performed in order to confirm and locate the transition state.

=== Analysis of the Molecular Orbitals (MO) ===

The Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) for the reactants and the TS are shown below and its energies were recorded in order to produce the MO diagram as shown in figure 2.

{| class="wikitable"
! Ethene - HOMO
! Ethene - LUMO
! Butadiene - HOMO
! Butadiene - LUMO
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Cc5115 exer1finalMO.png|thumb|x800px|800px|left|Figure 2: MO Diagram for the formation of Transition State of the Diels-Alder Reaction]]

The symmetric TS HOMO and LUMO are formed through the interactions between the HOMO of ethylene and the LUMO of butadiene, both of which are symmetric. On the other hand, the LUMO of ethylene and the HOMO of butadiene, both of which are asymmetric, interacts to give an asymmetric HOMO-1 and LUMO+1. What can be concluded about the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed, and that the reaction is forbidden when the symmetry of the molecular orbitals aren't the same. The orbital overlap integral, S<sub>AB</sub>, is a quantitative measure of orbital overlap of two different atoms. Orbitals of the same symmetry will lead to constructive overlap and gives a non-zero value while orbitals of different symmetry will lead to destructive overlap and an orbital overlap integral of zero. Thus the overlap integral are:

- Non-zero for symmetric-symmetric interaction

- Non-zero for asymmetric-asymmetric interaction

- Zero for symmetric-asymmetric interaction

As observed in the MO diagram, the energy gap between the HOMO and LUMO for butadiene is smaller that those for ethylene due to butadiene being more electron rich than ethylene. Furthermore, in a normal MO diagram, the bonding MO formed should have a lower energy compared to both atomic orbitals (AO) whilst the anti-bonding MO formed should have a higher energy than both AOs. The reason why figure 3 goes against the tide is because the MOs formed corresponds to the transition state where the electrons are very delocalised within the chemical environment of the molecule.

==== LOG Files ====

[[:File:Cc5115_ETHENE_MO.LOG]]

[[:File:Cc5115_BUTADIENE_MO.LOG]]

[[:File:Cc5115_OPT_MO.LOG]]

=== Analysis of the C-C bond lengths ===

{| class="wikitable"
! Bond Lengths (Å)
! C1-C2
! C2-C3
! C3-C4
! C4-C5
! C5-C6
! C6-C1
|-
| Ethylene
|
|
|
|
| 1.36
|
|-
| Butadiene
| 1.36
| 1.54
| 1.36
|
|
|
|-
| Transition State
| 1.38
| 1.41
| 1.38
| 2.11
| 1.38
| 2.12
|-
| Cyclohexadiene
| 1.49
| 1.33
| 1.49
| 1.54
| 1.54
| 1.54
|}

The numbering of the carbon bonds are according to the labels on figure 1. The typical C-C bond lengths are as follows:

{| class="wikitable"
! Bond Type
! Bond Length (Å)
|-
| sp<sup>3</sup>-sp<sup>3</sup> C-C bond
| 1.54
|-
| sp<sup>3</sup>-sp<sup>2</sup> C-C bond
| 1.50
|-
| sp<sup>2</sup>-sp<sup>2</sup> C-C bond
| 1.47
|-
| sp<sup>2</sup>-sp<sup>2</sup> C=C bond
| 1.34
|}

When the reaction proceeds to the transition state, the sp<sup>2</sup>-sp<sup>2</sup> C5-C6 bond (originally ethylene) becomes longer as the carbons starts to change from sp<sup>2</sup> hybridised to sp<sup>3</sup> hybridised.
This trait is also apparent with C1-C2 and C3-C4 bonds where it once was the double bonds on butadiene, however, the increase in length of these bonds is less than that of C5-C6 due to the formation of a new double bond between C2 and C3, thus these carbons still remain sp<sup>2</sup> hybridised. This also leads to the next observation, where the C2-C3 bond decreases in length as it moves from the reactants to the transition state then the product, cyclohexadiene. This is because it is changing from a sp<sup>3</sup>-sp<sup>3</sup> C-C bond to a sp<sup>2</sup>-sp<sup>2</sup> C=C bond where the increase in s character shortens the bond lengths. This reaction also leads to the formation of 2 new bonds, namely C4-C5 and C6-C1. The Van der Waals radius of a carbon atom is 1.7 Å, and so the distance between 2 carbon atoms should be 3.4 Å, which is relatively longer than the bonds C4-C5 and C6-C1 which has a length of 2.11 and 2.12 Å respectively. This shows that the bonds are already partially formed in the transition state and they are beginning to interact together. This bond then settled at 1.54 Å in the product which matches with the typical bond length for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond.

=== Analysis of the vibrations ===

The animation for the first vibration is shown below. As observed, the formation of the 2 new bonds are synchronous as the reacting termini of butadiene and ethylene approaches each other at the same rate.

{| class="wikitable"
! <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 2;rotate x -20; </script>
<uploadedFileContents>Cc5115 OPT MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| The vibrations
|}

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

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via either the endo or exo pathways to form 2 products with different stereochemistry. Method 3 was employed in order to compute the TS for this exercise. This time, the structures were further optimised with B3LYP/6-31G method and the results are shown and discussed below.

=== Analysis of Molecular Orbitals ===

There are two types of Diels-Alder (DA) reactions: one is with a normal electron demand where the dienophile is electron deficient and the diene is electron rich, and the other is with an inverse electron demand where the dienophile is electron rich and the diene is electron deficient.

For a normal electron demand DA reaction, the dienophile low-lying LUMO interacts with the diene HOMO which has a high energy. However, observing the energies of the reactants and the transition states, the MO diagram shows that this particular DA reaction has an inverse electron demand where the dienophile (1,3-dioxole) is electron rich (higher in energy) and the diene (cyclohexadiene) is electron poor (lower in energy). The interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene thus leads to the HOMO and LUMO of the transition state. Although opposing that of a normal electron demand DA, this reaction still follows the Woodword-Hoffman rule and is thermally allowed.

Similar to exercise 1, MOs of the same symmetry interact; the symmetrical dienophile HOMO and the diene LUMO interacts to give a symmetrical TS HOMO and LUMO, while the asymmetrical dienophile LUMO and diene HOMO gives the asymmetrical TS HOMO-1 and LUMO+1. It is also observable that the endo TS HOMO has a lower energy than the exo TS HOMO which suggests that the endo reaction is favoured. This will be discussed further in the Thermochemistry section of this exercise.

{| class="wikitable"
! ENDO TS - HOMO -1
! ENDO TS - HOMO
! ENDO TS - LUMO
! ENDO TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Log Files ====

[[File:Cc5115 ENDO B3.LOG]]

[[File:Cc5115 PLEASE WORK B3.LOG]]

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +149.70
| -77.52
|-
| Exo
| +157.52
| -73.92
|}

As discussed briefly in the introduction, the reactants need to pass the activation barrier (transition state) in order to reach to the products. The table regarding the reaction barriers and energies shows that the activation barrier for the endo reaction is less than that of the exo reaction, more-so confirming that the endo reaction is kinetically favoured. This links to the lower energy that the endo TS HOMO has compared to the exo TS. This observance can be explained by secondary orbital interation (SOI). The 2 non-bonding oxygen p-orbitals containing electron lone pairs can overlap with the LUMO of the diene through space thus stabilising the TS and consequentially lowering reaction barrier. However, the more negative reaction energy of the endo reaction can be explained with sterics; in the exo transition state, the steric interaction between the sp<sup>3</sup> bridging carbons and the rest of the 1,3-dioxole structure results in the exo product being higher in energy.

{| class="wikitable"
! Exo Secondary MO
! Endo Secondary MO
|-
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

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

=== IRC ===

{| class="wikitable"
! [[File:Cc5115 Exo IRC gif.gif|thumb|x500px|500px|left|IRC for Exo Product]]
! [[File:Cc5115 Endo IRC gif.gif|thumb|x500px|500px|left|IRC for Endo Product]]
! [[File:Chelatropic IRC gif.gif|thumb|x500px|500px|left|IRC for Chelatropic Product]]
|}

IRC (intrinsic reaction coordinate) show how reactions move in space during its reaction to form products. From the IRC animations, it can be seen that the formation of the new bonds differ to that of exercise 1. Here, in the exo and endo pathways, the formation of the 2 new bonds are asynchronous as one bond forms before the other. However, the bonds form synchronously in the chelatropic reaction leading to the symmetrical product.

The IRC reaction pathways also show a smaller activation barrier compared to that of exercise 1. This is because xylylene is highly unstable. Xylylene can exist with 4π electrons making it anti-aromatic, or either with 6π electrons an a diradical which is very unstable. On the flipside, the product formed is aromatic making the DA reaction extremely favourable. Naphthalene forces the diene to be rigid in its positions easing the overlap capabilities of the diene with the dienophile. This can be observed in the animation as naphthalene doesn't have to go through major rearrangements in order to form the products.

In the reaction, naphthalene initially has a C=C bond length of 1.35 Å and a C-C bond length averaging around 1.51 Å. This changes as the product is formed where all the carbon-carbon bonds on the 6 membered rings become 1.47 Å in length suggesting the formation of an aromatic 6-membered ring where the π electrons are delocalised throughout the ring. The change in bond length can also be seen with careful observation of the animations.

=== Thermochemistry ===

{| class="wikitable"

Rep:Mod:cc5115TS

2018-02-14T03:19:22Z

Cc5115: /* Exercise 3: Diels-Alder vs Cheletropic */

= Y3C Transition states and Reactivity =

== Introduction ==

This section aims to illustrate the 3 different computational techniques that can be utilised in order to analyse the transition state (TS) of a reaction. The TS is the state which has the highest energy along a reaction coordinate, as a result it is the least stable state. In the reaction, the reactants needs to have a certain amount of energy in order to surpass the activation barrier, also known as the transition state energy, and reach the product state. This computational lab allows for calculations leading to the location of the TS. The structure of the TS is crucial in determining the mechanism of a reaction.

A potential energy surface (PES) has a 3N-6 dimension, which coincides to the degrees of freedom that the molecule has, where N is the number of atoms that the molecule possesses. In a 3-D PES, the saddle point (also called the TS), is a local mixami amidst 2 minima, and can be sometimes identified through secondary derivatives as it would be negative in one direction and positive in all other directions.

There are 3 calculation methods available in order to determine the structure of the TS.

1. The first and fastest method requires only one step where a guessed structure of the TS is optimised to give an optimised TS. This means that one will need of the TS to quite an extent, furthermore this method is rather unreliable as there is a high chance that the guessed TS is incorrectly drawn.

2. The second method works from a pre-frozen guess structure of the TS where the reacting termini of the reactants are frozen in space before the remaining structure is optimised to a minima. After that, the molecules are optimised as a transition state. This allows for a more reliable representation of the TS. This method is sufficient for Exercise 1.

3. The third method is the longest and most reliable method. Here, one starts by either optimising from the reactants or the products to a minima. For the reactant case, each reactants are optimised to a minima, arranged to resemble the TS and the reacting termini are frozen and the rest of the method 2 is repeated. A similar case occurs with the product; when the product is optimised to a minima, the bonds formed in the reactions are removed, the 2 fragments are arranged to resemble the TS and the reacting termini are frozen and method 2 was used once more. This method allows for the most reliable representation of the TS and is used for Exercise 2 & 3.

In this computational lab, two methods of calculation were used on Gaussian in order to find the TS. During the optimisation, the position of the molecule is decided as it is built in Gaussian. The time-independent Schrödinger equation was solved whilst utilising the Born-Oppenheimer approximation in order to find the energy and the wavefunction φ which represents the electronic states for the fixed nuclear positions and is dependent on on frozen nuclei positions. This is also known as the self-consistent field method (SCF). The two methods employed are the semi-empirical method PM6, which is usually performed first and sometimes followed by the Density Functional Theory (DFT) method B3LYP. The semi-empirical method PM6, although based on the Hartree-Fock formalism, this method uses many approximations based on experimental data in order to solve the Schrodinger equations. This method is usually fast and reliable, but can be easily countered if the environment of the molecule that is being computed is not similar enough to the approximated parameters of this method. The other method is B3LYP, a hydrid functional which utilises the DFT in order to calculate the majority of the Hamiltonian while a small portion still utilises the Hartree-Fock theory to calculate the exchange integral term. B3LYP stands for Becke, 3-parameter, Lee-Yang-Parr and uses a 6-31G basis set as the electronic wavefunction in order to produce more accurate results at the cost of increased calculation time.

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

[[File:Ex1 general.png|thumb|x700px|700px|centre|Figure 1: Formation of Cyclohaxadiene]]

Also known as the Diels-Alder reaction, this exercise investigates the well-known [4+2] cycloaddition between a conjugated diene (butadiene) and a dienophile (ethylene). The electrophilic reaction involves 4 pi-electrons from the diene and 2 pi-electrons from the alkene, and is a popular method to form regio- and stereochemically controlled 6-membered rings.

Method 2 was used to compute the transition state (TS) for this exercise. All steps are optimised to the PM6 level. First, the reactants are optimised to a minimum. The carbons at the reacting termini were then frozen at around 2.20 Å before optimised to a minimum to give a frozen-guess TS. Then finally, the molecule was optimised as a TS and an IRC was performed in order to confirm and locate the transition state.

=== Analysis of the Molecular Orbitals (MO) ===

The Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) for the reactants and the TS are shown below and its energies were recorded in order to produce the MO diagram as shown in figure 2.

{| class="wikitable"
! Ethene - HOMO
! Ethene - LUMO
! Butadiene - HOMO
! Butadiene - LUMO
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Cc5115 exer1finalMO.png|thumb|x800px|800px|left|Figure 2: MO Diagram for the formation of Transition State of the Diels-Alder Reaction]]

The symmetric TS HOMO and LUMO are formed through the interactions between the HOMO of ethylene and the LUMO of butadiene, both of which are symmetric. On the other hand, the LUMO of ethylene and the HOMO of butadiene, both of which are asymmetric, interacts to give an asymmetric HOMO-1 and LUMO+1. What can be concluded about the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed, and that the reaction is forbidden when the symmetry of the molecular orbitals aren't the same. The orbital overlap integral, S<sub>AB</sub>, is a quantitative measure of orbital overlap of two different atoms. Orbitals of the same symmetry will lead to constructive overlap and gives a non-zero value while orbitals of different symmetry will lead to destructive overlap and an orbital overlap integral of zero. Thus the overlap integral are:

- Non-zero for symmetric-symmetric interaction

- Non-zero for asymmetric-asymmetric interaction

- Zero for symmetric-asymmetric interaction

As observed in the MO diagram, the energy gap between the HOMO and LUMO for butadiene is smaller that those for ethylene due to butadiene being more electron rich than ethylene. Furthermore, in a normal MO diagram, the bonding MO formed should have a lower energy compared to both atomic orbitals (AO) whilst the anti-bonding MO formed should have a higher energy than both AOs. The reason why figure 3 goes against the tide is because the MOs formed corresponds to the transition state where the electrons are very delocalised within the chemical environment of the molecule.

==== LOG Files ====

[[:File:Cc5115_ETHENE_MO.LOG]]

[[:File:Cc5115_BUTADIENE_MO.LOG]]

[[:File:Cc5115_OPT_MO.LOG]]

=== Analysis of the C-C bond lengths ===

{| class="wikitable"
! Bond Lengths (Å)
! C1-C2
! C2-C3
! C3-C4
! C4-C5
! C5-C6
! C6-C1
|-
| Ethylene
|
|
|
|
| 1.36
|
|-
| Butadiene
| 1.36
| 1.54
| 1.36
|
|
|
|-
| Transition State
| 1.38
| 1.41
| 1.38
| 2.11
| 1.38
| 2.12
|-
| Cyclohexadiene
| 1.49
| 1.33
| 1.49
| 1.54
| 1.54
| 1.54
|}

The numbering of the carbon bonds are according to the labels on figure 1. The typical C-C bond lengths are as follows:

{| class="wikitable"
! Bond Type
! Bond Length (Å)
|-
| sp<sup>3</sup>-sp<sup>3</sup> C-C bond
| 1.54
|-
| sp<sup>3</sup>-sp<sup>2</sup> C-C bond
| 1.50
|-
| sp<sup>2</sup>-sp<sup>2</sup> C-C bond
| 1.47
|-
| sp<sup>2</sup>-sp<sup>2</sup> C=C bond
| 1.34
|}

When the reaction proceeds to the transition state, the sp<sup>2</sup>-sp<sup>2</sup> C5-C6 bond (originally ethylene) becomes longer as the carbons starts to change from sp<sup>2</sup> hybridised to sp<sup>3</sup> hybridised.
This trait is also apparent with C1-C2 and C3-C4 bonds where it once was the double bonds on butadiene, however, the increase in length of these bonds is less than that of C5-C6 due to the formation of a new double bond between C2 and C3, thus these carbons still remain sp<sup>2</sup> hybridised. This also leads to the next observation, where the C2-C3 bond decreases in length as it moves from the reactants to the transition state then the product, cyclohexadiene. This is because it is changing from a sp<sup>3</sup>-sp<sup>3</sup> C-C bond to a sp<sup>2</sup>-sp<sup>2</sup> C=C bond where the increase in s character shortens the bond lengths. This reaction also leads to the formation of 2 new bonds, namely C4-C5 and C6-C1. The Van der Waals radius of a carbon atom is 1.7 Å, and so the distance between 2 carbon atoms should be 3.4 Å, which is relatively longer than the bonds C4-C5 and C6-C1 which has a length of 2.11 and 2.12 Å respectively. This shows that the bonds are already partially formed in the transition state and they are beginning to interact together. This bond then settled at 1.54 Å in the product which matches with the typical bond length for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond.

=== Analysis of the vibrations ===

The animation for the first vibration is shown below. As observed, the formation of the 2 new bonds are synchronous as the reacting termini of butadiene and ethylene approaches each other at the same rate.

{| class="wikitable"
! <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 2;rotate x -20; </script>
<uploadedFileContents>Cc5115 OPT MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| The vibrations
|}

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

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via either the endo or exo pathways to form 2 products with different stereochemistry. Method 3 was employed in order to compute the TS for this exercise. This time, the structures were further optimised with B3LYP/6-31G method and the results are shown and discussed below.

=== Analysis of Molecular Orbitals ===

There are two types of Diels-Alder (DA) reactions: one is with a normal electron demand where the dienophile is electron deficient and the diene is electron rich, and the other is with an inverse electron demand where the dienophile is electron rich and the diene is electron deficient.

For a normal electron demand DA reaction, the dienophile low-lying LUMO interacts with the diene HOMO which has a high energy. However, observing the energies of the reactants and the transition states, the MO diagram shows that this particular DA reaction has an inverse electron demand where the dienophile (1,3-dioxole) is electron rich (higher in energy) and the diene (cyclohexadiene) is electron poor (lower in energy). The interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene thus leads to the HOMO and LUMO of the transition state. Although opposing that of a normal electron demand DA, this reaction still follows the Woodword-Hoffman rule and is thermally allowed.

Similar to exercise 1, MOs of the same symmetry interact; the symmetrical dienophile HOMO and the diene LUMO interacts to give a symmetrical TS HOMO and LUMO, while the asymmetrical dienophile LUMO and diene HOMO gives the asymmetrical TS HOMO-1 and LUMO+1. It is also observable that the endo TS HOMO has a lower energy than the exo TS HOMO which suggests that the endo reaction is favoured. This will be discussed further in the Thermochemistry section of this exercise.

{| class="wikitable"
! ENDO TS - HOMO -1
! ENDO TS - HOMO
! ENDO TS - LUMO
! ENDO TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Log Files ====

[[File:Cc5115 ENDO B3.LOG]]

[[File:Cc5115 PLEASE WORK B3.LOG]]

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +149.70
| -77.52
|-
| Exo
| +157.52
| -73.92
|}

As discussed briefly in the introduction, the reactants need to pass the activation barrier (transition state) in order to reach to the products. The table regarding the reaction barriers and energies shows that the activation barrier for the endo reaction is less than that of the exo reaction, more-so confirming that the endo reaction is kinetically favoured. This links to the lower energy that the endo TS HOMO has compared to the exo TS. This observance can be explained by secondary orbital interation (SOI). The 2 non-bonding oxygen p-orbitals containing electron lone pairs can overlap with the LUMO of the diene through space thus stabilising the TS and consequentially lowering reaction barrier. However, the more negative reaction energy of the endo reaction can be explained with sterics; in the exo transition state, the steric interaction between the sp<sup>3</sup> bridging carbons and the rest of the 1,3-dioxole structure results in the exo product being higher in energy.

{| class="wikitable"
! Exo Secondary MO
! Endo Secondary MO
|-
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

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

=== IRC ===

{| class="wikitable"
! [[File:Cc5115 Exo IRC gif.gif|thumb|x500px|500px|left|IRC for Exo Product]]
! [[File:Cc5115 Endo IRC gif.gif|thumb|x500px|500px|left|IRC for Endo Product]]
! [[File:Chelatropic IRC gif.gif|thumb|x500px|500px|left|IRC for Chelatropic Product]]
|}

IRC (intrinsic reaction coordinate) show how reactions move in space during its reaction to form products. From the IRC animations, it can be seen that the formation of the new bonds differ to that of exercise 1. Here, in the exo and endo pathways, the formation of the 2 new bonds are asynchronous as one bond forms before the other. However, the bonds form synchronously in the chelatropic reaction leading to the symmetrical product.

The IRC reaction pathways also show a smaller activation barrier compared to that of exercise 1. This is because xylylene is highly unstable. Xylylene can exist with 4π electrons making it anti-aromatic, or either with 6π electrons an a diradical which is very unstable. On the flipside, the product formed is aromatic making the DA reaction extremely favourable. Naphthalene forces the diene to be rigid in its positions easing the overlap capabilities of the diene with the dienophile. This can be observed in the animation as naphthalene doesn't have to go through major rearrangements in order to form the products.

In the reaction, naphthalene initially has a C=C bond length of 1.35 Å and a C-C bond length averaging around 1.51 Å. This changes as the product is formed where all the carbon-carbon bonds on the 6 membered rings become 1.47 Å in length suggesting the formation of an aromatic 6-membered ring where the π electrons are delocalised throughout the ring. The change in bond length can also be seen with careful observation of the animations.

=== Thermochemistry ===

Rep:Mod:cc5115TS

2018-02-14T03:06:10Z

Cc5115: /* IRC */

= Y3C Transition states and Reactivity =

== Introduction ==

This section aims to illustrate the 3 different computational techniques that can be utilised in order to analyse the transition state (TS) of a reaction. The TS is the state which has the highest energy along a reaction coordinate, as a result it is the least stable state. In the reaction, the reactants needs to have a certain amount of energy in order to surpass the activation barrier, also known as the transition state energy, and reach the product state. This computational lab allows for calculations leading to the location of the TS. The structure of the TS is crucial in determining the mechanism of a reaction.

A potential energy surface (PES) has a 3N-6 dimension, which coincides to the degrees of freedom that the molecule has, where N is the number of atoms that the molecule possesses. In a 3-D PES, the saddle point (also called the TS), is a local mixami amidst 2 minima, and can be sometimes identified through secondary derivatives as it would be negative in one direction and positive in all other directions.

There are 3 calculation methods available in order to determine the structure of the TS.

1. The first and fastest method requires only one step where a guessed structure of the TS is optimised to give an optimised TS. This means that one will need of the TS to quite an extent, furthermore this method is rather unreliable as there is a high chance that the guessed TS is incorrectly drawn.

2. The second method works from a pre-frozen guess structure of the TS where the reacting termini of the reactants are frozen in space before the remaining structure is optimised to a minima. After that, the molecules are optimised as a transition state. This allows for a more reliable representation of the TS. This method is sufficient for Exercise 1.

3. The third method is the longest and most reliable method. Here, one starts by either optimising from the reactants or the products to a minima. For the reactant case, each reactants are optimised to a minima, arranged to resemble the TS and the reacting termini are frozen and the rest of the method 2 is repeated. A similar case occurs with the product; when the product is optimised to a minima, the bonds formed in the reactions are removed, the 2 fragments are arranged to resemble the TS and the reacting termini are frozen and method 2 was used once more. This method allows for the most reliable representation of the TS and is used for Exercise 2 & 3.

In this computational lab, two methods of calculation were used on Gaussian in order to find the TS. During the optimisation, the position of the molecule is decided as it is built in Gaussian. The time-independent Schrödinger equation was solved whilst utilising the Born-Oppenheimer approximation in order to find the energy and the wavefunction φ which represents the electronic states for the fixed nuclear positions and is dependent on on frozen nuclei positions. This is also known as the self-consistent field method (SCF). The two methods employed are the semi-empirical method PM6, which is usually performed first and sometimes followed by the Density Functional Theory (DFT) method B3LYP. The semi-empirical method PM6, although based on the Hartree-Fock formalism, this method uses many approximations based on experimental data in order to solve the Schrodinger equations. This method is usually fast and reliable, but can be easily countered if the environment of the molecule that is being computed is not similar enough to the approximated parameters of this method. The other method is B3LYP, a hydrid functional which utilises the DFT in order to calculate the majority of the Hamiltonian while a small portion still utilises the Hartree-Fock theory to calculate the exchange integral term. B3LYP stands for Becke, 3-parameter, Lee-Yang-Parr and uses a 6-31G basis set as the electronic wavefunction in order to produce more accurate results at the cost of increased calculation time.

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

[[File:Ex1 general.png|thumb|x700px|700px|centre|Figure 1: Formation of Cyclohaxadiene]]

Also known as the Diels-Alder reaction, this exercise investigates the well-known [4+2] cycloaddition between a conjugated diene (butadiene) and a dienophile (ethylene). The electrophilic reaction involves 4 pi-electrons from the diene and 2 pi-electrons from the alkene, and is a popular method to form regio- and stereochemically controlled 6-membered rings.

Method 2 was used to compute the transition state (TS) for this exercise. All steps are optimised to the PM6 level. First, the reactants are optimised to a minimum. The carbons at the reacting termini were then frozen at around 2.20 Å before optimised to a minimum to give a frozen-guess TS. Then finally, the molecule was optimised as a TS and an IRC was performed in order to confirm and locate the transition state.

=== Analysis of the Molecular Orbitals (MO) ===

The Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) for the reactants and the TS are shown below and its energies were recorded in order to produce the MO diagram as shown in figure 2.

{| class="wikitable"
! Ethene - HOMO
! Ethene - LUMO
! Butadiene - HOMO
! Butadiene - LUMO
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Cc5115 exer1finalMO.png|thumb|x800px|800px|left|Figure 2: MO Diagram for the formation of Transition State of the Diels-Alder Reaction]]

The symmetric TS HOMO and LUMO are formed through the interactions between the HOMO of ethylene and the LUMO of butadiene, both of which are symmetric. On the other hand, the LUMO of ethylene and the HOMO of butadiene, both of which are asymmetric, interacts to give an asymmetric HOMO-1 and LUMO+1. What can be concluded about the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed, and that the reaction is forbidden when the symmetry of the molecular orbitals aren't the same. The orbital overlap integral, S<sub>AB</sub>, is a quantitative measure of orbital overlap of two different atoms. Orbitals of the same symmetry will lead to constructive overlap and gives a non-zero value while orbitals of different symmetry will lead to destructive overlap and an orbital overlap integral of zero. Thus the overlap integral are:

- Non-zero for symmetric-symmetric interaction

- Non-zero for asymmetric-asymmetric interaction

- Zero for symmetric-asymmetric interaction

As observed in the MO diagram, the energy gap between the HOMO and LUMO for butadiene is smaller that those for ethylene due to butadiene being more electron rich than ethylene. Furthermore, in a normal MO diagram, the bonding MO formed should have a lower energy compared to both atomic orbitals (AO) whilst the anti-bonding MO formed should have a higher energy than both AOs. The reason why figure 3 goes against the tide is because the MOs formed corresponds to the transition state where the electrons are very delocalised within the chemical environment of the molecule.

==== LOG Files ====

[[:File:Cc5115_ETHENE_MO.LOG]]

[[:File:Cc5115_BUTADIENE_MO.LOG]]

[[:File:Cc5115_OPT_MO.LOG]]

=== Analysis of the C-C bond lengths ===

{| class="wikitable"
! Bond Lengths (Å)
! C1-C2
! C2-C3
! C3-C4
! C4-C5
! C5-C6
! C6-C1
|-
| Ethylene
|
|
|
|
| 1.36
|
|-
| Butadiene
| 1.36
| 1.54
| 1.36
|
|
|
|-
| Transition State
| 1.38
| 1.41
| 1.38
| 2.11
| 1.38
| 2.12
|-
| Cyclohexadiene
| 1.49
| 1.33
| 1.49
| 1.54
| 1.54
| 1.54
|}

The numbering of the carbon bonds are according to the labels on figure 1. The typical C-C bond lengths are as follows:

{| class="wikitable"
! Bond Type
! Bond Length (Å)
|-
| sp<sup>3</sup>-sp<sup>3</sup> C-C bond
| 1.54
|-
| sp<sup>3</sup>-sp<sup>2</sup> C-C bond
| 1.50
|-
| sp<sup>2</sup>-sp<sup>2</sup> C-C bond
| 1.47
|-
| sp<sup>2</sup>-sp<sup>2</sup> C=C bond
| 1.34
|}

When the reaction proceeds to the transition state, the sp<sup>2</sup>-sp<sup>2</sup> C5-C6 bond (originally ethylene) becomes longer as the carbons starts to change from sp<sup>2</sup> hybridised to sp<sup>3</sup> hybridised.
This trait is also apparent with C1-C2 and C3-C4 bonds where it once was the double bonds on butadiene, however, the increase in length of these bonds is less than that of C5-C6 due to the formation of a new double bond between C2 and C3, thus these carbons still remain sp<sup>2</sup> hybridised. This also leads to the next observation, where the C2-C3 bond decreases in length as it moves from the reactants to the transition state then the product, cyclohexadiene. This is because it is changing from a sp<sup>3</sup>-sp<sup>3</sup> C-C bond to a sp<sup>2</sup>-sp<sup>2</sup> C=C bond where the increase in s character shortens the bond lengths. This reaction also leads to the formation of 2 new bonds, namely C4-C5 and C6-C1. The Van der Waals radius of a carbon atom is 1.7 Å, and so the distance between 2 carbon atoms should be 3.4 Å, which is relatively longer than the bonds C4-C5 and C6-C1 which has a length of 2.11 and 2.12 Å respectively. This shows that the bonds are already partially formed in the transition state and they are beginning to interact together. This bond then settled at 1.54 Å in the product which matches with the typical bond length for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond.

=== Analysis of the vibrations ===

The animation for the first vibration is shown below. As observed, the formation of the 2 new bonds are synchronous as the reacting termini of butadiene and ethylene approaches each other at the same rate.

{| class="wikitable"
! <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 2;rotate x -20; </script>
<uploadedFileContents>Cc5115 OPT MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| The vibrations
|}

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

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via either the endo or exo pathways to form 2 products with different stereochemistry. Method 3 was employed in order to compute the TS for this exercise. This time, the structures were further optimised with B3LYP/6-31G method and the results are shown and discussed below.

=== Analysis of Molecular Orbitals ===

There are two types of Diels-Alder (DA) reactions: one is with a normal electron demand where the dienophile is electron deficient and the diene is electron rich, and the other is with an inverse electron demand where the dienophile is electron rich and the diene is electron deficient.

For a normal electron demand DA reaction, the dienophile low-lying LUMO interacts with the diene HOMO which has a high energy. However, observing the energies of the reactants and the transition states, the MO diagram shows that this particular DA reaction has an inverse electron demand where the dienophile (1,3-dioxole) is electron rich (higher in energy) and the diene (cyclohexadiene) is electron poor (lower in energy). The interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene thus leads to the HOMO and LUMO of the transition state. Although opposing that of a normal electron demand DA, this reaction still follows the Woodword-Hoffman rule and is thermally allowed.

Similar to exercise 1, MOs of the same symmetry interact; the symmetrical dienophile HOMO and the diene LUMO interacts to give a symmetrical TS HOMO and LUMO, while the asymmetrical dienophile LUMO and diene HOMO gives the asymmetrical TS HOMO-1 and LUMO+1. It is also observable that the endo TS HOMO has a lower energy than the exo TS HOMO which suggests that the endo reaction is favoured. This will be discussed further in the Thermochemistry section of this exercise.

{| class="wikitable"
! ENDO TS - HOMO -1
! ENDO TS - HOMO
! ENDO TS - LUMO
! ENDO TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Log Files ====

[[File:Cc5115 ENDO B3.LOG]]

[[File:Cc5115 PLEASE WORK B3.LOG]]

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +149.70
| -77.52
|-
| Exo
| +157.52
| -73.92
|}

As discussed briefly in the introduction, the reactants need to pass the activation barrier (transition state) in order to reach to the products. The table regarding the reaction barriers and energies shows that the activation barrier for the endo reaction is less than that of the exo reaction, more-so confirming that the endo reaction is kinetically favoured. This links to the lower energy that the endo TS HOMO has compared to the exo TS. This observance can be explained by secondary orbital interation (SOI). The 2 non-bonding oxygen p-orbitals containing electron lone pairs can overlap with the LUMO of the diene through space thus stabilising the TS and consequentially lowering reaction barrier. However, the more negative reaction energy of the endo reaction can be explained with sterics; in the exo transition state, the steric interaction between the sp<sup>3</sup> bridging carbons and the rest of the 1,3-dioxole structure results in the exo product being higher in energy.

{| class="wikitable"
! Exo Secondary MO
! Endo Secondary MO
|-
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

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

=== IRC ===

{| class="wikitable"
! [[File:Cc5115 Exo IRC gif.gif|thumb|x500px|500px|left|IRC for Exo Product]]
! [[File:Cc5115 Endo IRC gif.gif|thumb|x500px|500px|left|IRC for Endo Product]]
! [[File:Chelatropic IRC gif.gif|thumb|x500px|500px|left|IRC for Chelatropic Product]]
|}

IRC (intrinsic reaction coordinate) show how reactions move in space during its reaction to form products. From the IRC animations, it can be seen that the formation of the new bonds differ to that of exercise 1. Here, in the exo and endo pathways, the formation of the 2 new bonds are asynchronous as one bond forms before the other. However, the bonds form synchronously in the chelatropic reaction leading to the symmetrical product.

The IRC reaction pathways also show a smaller activation barrier compared to that of exercise 1. This is because xylylene is highly unstable. Xylylene can exist with 4π electrons making it anti-aromatic, or either with 6π electrons an a diradical which is very unstable. On the flipside, the product formed is aromatic making the DA reaction extremely favourable. Naphthalene forces the diene to be rigid in its positions easing the overlap capabilities of the diene with the dienophile. This can be observed in the animation as naphthalene doesn't have to go through major rearrangements in order to form the products.

In the reaction, naphthalene initially has a C=C bond length of 1.35 Å and a C-C bond length averaging around 1.51 Å. This changes as the product is formed where all the carbon-carbon bonds on the 6 membered rings become 1.47 Å in length suggesting the formation of an aromatic 6-membered ring where the π electrons are delocalised throughout the ring. The change in bond length can also be seen with careful observation of the animations.

Rep:Mod:cc5115TS

2018-02-14T03:05:30Z

Cc5115: /* IRC */

= Y3C Transition states and Reactivity =

== Introduction ==

This section aims to illustrate the 3 different computational techniques that can be utilised in order to analyse the transition state (TS) of a reaction. The TS is the state which has the highest energy along a reaction coordinate, as a result it is the least stable state. In the reaction, the reactants needs to have a certain amount of energy in order to surpass the activation barrier, also known as the transition state energy, and reach the product state. This computational lab allows for calculations leading to the location of the TS. The structure of the TS is crucial in determining the mechanism of a reaction.

A potential energy surface (PES) has a 3N-6 dimension, which coincides to the degrees of freedom that the molecule has, where N is the number of atoms that the molecule possesses. In a 3-D PES, the saddle point (also called the TS), is a local mixami amidst 2 minima, and can be sometimes identified through secondary derivatives as it would be negative in one direction and positive in all other directions.

There are 3 calculation methods available in order to determine the structure of the TS.

1. The first and fastest method requires only one step where a guessed structure of the TS is optimised to give an optimised TS. This means that one will need of the TS to quite an extent, furthermore this method is rather unreliable as there is a high chance that the guessed TS is incorrectly drawn.

2. The second method works from a pre-frozen guess structure of the TS where the reacting termini of the reactants are frozen in space before the remaining structure is optimised to a minima. After that, the molecules are optimised as a transition state. This allows for a more reliable representation of the TS. This method is sufficient for Exercise 1.

3. The third method is the longest and most reliable method. Here, one starts by either optimising from the reactants or the products to a minima. For the reactant case, each reactants are optimised to a minima, arranged to resemble the TS and the reacting termini are frozen and the rest of the method 2 is repeated. A similar case occurs with the product; when the product is optimised to a minima, the bonds formed in the reactions are removed, the 2 fragments are arranged to resemble the TS and the reacting termini are frozen and method 2 was used once more. This method allows for the most reliable representation of the TS and is used for Exercise 2 & 3.

In this computational lab, two methods of calculation were used on Gaussian in order to find the TS. During the optimisation, the position of the molecule is decided as it is built in Gaussian. The time-independent Schrödinger equation was solved whilst utilising the Born-Oppenheimer approximation in order to find the energy and the wavefunction φ which represents the electronic states for the fixed nuclear positions and is dependent on on frozen nuclei positions. This is also known as the self-consistent field method (SCF). The two methods employed are the semi-empirical method PM6, which is usually performed first and sometimes followed by the Density Functional Theory (DFT) method B3LYP. The semi-empirical method PM6, although based on the Hartree-Fock formalism, this method uses many approximations based on experimental data in order to solve the Schrodinger equations. This method is usually fast and reliable, but can be easily countered if the environment of the molecule that is being computed is not similar enough to the approximated parameters of this method. The other method is B3LYP, a hydrid functional which utilises the DFT in order to calculate the majority of the Hamiltonian while a small portion still utilises the Hartree-Fock theory to calculate the exchange integral term. B3LYP stands for Becke, 3-parameter, Lee-Yang-Parr and uses a 6-31G basis set as the electronic wavefunction in order to produce more accurate results at the cost of increased calculation time.

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

[[File:Ex1 general.png|thumb|x700px|700px|centre|Figure 1: Formation of Cyclohaxadiene]]

Also known as the Diels-Alder reaction, this exercise investigates the well-known [4+2] cycloaddition between a conjugated diene (butadiene) and a dienophile (ethylene). The electrophilic reaction involves 4 pi-electrons from the diene and 2 pi-electrons from the alkene, and is a popular method to form regio- and stereochemically controlled 6-membered rings.

Method 2 was used to compute the transition state (TS) for this exercise. All steps are optimised to the PM6 level. First, the reactants are optimised to a minimum. The carbons at the reacting termini were then frozen at around 2.20 Å before optimised to a minimum to give a frozen-guess TS. Then finally, the molecule was optimised as a TS and an IRC was performed in order to confirm and locate the transition state.

=== Analysis of the Molecular Orbitals (MO) ===

The Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) for the reactants and the TS are shown below and its energies were recorded in order to produce the MO diagram as shown in figure 2.

{| class="wikitable"
! Ethene - HOMO
! Ethene - LUMO
! Butadiene - HOMO
! Butadiene - LUMO
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Cc5115 exer1finalMO.png|thumb|x800px|800px|left|Figure 2: MO Diagram for the formation of Transition State of the Diels-Alder Reaction]]

The symmetric TS HOMO and LUMO are formed through the interactions between the HOMO of ethylene and the LUMO of butadiene, both of which are symmetric. On the other hand, the LUMO of ethylene and the HOMO of butadiene, both of which are asymmetric, interacts to give an asymmetric HOMO-1 and LUMO+1. What can be concluded about the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed, and that the reaction is forbidden when the symmetry of the molecular orbitals aren't the same. The orbital overlap integral, S<sub>AB</sub>, is a quantitative measure of orbital overlap of two different atoms. Orbitals of the same symmetry will lead to constructive overlap and gives a non-zero value while orbitals of different symmetry will lead to destructive overlap and an orbital overlap integral of zero. Thus the overlap integral are:

- Non-zero for symmetric-symmetric interaction

- Non-zero for asymmetric-asymmetric interaction

- Zero for symmetric-asymmetric interaction

As observed in the MO diagram, the energy gap between the HOMO and LUMO for butadiene is smaller that those for ethylene due to butadiene being more electron rich than ethylene. Furthermore, in a normal MO diagram, the bonding MO formed should have a lower energy compared to both atomic orbitals (AO) whilst the anti-bonding MO formed should have a higher energy than both AOs. The reason why figure 3 goes against the tide is because the MOs formed corresponds to the transition state where the electrons are very delocalised within the chemical environment of the molecule.

==== LOG Files ====

[[:File:Cc5115_ETHENE_MO.LOG]]

[[:File:Cc5115_BUTADIENE_MO.LOG]]

[[:File:Cc5115_OPT_MO.LOG]]

=== Analysis of the C-C bond lengths ===

{| class="wikitable"
! Bond Lengths (Å)
! C1-C2
! C2-C3
! C3-C4
! C4-C5
! C5-C6
! C6-C1
|-
| Ethylene
|
|
|
|
| 1.36
|
|-
| Butadiene
| 1.36
| 1.54
| 1.36
|
|
|
|-
| Transition State
| 1.38
| 1.41
| 1.38
| 2.11
| 1.38
| 2.12
|-
| Cyclohexadiene
| 1.49
| 1.33
| 1.49
| 1.54
| 1.54
| 1.54
|}

The numbering of the carbon bonds are according to the labels on figure 1. The typical C-C bond lengths are as follows:

{| class="wikitable"
! Bond Type
! Bond Length (Å)
|-
| sp<sup>3</sup>-sp<sup>3</sup> C-C bond
| 1.54
|-
| sp<sup>3</sup>-sp<sup>2</sup> C-C bond
| 1.50
|-
| sp<sup>2</sup>-sp<sup>2</sup> C-C bond
| 1.47
|-
| sp<sup>2</sup>-sp<sup>2</sup> C=C bond
| 1.34
|}

When the reaction proceeds to the transition state, the sp<sup>2</sup>-sp<sup>2</sup> C5-C6 bond (originally ethylene) becomes longer as the carbons starts to change from sp<sup>2</sup> hybridised to sp<sup>3</sup> hybridised.
This trait is also apparent with C1-C2 and C3-C4 bonds where it once was the double bonds on butadiene, however, the increase in length of these bonds is less than that of C5-C6 due to the formation of a new double bond between C2 and C3, thus these carbons still remain sp<sup>2</sup> hybridised. This also leads to the next observation, where the C2-C3 bond decreases in length as it moves from the reactants to the transition state then the product, cyclohexadiene. This is because it is changing from a sp<sup>3</sup>-sp<sup>3</sup> C-C bond to a sp<sup>2</sup>-sp<sup>2</sup> C=C bond where the increase in s character shortens the bond lengths. This reaction also leads to the formation of 2 new bonds, namely C4-C5 and C6-C1. The Van der Waals radius of a carbon atom is 1.7 Å, and so the distance between 2 carbon atoms should be 3.4 Å, which is relatively longer than the bonds C4-C5 and C6-C1 which has a length of 2.11 and 2.12 Å respectively. This shows that the bonds are already partially formed in the transition state and they are beginning to interact together. This bond then settled at 1.54 Å in the product which matches with the typical bond length for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond.

=== Analysis of the vibrations ===

The animation for the first vibration is shown below. As observed, the formation of the 2 new bonds are synchronous as the reacting termini of butadiene and ethylene approaches each other at the same rate.

{| class="wikitable"
! <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 2;rotate x -20; </script>
<uploadedFileContents>Cc5115 OPT MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| The vibrations
|}

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

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via either the endo or exo pathways to form 2 products with different stereochemistry. Method 3 was employed in order to compute the TS for this exercise. This time, the structures were further optimised with B3LYP/6-31G method and the results are shown and discussed below.

=== Analysis of Molecular Orbitals ===

There are two types of Diels-Alder (DA) reactions: one is with a normal electron demand where the dienophile is electron deficient and the diene is electron rich, and the other is with an inverse electron demand where the dienophile is electron rich and the diene is electron deficient.

For a normal electron demand DA reaction, the dienophile low-lying LUMO interacts with the diene HOMO which has a high energy. However, observing the energies of the reactants and the transition states, the MO diagram shows that this particular DA reaction has an inverse electron demand where the dienophile (1,3-dioxole) is electron rich (higher in energy) and the diene (cyclohexadiene) is electron poor (lower in energy). The interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene thus leads to the HOMO and LUMO of the transition state. Although opposing that of a normal electron demand DA, this reaction still follows the Woodword-Hoffman rule and is thermally allowed.

Similar to exercise 1, MOs of the same symmetry interact; the symmetrical dienophile HOMO and the diene LUMO interacts to give a symmetrical TS HOMO and LUMO, while the asymmetrical dienophile LUMO and diene HOMO gives the asymmetrical TS HOMO-1 and LUMO+1. It is also observable that the endo TS HOMO has a lower energy than the exo TS HOMO which suggests that the endo reaction is favoured. This will be discussed further in the Thermochemistry section of this exercise.

{| class="wikitable"
! ENDO TS - HOMO -1
! ENDO TS - HOMO
! ENDO TS - LUMO
! ENDO TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Log Files ====

[[File:Cc5115 ENDO B3.LOG]]

[[File:Cc5115 PLEASE WORK B3.LOG]]

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +149.70
| -77.52
|-
| Exo
| +157.52
| -73.92
|}

As discussed briefly in the introduction, the reactants need to pass the activation barrier (transition state) in order to reach to the products. The table regarding the reaction barriers and energies shows that the activation barrier for the endo reaction is less than that of the exo reaction, more-so confirming that the endo reaction is kinetically favoured. This links to the lower energy that the endo TS HOMO has compared to the exo TS. This observance can be explained by secondary orbital interation (SOI). The 2 non-bonding oxygen p-orbitals containing electron lone pairs can overlap with the LUMO of the diene through space thus stabilising the TS and consequentially lowering reaction barrier. However, the more negative reaction energy of the endo reaction can be explained with sterics; in the exo transition state, the steric interaction between the sp<sup>3</sup> bridging carbons and the rest of the 1,3-dioxole structure results in the exo product being higher in energy.

{| class="wikitable"
! Exo Secondary MO
! Endo Secondary MO
|-
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

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

=== IRC ===

{| class="wikitable"
| [[File:Cc5115 IRC exo.png|thumb|x500px|500px|left|IRC for Exo Product]]
| [[File:Cc5115 IRC endo.png|thumb|x500px|500px|centre|IRC for Exo Product]]
| [[File:Cc5115 IRC chela.png|thumb|x500px|500px|right|IRC for Chelatropic Product]]
|}

{| class="wikitable"
! [[File:Cc5115 Exo IRC gif.gif|thumb|x500px|500px|left|IRC for Exo Product]]
! [[File:Cc5115 Endo IRC gif.gif|thumb|x500px|500px|left|IRC for Endo Product]]
! [[File:Chelatropic IRC gif.gif|thumb|x500px|500px|left|IRC for Chelatropic Product]]
|}

IRC (intrinsic reaction coordinate) show how reactions move in space during its reaction to form products. From the IRC animations, it can be seen that the formation of the new bonds differ to that of exercise 1. Here, in the exo and endo pathways, the formation of the 2 new bonds are asynchronous as one bond forms before the other. However, the bonds form synchronously in the chelatropic reaction leading to the symmetrical product.

The IRC reaction pathways also show a smaller activation barrier compared to that of exercise 1. This is because xylylene is highly unstable. Xylylene can exist with 4π electrons making it anti-aromatic, or either with 6π electrons an a diradical which is very unstable. On the flipside, the product formed is aromatic making the DA reaction extremely favourable. Naphthalene forces the diene to be rigid in its positions easing the overlap capabilities of the diene with the dienophile. This can be observed in the animation as naphthalene doesn't have to go through major rearrangements in order to form the products.

In the reaction, naphthalene initially has a C=C bond length of 1.35 Å and a C-C bond length averaging around 1.51 Å. This changes as the product is formed where all the carbon-carbon bonds on the 6 membered rings become 1.47 Å in length suggesting the formation of an aromatic 6-membered ring where the π electrons are delocalised throughout the ring. The change in bond length can also be seen with careful observation of the animations.

File:Chelatropic IRC gif.gif

2018-02-14T03:05:12Z

Cc5115:

File:Cc5115 Endo IRC gif.gif

2018-02-14T03:04:08Z

Cc5115:

Rep:Mod:cc5115TS

2018-02-14T03:03:40Z

Cc5115: /* IRC */

= Y3C Transition states and Reactivity =

== Introduction ==

This section aims to illustrate the 3 different computational techniques that can be utilised in order to analyse the transition state (TS) of a reaction. The TS is the state which has the highest energy along a reaction coordinate, as a result it is the least stable state. In the reaction, the reactants needs to have a certain amount of energy in order to surpass the activation barrier, also known as the transition state energy, and reach the product state. This computational lab allows for calculations leading to the location of the TS. The structure of the TS is crucial in determining the mechanism of a reaction.

A potential energy surface (PES) has a 3N-6 dimension, which coincides to the degrees of freedom that the molecule has, where N is the number of atoms that the molecule possesses. In a 3-D PES, the saddle point (also called the TS), is a local mixami amidst 2 minima, and can be sometimes identified through secondary derivatives as it would be negative in one direction and positive in all other directions.

There are 3 calculation methods available in order to determine the structure of the TS.

1. The first and fastest method requires only one step where a guessed structure of the TS is optimised to give an optimised TS. This means that one will need of the TS to quite an extent, furthermore this method is rather unreliable as there is a high chance that the guessed TS is incorrectly drawn.

2. The second method works from a pre-frozen guess structure of the TS where the reacting termini of the reactants are frozen in space before the remaining structure is optimised to a minima. After that, the molecules are optimised as a transition state. This allows for a more reliable representation of the TS. This method is sufficient for Exercise 1.

3. The third method is the longest and most reliable method. Here, one starts by either optimising from the reactants or the products to a minima. For the reactant case, each reactants are optimised to a minima, arranged to resemble the TS and the reacting termini are frozen and the rest of the method 2 is repeated. A similar case occurs with the product; when the product is optimised to a minima, the bonds formed in the reactions are removed, the 2 fragments are arranged to resemble the TS and the reacting termini are frozen and method 2 was used once more. This method allows for the most reliable representation of the TS and is used for Exercise 2 & 3.

In this computational lab, two methods of calculation were used on Gaussian in order to find the TS. During the optimisation, the position of the molecule is decided as it is built in Gaussian. The time-independent Schrödinger equation was solved whilst utilising the Born-Oppenheimer approximation in order to find the energy and the wavefunction φ which represents the electronic states for the fixed nuclear positions and is dependent on on frozen nuclei positions. This is also known as the self-consistent field method (SCF). The two methods employed are the semi-empirical method PM6, which is usually performed first and sometimes followed by the Density Functional Theory (DFT) method B3LYP. The semi-empirical method PM6, although based on the Hartree-Fock formalism, this method uses many approximations based on experimental data in order to solve the Schrodinger equations. This method is usually fast and reliable, but can be easily countered if the environment of the molecule that is being computed is not similar enough to the approximated parameters of this method. The other method is B3LYP, a hydrid functional which utilises the DFT in order to calculate the majority of the Hamiltonian while a small portion still utilises the Hartree-Fock theory to calculate the exchange integral term. B3LYP stands for Becke, 3-parameter, Lee-Yang-Parr and uses a 6-31G basis set as the electronic wavefunction in order to produce more accurate results at the cost of increased calculation time.

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

[[File:Ex1 general.png|thumb|x700px|700px|centre|Figure 1: Formation of Cyclohaxadiene]]

Also known as the Diels-Alder reaction, this exercise investigates the well-known [4+2] cycloaddition between a conjugated diene (butadiene) and a dienophile (ethylene). The electrophilic reaction involves 4 pi-electrons from the diene and 2 pi-electrons from the alkene, and is a popular method to form regio- and stereochemically controlled 6-membered rings.

Method 2 was used to compute the transition state (TS) for this exercise. All steps are optimised to the PM6 level. First, the reactants are optimised to a minimum. The carbons at the reacting termini were then frozen at around 2.20 Å before optimised to a minimum to give a frozen-guess TS. Then finally, the molecule was optimised as a TS and an IRC was performed in order to confirm and locate the transition state.

=== Analysis of the Molecular Orbitals (MO) ===

The Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) for the reactants and the TS are shown below and its energies were recorded in order to produce the MO diagram as shown in figure 2.

{| class="wikitable"
! Ethene - HOMO
! Ethene - LUMO
! Butadiene - HOMO
! Butadiene - LUMO
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Cc5115 exer1finalMO.png|thumb|x800px|800px|left|Figure 2: MO Diagram for the formation of Transition State of the Diels-Alder Reaction]]

The symmetric TS HOMO and LUMO are formed through the interactions between the HOMO of ethylene and the LUMO of butadiene, both of which are symmetric. On the other hand, the LUMO of ethylene and the HOMO of butadiene, both of which are asymmetric, interacts to give an asymmetric HOMO-1 and LUMO+1. What can be concluded about the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed, and that the reaction is forbidden when the symmetry of the molecular orbitals aren't the same. The orbital overlap integral, S<sub>AB</sub>, is a quantitative measure of orbital overlap of two different atoms. Orbitals of the same symmetry will lead to constructive overlap and gives a non-zero value while orbitals of different symmetry will lead to destructive overlap and an orbital overlap integral of zero. Thus the overlap integral are:

- Non-zero for symmetric-symmetric interaction

- Non-zero for asymmetric-asymmetric interaction

- Zero for symmetric-asymmetric interaction

As observed in the MO diagram, the energy gap between the HOMO and LUMO for butadiene is smaller that those for ethylene due to butadiene being more electron rich than ethylene. Furthermore, in a normal MO diagram, the bonding MO formed should have a lower energy compared to both atomic orbitals (AO) whilst the anti-bonding MO formed should have a higher energy than both AOs. The reason why figure 3 goes against the tide is because the MOs formed corresponds to the transition state where the electrons are very delocalised within the chemical environment of the molecule.

==== LOG Files ====

[[:File:Cc5115_ETHENE_MO.LOG]]

[[:File:Cc5115_BUTADIENE_MO.LOG]]

[[:File:Cc5115_OPT_MO.LOG]]

=== Analysis of the C-C bond lengths ===

{| class="wikitable"
! Bond Lengths (Å)
! C1-C2
! C2-C3
! C3-C4
! C4-C5
! C5-C6
! C6-C1
|-
| Ethylene
|
|
|
|
| 1.36
|
|-
| Butadiene
| 1.36
| 1.54
| 1.36
|
|
|
|-
| Transition State
| 1.38
| 1.41
| 1.38
| 2.11
| 1.38
| 2.12
|-
| Cyclohexadiene
| 1.49
| 1.33
| 1.49
| 1.54
| 1.54
| 1.54
|}

The numbering of the carbon bonds are according to the labels on figure 1. The typical C-C bond lengths are as follows:

{| class="wikitable"
! Bond Type
! Bond Length (Å)
|-
| sp<sup>3</sup>-sp<sup>3</sup> C-C bond
| 1.54
|-
| sp<sup>3</sup>-sp<sup>2</sup> C-C bond
| 1.50
|-
| sp<sup>2</sup>-sp<sup>2</sup> C-C bond
| 1.47
|-
| sp<sup>2</sup>-sp<sup>2</sup> C=C bond
| 1.34
|}

When the reaction proceeds to the transition state, the sp<sup>2</sup>-sp<sup>2</sup> C5-C6 bond (originally ethylene) becomes longer as the carbons starts to change from sp<sup>2</sup> hybridised to sp<sup>3</sup> hybridised.
This trait is also apparent with C1-C2 and C3-C4 bonds where it once was the double bonds on butadiene, however, the increase in length of these bonds is less than that of C5-C6 due to the formation of a new double bond between C2 and C3, thus these carbons still remain sp<sup>2</sup> hybridised. This also leads to the next observation, where the C2-C3 bond decreases in length as it moves from the reactants to the transition state then the product, cyclohexadiene. This is because it is changing from a sp<sup>3</sup>-sp<sup>3</sup> C-C bond to a sp<sup>2</sup>-sp<sup>2</sup> C=C bond where the increase in s character shortens the bond lengths. This reaction also leads to the formation of 2 new bonds, namely C4-C5 and C6-C1. The Van der Waals radius of a carbon atom is 1.7 Å, and so the distance between 2 carbon atoms should be 3.4 Å, which is relatively longer than the bonds C4-C5 and C6-C1 which has a length of 2.11 and 2.12 Å respectively. This shows that the bonds are already partially formed in the transition state and they are beginning to interact together. This bond then settled at 1.54 Å in the product which matches with the typical bond length for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond.

=== Analysis of the vibrations ===

The animation for the first vibration is shown below. As observed, the formation of the 2 new bonds are synchronous as the reacting termini of butadiene and ethylene approaches each other at the same rate.

{| class="wikitable"
! <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 2;rotate x -20; </script>
<uploadedFileContents>Cc5115 OPT MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| The vibrations
|}

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

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via either the endo or exo pathways to form 2 products with different stereochemistry. Method 3 was employed in order to compute the TS for this exercise. This time, the structures were further optimised with B3LYP/6-31G method and the results are shown and discussed below.

=== Analysis of Molecular Orbitals ===

There are two types of Diels-Alder (DA) reactions: one is with a normal electron demand where the dienophile is electron deficient and the diene is electron rich, and the other is with an inverse electron demand where the dienophile is electron rich and the diene is electron deficient.

For a normal electron demand DA reaction, the dienophile low-lying LUMO interacts with the diene HOMO which has a high energy. However, observing the energies of the reactants and the transition states, the MO diagram shows that this particular DA reaction has an inverse electron demand where the dienophile (1,3-dioxole) is electron rich (higher in energy) and the diene (cyclohexadiene) is electron poor (lower in energy). The interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene thus leads to the HOMO and LUMO of the transition state. Although opposing that of a normal electron demand DA, this reaction still follows the Woodword-Hoffman rule and is thermally allowed.

Similar to exercise 1, MOs of the same symmetry interact; the symmetrical dienophile HOMO and the diene LUMO interacts to give a symmetrical TS HOMO and LUMO, while the asymmetrical dienophile LUMO and diene HOMO gives the asymmetrical TS HOMO-1 and LUMO+1. It is also observable that the endo TS HOMO has a lower energy than the exo TS HOMO which suggests that the endo reaction is favoured. This will be discussed further in the Thermochemistry section of this exercise.

{| class="wikitable"
! ENDO TS - HOMO -1
! ENDO TS - HOMO
! ENDO TS - LUMO
! ENDO TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Log Files ====

[[File:Cc5115 ENDO B3.LOG]]

[[File:Cc5115 PLEASE WORK B3.LOG]]

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +149.70
| -77.52
|-
| Exo
| +157.52
| -73.92
|}

As discussed briefly in the introduction, the reactants need to pass the activation barrier (transition state) in order to reach to the products. The table regarding the reaction barriers and energies shows that the activation barrier for the endo reaction is less than that of the exo reaction, more-so confirming that the endo reaction is kinetically favoured. This links to the lower energy that the endo TS HOMO has compared to the exo TS. This observance can be explained by secondary orbital interation (SOI). The 2 non-bonding oxygen p-orbitals containing electron lone pairs can overlap with the LUMO of the diene through space thus stabilising the TS and consequentially lowering reaction barrier. However, the more negative reaction energy of the endo reaction can be explained with sterics; in the exo transition state, the steric interaction between the sp<sup>3</sup> bridging carbons and the rest of the 1,3-dioxole structure results in the exo product being higher in energy.

{| class="wikitable"
! Exo Secondary MO
! Endo Secondary MO
|-
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

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

=== IRC ===

{| class="wikitable"
| [[File:Cc5115 IRC exo.png|thumb|x500px|500px|left|IRC for Exo Product]]
| [[File:Cc5115 IRC endo.png|thumb|x500px|500px|centre|IRC for Exo Product]]
| [[File:Cc5115 IRC chela.png|thumb|x500px|500px|right|IRC for Chelatropic Product]]
|}

{| class="wikitable"
! [[File:Cc5115 Exo IRC gif.gif|thumb|x500px|500px|left|IRC for Exo Product]]
| The vibrations
|}

IRC (intrinsic reaction coordinate) show how reactions move in space during its reaction to form products. From the IRC animations, it can be seen that the formation of the new bonds differ to that of exercise 1. Here, in the exo and endo pathways, the formation of the 2 new bonds are asynchronous as one bond forms before the other. However, the bonds form synchronously in the chelatropic reaction leading to the symmetrical product.

The IRC reaction pathways also show a smaller activation barrier compared to that of exercise 1. This is because xylylene is highly unstable. Xylylene can exist with 4π electrons making it anti-aromatic, or either with 6π electrons an a diradical which is very unstable. On the flipside, the product formed is aromatic making the DA reaction extremely favourable. Naphthalene forces the diene to be rigid in its positions easing the overlap capabilities of the diene with the dienophile. This can be observed in the animation as naphthalene doesn't have to go through major rearrangements in order to form the products.

In the reaction, naphthalene initially has a C=C bond length of 1.35 Å and a C-C bond length averaging around 1.51 Å. This changes as the product is formed where all the carbon-carbon bonds on the 6 membered rings become 1.47 Å in length suggesting the formation of an aromatic 6-membered ring where the π electrons are delocalised throughout the ring. The change in bond length can also be seen with careful observation of the animations.

File:Cc5115 Exo IRC gif.gif

2018-02-14T03:03:14Z

Cc5115:

Rep:Mod:cc5115TS

2018-02-14T02:59:19Z

Cc5115: /* Exercise 3: Diels-Alder vs Cheletropic */

= Y3C Transition states and Reactivity =

== Introduction ==

This section aims to illustrate the 3 different computational techniques that can be utilised in order to analyse the transition state (TS) of a reaction. The TS is the state which has the highest energy along a reaction coordinate, as a result it is the least stable state. In the reaction, the reactants needs to have a certain amount of energy in order to surpass the activation barrier, also known as the transition state energy, and reach the product state. This computational lab allows for calculations leading to the location of the TS. The structure of the TS is crucial in determining the mechanism of a reaction.

A potential energy surface (PES) has a 3N-6 dimension, which coincides to the degrees of freedom that the molecule has, where N is the number of atoms that the molecule possesses. In a 3-D PES, the saddle point (also called the TS), is a local mixami amidst 2 minima, and can be sometimes identified through secondary derivatives as it would be negative in one direction and positive in all other directions.

There are 3 calculation methods available in order to determine the structure of the TS.

1. The first and fastest method requires only one step where a guessed structure of the TS is optimised to give an optimised TS. This means that one will need of the TS to quite an extent, furthermore this method is rather unreliable as there is a high chance that the guessed TS is incorrectly drawn.

2. The second method works from a pre-frozen guess structure of the TS where the reacting termini of the reactants are frozen in space before the remaining structure is optimised to a minima. After that, the molecules are optimised as a transition state. This allows for a more reliable representation of the TS. This method is sufficient for Exercise 1.

3. The third method is the longest and most reliable method. Here, one starts by either optimising from the reactants or the products to a minima. For the reactant case, each reactants are optimised to a minima, arranged to resemble the TS and the reacting termini are frozen and the rest of the method 2 is repeated. A similar case occurs with the product; when the product is optimised to a minima, the bonds formed in the reactions are removed, the 2 fragments are arranged to resemble the TS and the reacting termini are frozen and method 2 was used once more. This method allows for the most reliable representation of the TS and is used for Exercise 2 & 3.

In this computational lab, two methods of calculation were used on Gaussian in order to find the TS. During the optimisation, the position of the molecule is decided as it is built in Gaussian. The time-independent Schrödinger equation was solved whilst utilising the Born-Oppenheimer approximation in order to find the energy and the wavefunction φ which represents the electronic states for the fixed nuclear positions and is dependent on on frozen nuclei positions. This is also known as the self-consistent field method (SCF). The two methods employed are the semi-empirical method PM6, which is usually performed first and sometimes followed by the Density Functional Theory (DFT) method B3LYP. The semi-empirical method PM6, although based on the Hartree-Fock formalism, this method uses many approximations based on experimental data in order to solve the Schrodinger equations. This method is usually fast and reliable, but can be easily countered if the environment of the molecule that is being computed is not similar enough to the approximated parameters of this method. The other method is B3LYP, a hydrid functional which utilises the DFT in order to calculate the majority of the Hamiltonian while a small portion still utilises the Hartree-Fock theory to calculate the exchange integral term. B3LYP stands for Becke, 3-parameter, Lee-Yang-Parr and uses a 6-31G basis set as the electronic wavefunction in order to produce more accurate results at the cost of increased calculation time.

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

[[File:Ex1 general.png|thumb|x700px|700px|centre|Figure 1: Formation of Cyclohaxadiene]]

Also known as the Diels-Alder reaction, this exercise investigates the well-known [4+2] cycloaddition between a conjugated diene (butadiene) and a dienophile (ethylene). The electrophilic reaction involves 4 pi-electrons from the diene and 2 pi-electrons from the alkene, and is a popular method to form regio- and stereochemically controlled 6-membered rings.

Method 2 was used to compute the transition state (TS) for this exercise. All steps are optimised to the PM6 level. First, the reactants are optimised to a minimum. The carbons at the reacting termini were then frozen at around 2.20 Å before optimised to a minimum to give a frozen-guess TS. Then finally, the molecule was optimised as a TS and an IRC was performed in order to confirm and locate the transition state.

=== Analysis of the Molecular Orbitals (MO) ===

The Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) for the reactants and the TS are shown below and its energies were recorded in order to produce the MO diagram as shown in figure 2.

{| class="wikitable"
! Ethene - HOMO
! Ethene - LUMO
! Butadiene - HOMO
! Butadiene - LUMO
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Cc5115 exer1finalMO.png|thumb|x800px|800px|left|Figure 2: MO Diagram for the formation of Transition State of the Diels-Alder Reaction]]

The symmetric TS HOMO and LUMO are formed through the interactions between the HOMO of ethylene and the LUMO of butadiene, both of which are symmetric. On the other hand, the LUMO of ethylene and the HOMO of butadiene, both of which are asymmetric, interacts to give an asymmetric HOMO-1 and LUMO+1. What can be concluded about the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed, and that the reaction is forbidden when the symmetry of the molecular orbitals aren't the same. The orbital overlap integral, S<sub>AB</sub>, is a quantitative measure of orbital overlap of two different atoms. Orbitals of the same symmetry will lead to constructive overlap and gives a non-zero value while orbitals of different symmetry will lead to destructive overlap and an orbital overlap integral of zero. Thus the overlap integral are:

- Non-zero for symmetric-symmetric interaction

- Non-zero for asymmetric-asymmetric interaction

- Zero for symmetric-asymmetric interaction

As observed in the MO diagram, the energy gap between the HOMO and LUMO for butadiene is smaller that those for ethylene due to butadiene being more electron rich than ethylene. Furthermore, in a normal MO diagram, the bonding MO formed should have a lower energy compared to both atomic orbitals (AO) whilst the anti-bonding MO formed should have a higher energy than both AOs. The reason why figure 3 goes against the tide is because the MOs formed corresponds to the transition state where the electrons are very delocalised within the chemical environment of the molecule.

==== LOG Files ====

[[:File:Cc5115_ETHENE_MO.LOG]]

[[:File:Cc5115_BUTADIENE_MO.LOG]]

[[:File:Cc5115_OPT_MO.LOG]]

=== Analysis of the C-C bond lengths ===

{| class="wikitable"
! Bond Lengths (Å)
! C1-C2
! C2-C3
! C3-C4
! C4-C5
! C5-C6
! C6-C1
|-
| Ethylene
|
|
|
|
| 1.36
|
|-
| Butadiene
| 1.36
| 1.54
| 1.36
|
|
|
|-
| Transition State
| 1.38
| 1.41
| 1.38
| 2.11
| 1.38
| 2.12
|-
| Cyclohexadiene
| 1.49
| 1.33
| 1.49
| 1.54
| 1.54
| 1.54
|}

The numbering of the carbon bonds are according to the labels on figure 1. The typical C-C bond lengths are as follows:

{| class="wikitable"
! Bond Type
! Bond Length (Å)
|-
| sp<sup>3</sup>-sp<sup>3</sup> C-C bond
| 1.54
|-
| sp<sup>3</sup>-sp<sup>2</sup> C-C bond
| 1.50
|-
| sp<sup>2</sup>-sp<sup>2</sup> C-C bond
| 1.47
|-
| sp<sup>2</sup>-sp<sup>2</sup> C=C bond
| 1.34
|}

When the reaction proceeds to the transition state, the sp<sup>2</sup>-sp<sup>2</sup> C5-C6 bond (originally ethylene) becomes longer as the carbons starts to change from sp<sup>2</sup> hybridised to sp<sup>3</sup> hybridised.
This trait is also apparent with C1-C2 and C3-C4 bonds where it once was the double bonds on butadiene, however, the increase in length of these bonds is less than that of C5-C6 due to the formation of a new double bond between C2 and C3, thus these carbons still remain sp<sup>2</sup> hybridised. This also leads to the next observation, where the C2-C3 bond decreases in length as it moves from the reactants to the transition state then the product, cyclohexadiene. This is because it is changing from a sp<sup>3</sup>-sp<sup>3</sup> C-C bond to a sp<sup>2</sup>-sp<sup>2</sup> C=C bond where the increase in s character shortens the bond lengths. This reaction also leads to the formation of 2 new bonds, namely C4-C5 and C6-C1. The Van der Waals radius of a carbon atom is 1.7 Å, and so the distance between 2 carbon atoms should be 3.4 Å, which is relatively longer than the bonds C4-C5 and C6-C1 which has a length of 2.11 and 2.12 Å respectively. This shows that the bonds are already partially formed in the transition state and they are beginning to interact together. This bond then settled at 1.54 Å in the product which matches with the typical bond length for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond.

=== Analysis of the vibrations ===

The animation for the first vibration is shown below. As observed, the formation of the 2 new bonds are synchronous as the reacting termini of butadiene and ethylene approaches each other at the same rate.

{| class="wikitable"
! <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 2;rotate x -20; </script>
<uploadedFileContents>Cc5115 OPT MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| The vibrations
|}

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

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via either the endo or exo pathways to form 2 products with different stereochemistry. Method 3 was employed in order to compute the TS for this exercise. This time, the structures were further optimised with B3LYP/6-31G method and the results are shown and discussed below.

=== Analysis of Molecular Orbitals ===

There are two types of Diels-Alder (DA) reactions: one is with a normal electron demand where the dienophile is electron deficient and the diene is electron rich, and the other is with an inverse electron demand where the dienophile is electron rich and the diene is electron deficient.

For a normal electron demand DA reaction, the dienophile low-lying LUMO interacts with the diene HOMO which has a high energy. However, observing the energies of the reactants and the transition states, the MO diagram shows that this particular DA reaction has an inverse electron demand where the dienophile (1,3-dioxole) is electron rich (higher in energy) and the diene (cyclohexadiene) is electron poor (lower in energy). The interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene thus leads to the HOMO and LUMO of the transition state. Although opposing that of a normal electron demand DA, this reaction still follows the Woodword-Hoffman rule and is thermally allowed.

Similar to exercise 1, MOs of the same symmetry interact; the symmetrical dienophile HOMO and the diene LUMO interacts to give a symmetrical TS HOMO and LUMO, while the asymmetrical dienophile LUMO and diene HOMO gives the asymmetrical TS HOMO-1 and LUMO+1. It is also observable that the endo TS HOMO has a lower energy than the exo TS HOMO which suggests that the endo reaction is favoured. This will be discussed further in the Thermochemistry section of this exercise.

{| class="wikitable"
! ENDO TS - HOMO -1
! ENDO TS - HOMO
! ENDO TS - LUMO
! ENDO TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Log Files ====

[[File:Cc5115 ENDO B3.LOG]]

[[File:Cc5115 PLEASE WORK B3.LOG]]

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +149.70
| -77.52
|-
| Exo
| +157.52
| -73.92
|}

As discussed briefly in the introduction, the reactants need to pass the activation barrier (transition state) in order to reach to the products. The table regarding the reaction barriers and energies shows that the activation barrier for the endo reaction is less than that of the exo reaction, more-so confirming that the endo reaction is kinetically favoured. This links to the lower energy that the endo TS HOMO has compared to the exo TS. This observance can be explained by secondary orbital interation (SOI). The 2 non-bonding oxygen p-orbitals containing electron lone pairs can overlap with the LUMO of the diene through space thus stabilising the TS and consequentially lowering reaction barrier. However, the more negative reaction energy of the endo reaction can be explained with sterics; in the exo transition state, the steric interaction between the sp<sup>3</sup> bridging carbons and the rest of the 1,3-dioxole structure results in the exo product being higher in energy.

{| class="wikitable"
! Exo Secondary MO
! Endo Secondary MO
|-
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

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

=== IRC ===

{| class="wikitable"
| [[File:Cc5115 IRC exo.png|thumb|x500px|500px|left|IRC for Exo Product]]
| [[File:Cc5115 IRC endo.png|thumb|x500px|500px|centre|IRC for Exo Product]]
| [[File:Cc5115 IRC chela.png|thumb|x500px|500px|right|IRC for Chelatropic Product]]
|}

IRC (intrinsic reaction coordinate) show how reactions move in space during its reaction to form products. From the IRC animations, it can be seen that the formation of the new bonds differ to that of exercise 1. Here, in the exo and endo pathways, the formation of the 2 new bonds are asynchronous as one bond forms before the other. However, the bonds form synchronously in the chelatropic reaction leading to the symmetrical product.

The IRC reaction pathways also show a smaller activation barrier compared to that of exercise 1. This is because xylylene is highly unstable. Xylylene can exist with 4π electrons making it anti-aromatic, or either with 6π electrons an a diradical which is very unstable. On the flipside, the product formed is aromatic making the DA reaction extremely favourable. Naphthalene forces the diene to be rigid in its positions easing the overlap capabilities of the diene with the dienophile. This can be observed in the animation as naphthalene doesn't have to go through major rearrangements in order to form the products.

In the reaction, naphthalene initially has a C=C bond length of 1.35 Å and a C-C bond length averaging around 1.51 Å. This changes as the product is formed where all the carbon-carbon bonds on the 6 membered rings become 1.47 Å in length suggesting the formation of an aromatic 6-membered ring where the π electrons are delocalised throughout the ring. The change in bond length can also be seen with careful observation of the animations.

Rep:Mod:cc5115TS

2018-02-14T02:30:25Z

Cc5115: /* Analysis of Molecular Orbitals */

= Y3C Transition states and Reactivity =

== Introduction ==

This section aims to illustrate the 3 different computational techniques that can be utilised in order to analyse the transition state (TS) of a reaction. The TS is the state which has the highest energy along a reaction coordinate, as a result it is the least stable state. In the reaction, the reactants needs to have a certain amount of energy in order to surpass the activation barrier, also known as the transition state energy, and reach the product state. This computational lab allows for calculations leading to the location of the TS. The structure of the TS is crucial in determining the mechanism of a reaction.

A potential energy surface (PES) has a 3N-6 dimension, which coincides to the degrees of freedom that the molecule has, where N is the number of atoms that the molecule possesses. In a 3-D PES, the saddle point (also called the TS), is a local mixami amidst 2 minima, and can be sometimes identified through secondary derivatives as it would be negative in one direction and positive in all other directions.

There are 3 calculation methods available in order to determine the structure of the TS.

1. The first and fastest method requires only one step where a guessed structure of the TS is optimised to give an optimised TS. This means that one will need of the TS to quite an extent, furthermore this method is rather unreliable as there is a high chance that the guessed TS is incorrectly drawn.

2. The second method works from a pre-frozen guess structure of the TS where the reacting termini of the reactants are frozen in space before the remaining structure is optimised to a minima. After that, the molecules are optimised as a transition state. This allows for a more reliable representation of the TS. This method is sufficient for Exercise 1.

3. The third method is the longest and most reliable method. Here, one starts by either optimising from the reactants or the products to a minima. For the reactant case, each reactants are optimised to a minima, arranged to resemble the TS and the reacting termini are frozen and the rest of the method 2 is repeated. A similar case occurs with the product; when the product is optimised to a minima, the bonds formed in the reactions are removed, the 2 fragments are arranged to resemble the TS and the reacting termini are frozen and method 2 was used once more. This method allows for the most reliable representation of the TS and is used for Exercise 2 & 3.

In this computational lab, two methods of calculation were used on Gaussian in order to find the TS. During the optimisation, the position of the molecule is decided as it is built in Gaussian. The time-independent Schrödinger equation was solved whilst utilising the Born-Oppenheimer approximation in order to find the energy and the wavefunction φ which represents the electronic states for the fixed nuclear positions and is dependent on on frozen nuclei positions. This is also known as the self-consistent field method (SCF). The two methods employed are the semi-empirical method PM6, which is usually performed first and sometimes followed by the Density Functional Theory (DFT) method B3LYP. The semi-empirical method PM6, although based on the Hartree-Fock formalism, this method uses many approximations based on experimental data in order to solve the Schrodinger equations. This method is usually fast and reliable, but can be easily countered if the environment of the molecule that is being computed is not similar enough to the approximated parameters of this method. The other method is B3LYP, a hydrid functional which utilises the DFT in order to calculate the majority of the Hamiltonian while a small portion still utilises the Hartree-Fock theory to calculate the exchange integral term. B3LYP stands for Becke, 3-parameter, Lee-Yang-Parr and uses a 6-31G basis set as the electronic wavefunction in order to produce more accurate results at the cost of increased calculation time.

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

[[File:Ex1 general.png|thumb|x700px|700px|centre|Figure 1: Formation of Cyclohaxadiene]]

Also known as the Diels-Alder reaction, this exercise investigates the well-known [4+2] cycloaddition between a conjugated diene (butadiene) and a dienophile (ethylene). The electrophilic reaction involves 4 pi-electrons from the diene and 2 pi-electrons from the alkene, and is a popular method to form regio- and stereochemically controlled 6-membered rings.

Method 2 was used to compute the transition state (TS) for this exercise. All steps are optimised to the PM6 level. First, the reactants are optimised to a minimum. The carbons at the reacting termini were then frozen at around 2.20 Å before optimised to a minimum to give a frozen-guess TS. Then finally, the molecule was optimised as a TS and an IRC was performed in order to confirm and locate the transition state.

=== Analysis of the Molecular Orbitals (MO) ===

The Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) for the reactants and the TS are shown below and its energies were recorded in order to produce the MO diagram as shown in figure 2.

{| class="wikitable"
! Ethene - HOMO
! Ethene - LUMO
! Butadiene - HOMO
! Butadiene - LUMO
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Cc5115 exer1finalMO.png|thumb|x800px|800px|left|Figure 2: MO Diagram for the formation of Transition State of the Diels-Alder Reaction]]

The symmetric TS HOMO and LUMO are formed through the interactions between the HOMO of ethylene and the LUMO of butadiene, both of which are symmetric. On the other hand, the LUMO of ethylene and the HOMO of butadiene, both of which are asymmetric, interacts to give an asymmetric HOMO-1 and LUMO+1. What can be concluded about the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed, and that the reaction is forbidden when the symmetry of the molecular orbitals aren't the same. The orbital overlap integral, S<sub>AB</sub>, is a quantitative measure of orbital overlap of two different atoms. Orbitals of the same symmetry will lead to constructive overlap and gives a non-zero value while orbitals of different symmetry will lead to destructive overlap and an orbital overlap integral of zero. Thus the overlap integral are:

- Non-zero for symmetric-symmetric interaction

- Non-zero for asymmetric-asymmetric interaction

- Zero for symmetric-asymmetric interaction

As observed in the MO diagram, the energy gap between the HOMO and LUMO for butadiene is smaller that those for ethylene due to butadiene being more electron rich than ethylene. Furthermore, in a normal MO diagram, the bonding MO formed should have a lower energy compared to both atomic orbitals (AO) whilst the anti-bonding MO formed should have a higher energy than both AOs. The reason why figure 3 goes against the tide is because the MOs formed corresponds to the transition state where the electrons are very delocalised within the chemical environment of the molecule.

==== LOG Files ====

[[:File:Cc5115_ETHENE_MO.LOG]]

[[:File:Cc5115_BUTADIENE_MO.LOG]]

[[:File:Cc5115_OPT_MO.LOG]]

=== Analysis of the C-C bond lengths ===

{| class="wikitable"
! Bond Lengths (Å)
! C1-C2
! C2-C3
! C3-C4
! C4-C5
! C5-C6
! C6-C1
|-
| Ethylene
|
|
|
|
| 1.36
|
|-
| Butadiene
| 1.36
| 1.54
| 1.36
|
|
|
|-
| Transition State
| 1.38
| 1.41
| 1.38
| 2.11
| 1.38
| 2.12
|-
| Cyclohexadiene
| 1.49
| 1.33
| 1.49
| 1.54
| 1.54
| 1.54
|}

The numbering of the carbon bonds are according to the labels on figure 1. The typical C-C bond lengths are as follows:

{| class="wikitable"
! Bond Type
! Bond Length (Å)
|-
| sp<sup>3</sup>-sp<sup>3</sup> C-C bond
| 1.54
|-
| sp<sup>3</sup>-sp<sup>2</sup> C-C bond
| 1.50
|-
| sp<sup>2</sup>-sp<sup>2</sup> C-C bond
| 1.47
|-
| sp<sup>2</sup>-sp<sup>2</sup> C=C bond
| 1.34
|}

When the reaction proceeds to the transition state, the sp<sup>2</sup>-sp<sup>2</sup> C5-C6 bond (originally ethylene) becomes longer as the carbons starts to change from sp<sup>2</sup> hybridised to sp<sup>3</sup> hybridised.
This trait is also apparent with C1-C2 and C3-C4 bonds where it once was the double bonds on butadiene, however, the increase in length of these bonds is less than that of C5-C6 due to the formation of a new double bond between C2 and C3, thus these carbons still remain sp<sup>2</sup> hybridised. This also leads to the next observation, where the C2-C3 bond decreases in length as it moves from the reactants to the transition state then the product, cyclohexadiene. This is because it is changing from a sp<sup>3</sup>-sp<sup>3</sup> C-C bond to a sp<sup>2</sup>-sp<sup>2</sup> C=C bond where the increase in s character shortens the bond lengths. This reaction also leads to the formation of 2 new bonds, namely C4-C5 and C6-C1. The Van der Waals radius of a carbon atom is 1.7 Å, and so the distance between 2 carbon atoms should be 3.4 Å, which is relatively longer than the bonds C4-C5 and C6-C1 which has a length of 2.11 and 2.12 Å respectively. This shows that the bonds are already partially formed in the transition state and they are beginning to interact together. This bond then settled at 1.54 Å in the product which matches with the typical bond length for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond.

=== Analysis of the vibrations ===

The animation for the first vibration is shown below. As observed, the formation of the 2 new bonds are synchronous as the reacting termini of butadiene and ethylene approaches each other at the same rate.

{| class="wikitable"
! <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 2;rotate x -20; </script>
<uploadedFileContents>Cc5115 OPT MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| The vibrations
|}

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

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via either the endo or exo pathways to form 2 products with different stereochemistry. Method 3 was employed in order to compute the TS for this exercise. This time, the structures were further optimised with B3LYP/6-31G method and the results are shown and discussed below.

=== Analysis of Molecular Orbitals ===

There are two types of Diels-Alder (DA) reactions: one is with a normal electron demand where the dienophile is electron deficient and the diene is electron rich, and the other is with an inverse electron demand where the dienophile is electron rich and the diene is electron deficient.

For a normal electron demand DA reaction, the dienophile low-lying LUMO interacts with the diene HOMO which has a high energy. However, observing the energies of the reactants and the transition states, the MO diagram shows that this particular DA reaction has an inverse electron demand where the dienophile (1,3-dioxole) is electron rich (higher in energy) and the diene (cyclohexadiene) is electron poor (lower in energy). The interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene thus leads to the HOMO and LUMO of the transition state. Although opposing that of a normal electron demand DA, this reaction still follows the Woodword-Hoffman rule and is thermally allowed.

Similar to exercise 1, MOs of the same symmetry interact; the symmetrical dienophile HOMO and the diene LUMO interacts to give a symmetrical TS HOMO and LUMO, while the asymmetrical dienophile LUMO and diene HOMO gives the asymmetrical TS HOMO-1 and LUMO+1. It is also observable that the endo TS HOMO has a lower energy than the exo TS HOMO which suggests that the endo reaction is favoured. This will be discussed further in the Thermochemistry section of this exercise.

{| class="wikitable"
! ENDO TS - HOMO -1
! ENDO TS - HOMO
! ENDO TS - LUMO
! ENDO TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Log Files ====

[[File:Cc5115 ENDO B3.LOG]]

[[File:Cc5115 PLEASE WORK B3.LOG]]

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +149.70
| -77.52
|-
| Exo
| +157.52
| -73.92
|}

As discussed briefly in the introduction, the reactants need to pass the activation barrier (transition state) in order to reach to the products. The table regarding the reaction barriers and energies shows that the activation barrier for the endo reaction is less than that of the exo reaction, more-so confirming that the endo reaction is kinetically favoured. This links to the lower energy that the endo TS HOMO has compared to the exo TS. This observance can be explained by secondary orbital interation (SOI). The 2 non-bonding oxygen p-orbitals containing electron lone pairs can overlap with the LUMO of the diene through space thus stabilising the TS and consequentially lowering reaction barrier. However, the more negative reaction energy of the endo reaction can be explained with sterics; in the exo transition state, the steric interaction between the sp<sup>3</sup> bridging carbons and the rest of the 1,3-dioxole structure results in the exo product being higher in energy.

{| class="wikitable"
! Exo Secondary MO
! Endo Secondary MO
|-
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

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

{| class="wikitable"
| [[File:Cc5115 IRC exo.png|thumb|x500px|500px|left|IRC for Exo Product]]
| [[File:Cc5115 IRC endo.png|thumb|x500px|500px|centre|IRC for Exo Product]]
| [[File:Cc5115 IRC chela.png|thumb|x500px|500px|right|IRC for Chelatropic Product]]
|}

Rep:Mod:cc5115TS

2018-02-14T02:30:05Z

Cc5115: /* Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole */

= Y3C Transition states and Reactivity =

== Introduction ==

This section aims to illustrate the 3 different computational techniques that can be utilised in order to analyse the transition state (TS) of a reaction. The TS is the state which has the highest energy along a reaction coordinate, as a result it is the least stable state. In the reaction, the reactants needs to have a certain amount of energy in order to surpass the activation barrier, also known as the transition state energy, and reach the product state. This computational lab allows for calculations leading to the location of the TS. The structure of the TS is crucial in determining the mechanism of a reaction.

A potential energy surface (PES) has a 3N-6 dimension, which coincides to the degrees of freedom that the molecule has, where N is the number of atoms that the molecule possesses. In a 3-D PES, the saddle point (also called the TS), is a local mixami amidst 2 minima, and can be sometimes identified through secondary derivatives as it would be negative in one direction and positive in all other directions.

There are 3 calculation methods available in order to determine the structure of the TS.

1. The first and fastest method requires only one step where a guessed structure of the TS is optimised to give an optimised TS. This means that one will need of the TS to quite an extent, furthermore this method is rather unreliable as there is a high chance that the guessed TS is incorrectly drawn.

2. The second method works from a pre-frozen guess structure of the TS where the reacting termini of the reactants are frozen in space before the remaining structure is optimised to a minima. After that, the molecules are optimised as a transition state. This allows for a more reliable representation of the TS. This method is sufficient for Exercise 1.

3. The third method is the longest and most reliable method. Here, one starts by either optimising from the reactants or the products to a minima. For the reactant case, each reactants are optimised to a minima, arranged to resemble the TS and the reacting termini are frozen and the rest of the method 2 is repeated. A similar case occurs with the product; when the product is optimised to a minima, the bonds formed in the reactions are removed, the 2 fragments are arranged to resemble the TS and the reacting termini are frozen and method 2 was used once more. This method allows for the most reliable representation of the TS and is used for Exercise 2 & 3.

In this computational lab, two methods of calculation were used on Gaussian in order to find the TS. During the optimisation, the position of the molecule is decided as it is built in Gaussian. The time-independent Schrödinger equation was solved whilst utilising the Born-Oppenheimer approximation in order to find the energy and the wavefunction φ which represents the electronic states for the fixed nuclear positions and is dependent on on frozen nuclei positions. This is also known as the self-consistent field method (SCF). The two methods employed are the semi-empirical method PM6, which is usually performed first and sometimes followed by the Density Functional Theory (DFT) method B3LYP. The semi-empirical method PM6, although based on the Hartree-Fock formalism, this method uses many approximations based on experimental data in order to solve the Schrodinger equations. This method is usually fast and reliable, but can be easily countered if the environment of the molecule that is being computed is not similar enough to the approximated parameters of this method. The other method is B3LYP, a hydrid functional which utilises the DFT in order to calculate the majority of the Hamiltonian while a small portion still utilises the Hartree-Fock theory to calculate the exchange integral term. B3LYP stands for Becke, 3-parameter, Lee-Yang-Parr and uses a 6-31G basis set as the electronic wavefunction in order to produce more accurate results at the cost of increased calculation time.

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

[[File:Ex1 general.png|thumb|x700px|700px|centre|Figure 1: Formation of Cyclohaxadiene]]

Also known as the Diels-Alder reaction, this exercise investigates the well-known [4+2] cycloaddition between a conjugated diene (butadiene) and a dienophile (ethylene). The electrophilic reaction involves 4 pi-electrons from the diene and 2 pi-electrons from the alkene, and is a popular method to form regio- and stereochemically controlled 6-membered rings.

Method 2 was used to compute the transition state (TS) for this exercise. All steps are optimised to the PM6 level. First, the reactants are optimised to a minimum. The carbons at the reacting termini were then frozen at around 2.20 Å before optimised to a minimum to give a frozen-guess TS. Then finally, the molecule was optimised as a TS and an IRC was performed in order to confirm and locate the transition state.

=== Analysis of the Molecular Orbitals (MO) ===

The Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) for the reactants and the TS are shown below and its energies were recorded in order to produce the MO diagram as shown in figure 2.

{| class="wikitable"
! Ethene - HOMO
! Ethene - LUMO
! Butadiene - HOMO
! Butadiene - LUMO
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Cc5115 exer1finalMO.png|thumb|x800px|800px|left|Figure 2: MO Diagram for the formation of Transition State of the Diels-Alder Reaction]]

The symmetric TS HOMO and LUMO are formed through the interactions between the HOMO of ethylene and the LUMO of butadiene, both of which are symmetric. On the other hand, the LUMO of ethylene and the HOMO of butadiene, both of which are asymmetric, interacts to give an asymmetric HOMO-1 and LUMO+1. What can be concluded about the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed, and that the reaction is forbidden when the symmetry of the molecular orbitals aren't the same. The orbital overlap integral, S<sub>AB</sub>, is a quantitative measure of orbital overlap of two different atoms. Orbitals of the same symmetry will lead to constructive overlap and gives a non-zero value while orbitals of different symmetry will lead to destructive overlap and an orbital overlap integral of zero. Thus the overlap integral are:

- Non-zero for symmetric-symmetric interaction

- Non-zero for asymmetric-asymmetric interaction

- Zero for symmetric-asymmetric interaction

As observed in the MO diagram, the energy gap between the HOMO and LUMO for butadiene is smaller that those for ethylene due to butadiene being more electron rich than ethylene. Furthermore, in a normal MO diagram, the bonding MO formed should have a lower energy compared to both atomic orbitals (AO) whilst the anti-bonding MO formed should have a higher energy than both AOs. The reason why figure 3 goes against the tide is because the MOs formed corresponds to the transition state where the electrons are very delocalised within the chemical environment of the molecule.

==== LOG Files ====

[[:File:Cc5115_ETHENE_MO.LOG]]

[[:File:Cc5115_BUTADIENE_MO.LOG]]

[[:File:Cc5115_OPT_MO.LOG]]

=== Analysis of the C-C bond lengths ===

{| class="wikitable"
! Bond Lengths (Å)
! C1-C2
! C2-C3
! C3-C4
! C4-C5
! C5-C6
! C6-C1
|-
| Ethylene
|
|
|
|
| 1.36
|
|-
| Butadiene
| 1.36
| 1.54
| 1.36
|
|
|
|-
| Transition State
| 1.38
| 1.41
| 1.38
| 2.11
| 1.38
| 2.12
|-
| Cyclohexadiene
| 1.49
| 1.33
| 1.49
| 1.54
| 1.54
| 1.54
|}

The numbering of the carbon bonds are according to the labels on figure 1. The typical C-C bond lengths are as follows:

{| class="wikitable"
! Bond Type
! Bond Length (Å)
|-
| sp<sup>3</sup>-sp<sup>3</sup> C-C bond
| 1.54
|-
| sp<sup>3</sup>-sp<sup>2</sup> C-C bond
| 1.50
|-
| sp<sup>2</sup>-sp<sup>2</sup> C-C bond
| 1.47
|-
| sp<sup>2</sup>-sp<sup>2</sup> C=C bond
| 1.34
|}

When the reaction proceeds to the transition state, the sp<sup>2</sup>-sp<sup>2</sup> C5-C6 bond (originally ethylene) becomes longer as the carbons starts to change from sp<sup>2</sup> hybridised to sp<sup>3</sup> hybridised.
This trait is also apparent with C1-C2 and C3-C4 bonds where it once was the double bonds on butadiene, however, the increase in length of these bonds is less than that of C5-C6 due to the formation of a new double bond between C2 and C3, thus these carbons still remain sp<sup>2</sup> hybridised. This also leads to the next observation, where the C2-C3 bond decreases in length as it moves from the reactants to the transition state then the product, cyclohexadiene. This is because it is changing from a sp<sup>3</sup>-sp<sup>3</sup> C-C bond to a sp<sup>2</sup>-sp<sup>2</sup> C=C bond where the increase in s character shortens the bond lengths. This reaction also leads to the formation of 2 new bonds, namely C4-C5 and C6-C1. The Van der Waals radius of a carbon atom is 1.7 Å, and so the distance between 2 carbon atoms should be 3.4 Å, which is relatively longer than the bonds C4-C5 and C6-C1 which has a length of 2.11 and 2.12 Å respectively. This shows that the bonds are already partially formed in the transition state and they are beginning to interact together. This bond then settled at 1.54 Å in the product which matches with the typical bond length for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond.

=== Analysis of the vibrations ===

The animation for the first vibration is shown below. As observed, the formation of the 2 new bonds are synchronous as the reacting termini of butadiene and ethylene approaches each other at the same rate.

{| class="wikitable"
! <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 2;rotate x -20; </script>
<uploadedFileContents>Cc5115 OPT MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| The vibrations
|}

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

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via either the endo or exo pathways to form 2 products with different stereochemistry. Method 3 was employed in order to compute the TS for this exercise. This time, the structures were further optimised with B3LYP/6-31G method and the results are shown and discussed below.

=== Analysis of Molecular Orbitals ===

There are two types of Diels-Alder (DA) reactions: one is with a normal electron demand where the dienophile is electron deficient and the diene is electron rich, and the other is with an inverse electron demand where the dienophile is electron rich and the diene is electron deficient.

For a normal electron demand DA reaction, the dienophile low-lying LUMO interacts with the diene HOMO which has a high energy. However, observing the energies of the reactants and the transition states, the MO diagram shows that this particular DA reaction has an inverse electron demand where the dienophile (1,3-dioxole) is electron rich (higher in energy) and the diene (cyclohexadiene) is electron poor (lower in energy). The interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene thus leads to the HOMO and LUMO of the transition state. Although opposing that of a normal electron demand DA, this reaction still follows the Woodword-Hoffman rule and is thermally allowed.

Similar to exercise 1, MOs of the same symmetry interact; the symmetrical dienophile HOMO and the diene LUMO interacts to give a symmetrical TS HOMO and LUMO, while the asymmetrical dienophile LUMO and diene HOMO gives the asymmetrical TS HOMO-1 and LUMO+1. It is also observable that the endo TS HOMO has a lower energy than the exo TS HOMO which suggests that the endo reaction is favoured. This will be discussed further in the Thermochemistry section of this exercise.

{| class="wikitable"
! ENDO TS - HOMO -1
! ENDO TS - HOMO
! ENDO TS - LUMO
! ENDO TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
! Exo Secondary MO
! Endo Secondary MO
|-
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Log Files ====

[[File:Cc5115 ENDO B3.LOG]]

[[File:Cc5115 PLEASE WORK B3.LOG]]

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +149.70
| -77.52
|-
| Exo
| +157.52
| -73.92
|}

As discussed briefly in the introduction, the reactants need to pass the activation barrier (transition state) in order to reach to the products. The table regarding the reaction barriers and energies shows that the activation barrier for the endo reaction is less than that of the exo reaction, more-so confirming that the endo reaction is kinetically favoured. This links to the lower energy that the endo TS HOMO has compared to the exo TS. This observance can be explained by secondary orbital interation (SOI). The 2 non-bonding oxygen p-orbitals containing electron lone pairs can overlap with the LUMO of the diene through space thus stabilising the TS and consequentially lowering reaction barrier. However, the more negative reaction energy of the endo reaction can be explained with sterics; in the exo transition state, the steric interaction between the sp<sup>3</sup> bridging carbons and the rest of the 1,3-dioxole structure results in the exo product being higher in energy.

{| class="wikitable"
! Exo Secondary MO
! Endo Secondary MO
|-
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

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

{| class="wikitable"
| [[File:Cc5115 IRC exo.png|thumb|x500px|500px|left|IRC for Exo Product]]
| [[File:Cc5115 IRC endo.png|thumb|x500px|500px|centre|IRC for Exo Product]]
| [[File:Cc5115 IRC chela.png|thumb|x500px|500px|right|IRC for Chelatropic Product]]
|}

Rep:Mod:cc5115TS

2018-02-14T02:29:22Z

Cc5115: /* Thermochemistry */

= Y3C Transition states and Reactivity =

== Introduction ==

This section aims to illustrate the 3 different computational techniques that can be utilised in order to analyse the transition state (TS) of a reaction. The TS is the state which has the highest energy along a reaction coordinate, as a result it is the least stable state. In the reaction, the reactants needs to have a certain amount of energy in order to surpass the activation barrier, also known as the transition state energy, and reach the product state. This computational lab allows for calculations leading to the location of the TS. The structure of the TS is crucial in determining the mechanism of a reaction.

A potential energy surface (PES) has a 3N-6 dimension, which coincides to the degrees of freedom that the molecule has, where N is the number of atoms that the molecule possesses. In a 3-D PES, the saddle point (also called the TS), is a local mixami amidst 2 minima, and can be sometimes identified through secondary derivatives as it would be negative in one direction and positive in all other directions.

There are 3 calculation methods available in order to determine the structure of the TS.

1. The first and fastest method requires only one step where a guessed structure of the TS is optimised to give an optimised TS. This means that one will need of the TS to quite an extent, furthermore this method is rather unreliable as there is a high chance that the guessed TS is incorrectly drawn.

2. The second method works from a pre-frozen guess structure of the TS where the reacting termini of the reactants are frozen in space before the remaining structure is optimised to a minima. After that, the molecules are optimised as a transition state. This allows for a more reliable representation of the TS. This method is sufficient for Exercise 1.

3. The third method is the longest and most reliable method. Here, one starts by either optimising from the reactants or the products to a minima. For the reactant case, each reactants are optimised to a minima, arranged to resemble the TS and the reacting termini are frozen and the rest of the method 2 is repeated. A similar case occurs with the product; when the product is optimised to a minima, the bonds formed in the reactions are removed, the 2 fragments are arranged to resemble the TS and the reacting termini are frozen and method 2 was used once more. This method allows for the most reliable representation of the TS and is used for Exercise 2 & 3.

In this computational lab, two methods of calculation were used on Gaussian in order to find the TS. During the optimisation, the position of the molecule is decided as it is built in Gaussian. The time-independent Schrödinger equation was solved whilst utilising the Born-Oppenheimer approximation in order to find the energy and the wavefunction φ which represents the electronic states for the fixed nuclear positions and is dependent on on frozen nuclei positions. This is also known as the self-consistent field method (SCF). The two methods employed are the semi-empirical method PM6, which is usually performed first and sometimes followed by the Density Functional Theory (DFT) method B3LYP. The semi-empirical method PM6, although based on the Hartree-Fock formalism, this method uses many approximations based on experimental data in order to solve the Schrodinger equations. This method is usually fast and reliable, but can be easily countered if the environment of the molecule that is being computed is not similar enough to the approximated parameters of this method. The other method is B3LYP, a hydrid functional which utilises the DFT in order to calculate the majority of the Hamiltonian while a small portion still utilises the Hartree-Fock theory to calculate the exchange integral term. B3LYP stands for Becke, 3-parameter, Lee-Yang-Parr and uses a 6-31G basis set as the electronic wavefunction in order to produce more accurate results at the cost of increased calculation time.

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

[[File:Ex1 general.png|thumb|x700px|700px|centre|Figure 1: Formation of Cyclohaxadiene]]

Also known as the Diels-Alder reaction, this exercise investigates the well-known [4+2] cycloaddition between a conjugated diene (butadiene) and a dienophile (ethylene). The electrophilic reaction involves 4 pi-electrons from the diene and 2 pi-electrons from the alkene, and is a popular method to form regio- and stereochemically controlled 6-membered rings.

Method 2 was used to compute the transition state (TS) for this exercise. All steps are optimised to the PM6 level. First, the reactants are optimised to a minimum. The carbons at the reacting termini were then frozen at around 2.20 Å before optimised to a minimum to give a frozen-guess TS. Then finally, the molecule was optimised as a TS and an IRC was performed in order to confirm and locate the transition state.

=== Analysis of the Molecular Orbitals (MO) ===

The Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) for the reactants and the TS are shown below and its energies were recorded in order to produce the MO diagram as shown in figure 2.

{| class="wikitable"
! Ethene - HOMO
! Ethene - LUMO
! Butadiene - HOMO
! Butadiene - LUMO
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Cc5115 exer1finalMO.png|thumb|x800px|800px|left|Figure 2: MO Diagram for the formation of Transition State of the Diels-Alder Reaction]]

The symmetric TS HOMO and LUMO are formed through the interactions between the HOMO of ethylene and the LUMO of butadiene, both of which are symmetric. On the other hand, the LUMO of ethylene and the HOMO of butadiene, both of which are asymmetric, interacts to give an asymmetric HOMO-1 and LUMO+1. What can be concluded about the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed, and that the reaction is forbidden when the symmetry of the molecular orbitals aren't the same. The orbital overlap integral, S<sub>AB</sub>, is a quantitative measure of orbital overlap of two different atoms. Orbitals of the same symmetry will lead to constructive overlap and gives a non-zero value while orbitals of different symmetry will lead to destructive overlap and an orbital overlap integral of zero. Thus the overlap integral are:

- Non-zero for symmetric-symmetric interaction

- Non-zero for asymmetric-asymmetric interaction

- Zero for symmetric-asymmetric interaction

As observed in the MO diagram, the energy gap between the HOMO and LUMO for butadiene is smaller that those for ethylene due to butadiene being more electron rich than ethylene. Furthermore, in a normal MO diagram, the bonding MO formed should have a lower energy compared to both atomic orbitals (AO) whilst the anti-bonding MO formed should have a higher energy than both AOs. The reason why figure 3 goes against the tide is because the MOs formed corresponds to the transition state where the electrons are very delocalised within the chemical environment of the molecule.

==== LOG Files ====

[[:File:Cc5115_ETHENE_MO.LOG]]

[[:File:Cc5115_BUTADIENE_MO.LOG]]

[[:File:Cc5115_OPT_MO.LOG]]

=== Analysis of the C-C bond lengths ===

{| class="wikitable"
! Bond Lengths (Å)
! C1-C2
! C2-C3
! C3-C4
! C4-C5
! C5-C6
! C6-C1
|-
| Ethylene
|
|
|
|
| 1.36
|
|-
| Butadiene
| 1.36
| 1.54
| 1.36
|
|
|
|-
| Transition State
| 1.38
| 1.41
| 1.38
| 2.11
| 1.38
| 2.12
|-
| Cyclohexadiene
| 1.49
| 1.33
| 1.49
| 1.54
| 1.54
| 1.54
|}

The numbering of the carbon bonds are according to the labels on figure 1. The typical C-C bond lengths are as follows:

{| class="wikitable"
! Bond Type
! Bond Length (Å)
|-
| sp<sup>3</sup>-sp<sup>3</sup> C-C bond
| 1.54
|-
| sp<sup>3</sup>-sp<sup>2</sup> C-C bond
| 1.50
|-
| sp<sup>2</sup>-sp<sup>2</sup> C-C bond
| 1.47
|-
| sp<sup>2</sup>-sp<sup>2</sup> C=C bond
| 1.34
|}

When the reaction proceeds to the transition state, the sp<sup>2</sup>-sp<sup>2</sup> C5-C6 bond (originally ethylene) becomes longer as the carbons starts to change from sp<sup>2</sup> hybridised to sp<sup>3</sup> hybridised.
This trait is also apparent with C1-C2 and C3-C4 bonds where it once was the double bonds on butadiene, however, the increase in length of these bonds is less than that of C5-C6 due to the formation of a new double bond between C2 and C3, thus these carbons still remain sp<sup>2</sup> hybridised. This also leads to the next observation, where the C2-C3 bond decreases in length as it moves from the reactants to the transition state then the product, cyclohexadiene. This is because it is changing from a sp<sup>3</sup>-sp<sup>3</sup> C-C bond to a sp<sup>2</sup>-sp<sup>2</sup> C=C bond where the increase in s character shortens the bond lengths. This reaction also leads to the formation of 2 new bonds, namely C4-C5 and C6-C1. The Van der Waals radius of a carbon atom is 1.7 Å, and so the distance between 2 carbon atoms should be 3.4 Å, which is relatively longer than the bonds C4-C5 and C6-C1 which has a length of 2.11 and 2.12 Å respectively. This shows that the bonds are already partially formed in the transition state and they are beginning to interact together. This bond then settled at 1.54 Å in the product which matches with the typical bond length for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond.

=== Analysis of the vibrations ===

The animation for the first vibration is shown below. As observed, the formation of the 2 new bonds are synchronous as the reacting termini of butadiene and ethylene approaches each other at the same rate.

{| class="wikitable"
! <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 2;rotate x -20; </script>
<uploadedFileContents>Cc5115 OPT MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| The vibrations
|}

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

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via either the endo or exo pathways to form 2 products with different stereochemistry. Method 3 was employed in order to compute the TS for this exercise. This time, the structures were further optimised with B3LYP/6-31G method and the results are shown and discussed below.

=== Analysis of Molecular Orbitals ===

There are two types of Diels-Alder (DA) reactions: one is with a normal electron demand where the dienophile is electron deficient and the diene is electron rich, and the other is with an inverse electron demand where the dienophile is electron rich and the diene is electron deficient.

For a normal electron demand DA reaction, the dienophile low-lying LUMO interacts with the diene HOMO which has a high energy. However, observing the energies of the reactants and the transition states, the MO diagram shows that this particular DA reaction has an inverse electron demand where the dienophile (1,3-dioxole) is electron rich (higher in energy) and the diene (cyclohexadiene) is electron poor (lower in energy). The interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene thus leads to the HOMO and LUMO of the transition state. Although opposing that of a normal electron demand DA, this reaction still follows the Woodword-Hoffman rule and is thermally allowed.

Similar to exercise 1, MOs of the same symmetry interact; the symmetrical dienophile HOMO and the diene LUMO interacts to give a symmetrical TS HOMO and LUMO, while the asymmetrical dienophile LUMO and diene HOMO gives the asymmetrical TS HOMO-1 and LUMO+1. It is also observable that the endo TS HOMO has a lower energy than the exo TS HOMO which suggests that the endo reaction is favoured. This will be discussed further in the Thermochemistry section of this exercise.

{| class="wikitable"
! ENDO TS - HOMO -1
! ENDO TS - HOMO
! ENDO TS - LUMO
! ENDO TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
! Exo Secondary MO
! Endo Secondary MO
|-
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Log Files ====

[[File:Cc5115 ENDO B3.LOG]]

[[File:Cc5115 PLEASE WORK B3.LOG]]

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| +149.70
| -77.52
|-
| Exo
| +157.52
| -73.92
|}

As discussed briefly in the introduction, the reactants need to pass the activation barrier (transition state) in order to reach to the products. The table regarding the reaction barriers and energies shows that the activation barrier for the endo reaction is less than that of the exo reaction, more-so confirming that the endo reaction is kinetically favoured. This links to the lower energy that the endo TS HOMO has compared to the exo TS. This observance can be explained by secondary orbital interation (SOI). The 2 non-bonding oxygen p-orbitals containing electron lone pairs can overlap with the LUMO of the diene through space thus stabilising the TS and consequentially lowering reaction barrier. However, the more negative reaction energy of the endo reaction can be explained with sterics; in the exo transition state, the steric interaction between the sp<sup>3</sup> bridging carbons and the rest of the 1,3-dioxole structure results in the exo product being higher in energy.

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

{| class="wikitable"
| [[File:Cc5115 IRC exo.png|thumb|x500px|500px|left|IRC for Exo Product]]
| [[File:Cc5115 IRC endo.png|thumb|x500px|500px|centre|IRC for Exo Product]]
| [[File:Cc5115 IRC chela.png|thumb|x500px|500px|right|IRC for Chelatropic Product]]
|}

Rep:Mod:cc5115TS

2018-02-14T01:55:50Z

Cc5115: /* Thermochemistry */

= Y3C Transition states and Reactivity =

== Introduction ==

This section aims to illustrate the 3 different computational techniques that can be utilised in order to analyse the transition state (TS) of a reaction. The TS is the state which has the highest energy along a reaction coordinate, as a result it is the least stable state. In the reaction, the reactants needs to have a certain amount of energy in order to surpass the activation barrier, also known as the transition state energy, and reach the product state. This computational lab allows for calculations leading to the location of the TS. The structure of the TS is crucial in determining the mechanism of a reaction.

A potential energy surface (PES) has a 3N-6 dimension, which coincides to the degrees of freedom that the molecule has, where N is the number of atoms that the molecule possesses. In a 3-D PES, the saddle point (also called the TS), is a local mixami amidst 2 minima, and can be sometimes identified through secondary derivatives as it would be negative in one direction and positive in all other directions.

There are 3 calculation methods available in order to determine the structure of the TS.

1. The first and fastest method requires only one step where a guessed structure of the TS is optimised to give an optimised TS. This means that one will need of the TS to quite an extent, furthermore this method is rather unreliable as there is a high chance that the guessed TS is incorrectly drawn.

2. The second method works from a pre-frozen guess structure of the TS where the reacting termini of the reactants are frozen in space before the remaining structure is optimised to a minima. After that, the molecules are optimised as a transition state. This allows for a more reliable representation of the TS. This method is sufficient for Exercise 1.

3. The third method is the longest and most reliable method. Here, one starts by either optimising from the reactants or the products to a minima. For the reactant case, each reactants are optimised to a minima, arranged to resemble the TS and the reacting termini are frozen and the rest of the method 2 is repeated. A similar case occurs with the product; when the product is optimised to a minima, the bonds formed in the reactions are removed, the 2 fragments are arranged to resemble the TS and the reacting termini are frozen and method 2 was used once more. This method allows for the most reliable representation of the TS and is used for Exercise 2 & 3.

In this computational lab, two methods of calculation were used on Gaussian in order to find the TS. During the optimisation, the position of the molecule is decided as it is built in Gaussian. The time-independent Schrödinger equation was solved whilst utilising the Born-Oppenheimer approximation in order to find the energy and the wavefunction φ which represents the electronic states for the fixed nuclear positions and is dependent on on frozen nuclei positions. This is also known as the self-consistent field method (SCF). The two methods employed are the semi-empirical method PM6, which is usually performed first and sometimes followed by the Density Functional Theory (DFT) method B3LYP. The semi-empirical method PM6, although based on the Hartree-Fock formalism, this method uses many approximations based on experimental data in order to solve the Schrodinger equations. This method is usually fast and reliable, but can be easily countered if the environment of the molecule that is being computed is not similar enough to the approximated parameters of this method. The other method is B3LYP, a hydrid functional which utilises the DFT in order to calculate the majority of the Hamiltonian while a small portion still utilises the Hartree-Fock theory to calculate the exchange integral term. B3LYP stands for Becke, 3-parameter, Lee-Yang-Parr and uses a 6-31G basis set as the electronic wavefunction in order to produce more accurate results at the cost of increased calculation time.

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

[[File:Ex1 general.png|thumb|x700px|700px|centre|Figure 1: Formation of Cyclohaxadiene]]

Also known as the Diels-Alder reaction, this exercise investigates the well-known [4+2] cycloaddition between a conjugated diene (butadiene) and a dienophile (ethylene). The electrophilic reaction involves 4 pi-electrons from the diene and 2 pi-electrons from the alkene, and is a popular method to form regio- and stereochemically controlled 6-membered rings.

Method 2 was used to compute the transition state (TS) for this exercise. All steps are optimised to the PM6 level. First, the reactants are optimised to a minimum. The carbons at the reacting termini were then frozen at around 2.20 Å before optimised to a minimum to give a frozen-guess TS. Then finally, the molecule was optimised as a TS and an IRC was performed in order to confirm and locate the transition state.

=== Analysis of the Molecular Orbitals (MO) ===

The Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) for the reactants and the TS are shown below and its energies were recorded in order to produce the MO diagram as shown in figure 2.

{| class="wikitable"
! Ethene - HOMO
! Ethene - LUMO
! Butadiene - HOMO
! Butadiene - LUMO
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_ETHENE_MO.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 34; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_BUTADIENE_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 20; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115_OPT_MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Cc5115 exer1finalMO.png|thumb|x800px|800px|left|Figure 2: MO Diagram for the formation of Transition State of the Diels-Alder Reaction]]

The symmetric TS HOMO and LUMO are formed through the interactions between the HOMO of ethylene and the LUMO of butadiene, both of which are symmetric. On the other hand, the LUMO of ethylene and the HOMO of butadiene, both of which are asymmetric, interacts to give an asymmetric HOMO-1 and LUMO+1. What can be concluded about the requirements for symmetry is that molecular orbitals need to be of the same symmetry in order for the reaction to be allowed, and that the reaction is forbidden when the symmetry of the molecular orbitals aren't the same. The orbital overlap integral, S<sub>AB</sub>, is a quantitative measure of orbital overlap of two different atoms. Orbitals of the same symmetry will lead to constructive overlap and gives a non-zero value while orbitals of different symmetry will lead to destructive overlap and an orbital overlap integral of zero. Thus the overlap integral are:

- Non-zero for symmetric-symmetric interaction

- Non-zero for asymmetric-asymmetric interaction

- Zero for symmetric-asymmetric interaction

As observed in the MO diagram, the energy gap between the HOMO and LUMO for butadiene is smaller that those for ethylene due to butadiene being more electron rich than ethylene. Furthermore, in a normal MO diagram, the bonding MO formed should have a lower energy compared to both atomic orbitals (AO) whilst the anti-bonding MO formed should have a higher energy than both AOs. The reason why figure 3 goes against the tide is because the MOs formed corresponds to the transition state where the electrons are very delocalised within the chemical environment of the molecule.

==== LOG Files ====

[[:File:Cc5115_ETHENE_MO.LOG]]

[[:File:Cc5115_BUTADIENE_MO.LOG]]

[[:File:Cc5115_OPT_MO.LOG]]

=== Analysis of the C-C bond lengths ===

{| class="wikitable"
! Bond Lengths (Å)
! C1-C2
! C2-C3
! C3-C4
! C4-C5
! C5-C6
! C6-C1
|-
| Ethylene
|
|
|
|
| 1.36
|
|-
| Butadiene
| 1.36
| 1.54
| 1.36
|
|
|
|-
| Transition State
| 1.38
| 1.41
| 1.38
| 2.11
| 1.38
| 2.12
|-
| Cyclohexadiene
| 1.49
| 1.33
| 1.49
| 1.54
| 1.54
| 1.54
|}

The numbering of the carbon bonds are according to the labels on figure 1. The typical C-C bond lengths are as follows:

{| class="wikitable"
! Bond Type
! Bond Length (Å)
|-
| sp<sup>3</sup>-sp<sup>3</sup> C-C bond
| 1.54
|-
| sp<sup>3</sup>-sp<sup>2</sup> C-C bond
| 1.50
|-
| sp<sup>2</sup>-sp<sup>2</sup> C-C bond
| 1.47
|-
| sp<sup>2</sup>-sp<sup>2</sup> C=C bond
| 1.34
|}

When the reaction proceeds to the transition state, the sp<sup>2</sup>-sp<sup>2</sup> C5-C6 bond (originally ethylene) becomes longer as the carbons starts to change from sp<sup>2</sup> hybridised to sp<sup>3</sup> hybridised.
This trait is also apparent with C1-C2 and C3-C4 bonds where it once was the double bonds on butadiene, however, the increase in length of these bonds is less than that of C5-C6 due to the formation of a new double bond between C2 and C3, thus these carbons still remain sp<sup>2</sup> hybridised. This also leads to the next observation, where the C2-C3 bond decreases in length as it moves from the reactants to the transition state then the product, cyclohexadiene. This is because it is changing from a sp<sup>3</sup>-sp<sup>3</sup> C-C bond to a sp<sup>2</sup>-sp<sup>2</sup> C=C bond where the increase in s character shortens the bond lengths. This reaction also leads to the formation of 2 new bonds, namely C4-C5 and C6-C1. The Van der Waals radius of a carbon atom is 1.7 Å, and so the distance between 2 carbon atoms should be 3.4 Å, which is relatively longer than the bonds C4-C5 and C6-C1 which has a length of 2.11 and 2.12 Å respectively. This shows that the bonds are already partially formed in the transition state and they are beginning to interact together. This bond then settled at 1.54 Å in the product which matches with the typical bond length for a sp<sup>3</sup>-sp<sup>3</sup> C-C bond.

=== Analysis of the vibrations ===

The animation for the first vibration is shown below. As observed, the formation of the 2 new bonds are synchronous as the reacting termini of butadiene and ethylene approaches each other at the same rate.

{| class="wikitable"
! <jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 21; vibration 2;rotate x -20; </script>
<uploadedFileContents>Cc5115 OPT MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| The vibrations
|}

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

The Diels-Alder reaction between cyclohexadiene and 1,3-dioxole can proceed via either the endo or exo pathways to form 2 products with different stereochemistry. Method 3 was employed in order to compute the TS for this exercise. This time, the structures were further optimised with B3LYP/6-31G method and the results are shown and discussed below.

=== Analysis of Molecular Orbitals ===

There are two types of Diels-Alder (DA) reactions: one is with a normal electron demand where the dienophile is electron deficient and the diene is electron rich, and the other is with an inverse electron demand where the dienophile is electron rich and the diene is electron deficient.

For a normal electron demand DA reaction, the dienophile low-lying LUMO interacts with the diene HOMO which has a high energy. However, observing the energies of the reactants and the transition states, the MO diagram shows that this particular DA reaction has an inverse electron demand where the dienophile (1,3-dioxole) is electron rich (higher in energy) and the diene (cyclohexadiene) is electron poor (lower in energy). The interaction between the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene thus leads to the HOMO and LUMO of the transition state. Although opposing that of a normal electron demand DA, this reaction still follows the Woodword-Hoffman rule and is thermally allowed.

Similar to exercise 1, MOs of the same symmetry interact; the symmetrical dienophile HOMO and the diene LUMO interacts to give a symmetrical TS HOMO and LUMO, while the asymmetrical dienophile LUMO and diene HOMO gives the asymmetrical TS HOMO-1 and LUMO+1. It is also observable that the endo TS HOMO has a lower energy than the exo TS HOMO which suggests that the endo reaction is favoured. This will be discussed further in the Thermochemistry section of this exercise.

{| class="wikitable"
! ENDO TS - HOMO -1
! ENDO TS - HOMO
! ENDO TS - LUMO
! ENDO TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 32; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! TS - HOMO -1
! TS - HOMO
! TS - LUMO
! TS - LUMO +1
|-
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
! Exo Secondary MO
! Endo Secondary MO
|-
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 PLEASE WORK B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<$jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cc5115 ENDO B3.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Log Files ====

[[File:Cc5115 ENDO B3.LOG]]

[[File:Cc5115 PLEASE WORK B3.LOG]]

=== Thermochemistry ===

{| class="wikitable"
! Reaction Pathway
! Reacton Barrier (kJ/mol)
! Reaction Energy (kJ/mol)
|-
| Endo
| -149.70
| -77.52
|-
| Exo
| -157.52
| -73.92
|}

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

{| class="wikitable"
| [[File:Cc5115 IRC exo.png|thumb|x500px|500px|left|IRC for Exo Product]]
| [[File:Cc5115 IRC endo.png|thumb|x500px|500px|centre|IRC for Exo Product]]
| [[File:Cc5115 IRC chela.png|thumb|x500px|500px|right|IRC for Chelatropic Product]]
|}