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Rep:YZ20215TS

2018-02-27T23:06:36Z

Yz20215: /* Conclusion */

== Introduction ==

===Transition State ===
To investigate a reaction, it is crucial to firstly locate the Transition State of the reaction. The transition state of a reaction, on a 2D reaction coordinate, will be the highest point of energy connecting reactants and the products. In addition, it should also have the characteristics as shown below:

<math>\frac{\partial V}{\partial q_i}</math>= 0

<math>\frac{\partial^2 V}{\partial q_i^2}</math> < 0

Where as being a stationary point, its first derivative is equal to 0, while its second derivative should be negative as being the highest point on the reaction profile.

On a 3D PES (Potential Energy Surface), it is more difficult to determine the transition state, as it will be one saddle point among many other existing saddle points, however, being the maximum point on the minimum energy path, its first derivative and second derivative will both be equal to zero.

<math>\frac{\partial V}{\partial q_i}</math>= 0

<math>\frac{\partial^2 V}{\partial q_i^2}</math> = 0

=== Computational Methods ===

In this report, three different pericylic reactions were investigated using computational methods, including the PM6 and the B3LYP/6-31G(d) Methods.

PM6, with its full name being Parameterization Method 6, is a semi-empirical method. This method is based on the Hartree-Fock Model, and the model works by minimising the total molecular potential energy by varying the expansion coefficients, c<sub>μi</sub>, which is the coefficient in the equation of LCAO (Linear Combination of Atomic Orbitals).

This method is not perfect as it is based on the wrong assumption of accounting electrons as being largely independent of each other.<ref>Ot, W. J. (1990). Computational quantum chemistry. Journal of Molecular Structure: THEOCHEM (Vol. 207). </ref>

In reality, this is not true and the electrons will repulse each other due to their negative charge. Therefore, this method needs to be parameterised, which means the results fitted by a set of parameters, to product results that agree the most with experimental data.

While the other method, B3LYP, representing Becke, three-parameter, Lee-Yang-Parr, is based on Density Fucntional Theory (DFT), which is an incorporation of partly exact exchange from Hartree–Fock theory as well as exchange-correlation energy from other sources. It has an exchange-correlation functional as shown below:

<math>E_{\rm xc}^{\rm B3LYP} = E_{\rm x}^{\rm LDA} + a_0 (E_{\rm x}^{\rm HF} - E_{\rm x}^{\rm LDA}) + a_{\rm x} (E_{\rm x}^{\rm GGA} - E_{\rm x}^{\rm LDA}) + E_{\rm c}^{\rm LDA} + a_{\rm c} (E_{\rm c}^{\rm GGA} - E_{\rm c}^{\rm LDA}),</math>

where <math>a_0=0.20 \,\;</math>, <math>a_{\rm x}=0.72\,\;</math>, and <math>a_{\rm c}=0.81\,\;</math>. <ref>{{ cite journal |author1=K. Kim |author2=K. D. Jordan | title = Comparison of Density Functional and MP2 Calculations on the Water Monomer and Dimer | journal = J. Phys. Chem. | volume = 98 | issue = 40 | pages = 10089–10094 | year = 1994 | doi = 10.1021/j100091a024 }}</ref><ref>{{ cite journal |author1=P.J. Stephens |author2=F. J. Devlin |author3=C. F. Chabalowski |author4=M. J. Frisch | title = ''Ab Initio'' Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields | journal = J. Phys. Chem. | volume = 98 | pages = 11623–11627 | year = 1994 | doi = 10.1021/j100096a001 | issue = 45 }}</ref>

6-31G is a basis set of basis function among many others including 3-21G, etc.

=== Optimisation Methods ===

In this lab, three methods were used to optimise the TSs, with difficulty increasing from Method 1 to Method 3. Method 1 is the easiest and fastest one, but it is based on existing knowledge of the Transition State. Method 2, compared with Method 1, is more reliable as well as relatively fast, but it also has the limitation of requirement on knowledge of TS. Method 3 takes the most time to run, however, it does not have the limitation of the first two methods.

In this report, three pericylic reactions were investigated with all the Transition States being run with Method 3 and will be shown below.

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 1(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 1(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 1(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 2. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 3. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 4(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 4(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Therefore, in normal electron demand DA reactions, the orbitals of the electron-rich diene will be higher, therefore, favourable interaction occurs between the HOMO of diene and the LUMO of dienophile; while for inverse electron demand reactions, the LUMO of diene will interact with the HOMO of the dienophile.

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

In this reaction, due to the presence of a heterocyclic reactant, 1,3-dioxole, it is postulated that the reaction could possibly have an inverse electron demand, therefore, energy calculations were done and their single point energies determined in the following section to confirm the postulation.

==== Single point energies ====

{| class="wikitable"
|+ Table 11. Single point energies of reactants
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy of HOMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy of LUMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy difference between this HOMO and the LUMO of the other reactant/ a.u.'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |-0.20554
| style="text-align: center;" |-0.01711
| style="text-align: center;" |0.24349
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-0.19594
| style="text-align: center;" |0.03795
| style="text-align: center;" |0.17883
|}

In this reaction, the energy difference between the HOMO of the dienophile with the LUMO of diene is smaller than that of the other pair, therefore, they will give to a larger overlap of orbitals and more favourable interaciton.

Therefore, we can conclude from the data above that the reaction has an inverse electron demand. This is due to the presence of two oxygen atoms donating their lone pairs, making the dienophile electron rich.

=== Energy analysis ===

{| class="wikitable"
|+ Table 12. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 13. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 14. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
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| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure 5. Secondary orbital interactions in both Endo and Exo TS]]
|}

=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

[[File:Yz20215 E3 scheme.png|x400px|400px|thumb|centre|Scheme 3 Diels-Alder and Cheletropic reaction between Xylylene and Sulfur dioxide]]

The reaction between xylylene and sulfur dioxide was investigated.

The reaction between the reactants could occur either via a Diels-Alder reaction or cheletropic reaction as shown above in Scheme 3. For the Diels-Alder reaction between two, the product could be formed in an Endo or an Exo conformation.

In this exercise, the reactants, Transition States and products were optimised using PM6 Method using GaussView software. Also, the energies of different species were obtained to determine the activation energy and the energy change of reaction with reaction energy profile plotted. Therefore, the most thermodynamically and the most kinetically favoured product was determined.

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 15. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
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=== IRC calculations ===

{| class="wikitable"
|+ Table 16. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

Looking at IRC of these three reactions, we could see that the activation barrier of the reaction is quite small, this is due to one of the reactants, xylylene, being very unstable and high in energy.

This is because, according to Huckle's Rule, it has only 8 π electrons, which is (4n) instead of (4n+2), therefore, it is antiaromatic. However, due to structure constraint, both of the dienes are cis in xylylene, which is favourable as no energy expense on converting into trans conformation.

During the reaction, the xylyene part will react with the sulfur dioxide molecule to form a bicyclic ring, containing a benzene ring, which is aromatic and stable. Therefore, making it favourable to form the products.

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 17. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.021698
| style="text-align: center;" |56.9681033
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.021454
| style="text-align: center;" |56.3274813
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |-0.000002
| style="text-align: center;" |-0.0052510004
|}

{| class="wikitable"
|+ Table 18. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |83.4410224
| style="text-align: center;" |-97.3535473
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |87.4239054
| style="text-align: center;" |-97.9941693
|-
| style="text-align: center;" |Cheletropic
| style="text-align: center;" |105.7656504
| style="text-align: center;" |-154.3269016
|}

The energies of the reactants, Transition States, and different products were obtained from the optimised LOG. files in GaussView, and the reaction profile is plotted showing their relative energies with the proceeding of the three reactions.

All TS and product energies are normalised with respect to reactant energy (reactant energy=0). The reaction profile is shown below.

=== Reaction Profiles ===

[[File:Yz20215 E3 reaction profile.png|x700px|700px|thumb|centre|Figure 6. Reaction profile of three different reaction paths]]

In this profile, we could see that the '''endo TS''' is the lowest in energy, therefore will be formed faster compared with other two, and will be the '''kinetic product''' of the reaction. The Exo TS has slightly higher but close energy, while the cheletropic TS has the largest activation barrier.

However, if we compare the energies of the products, we could see that the Endo and the Exo products are very close in energy at approximately -98 kJ mol <sup>-1</sup> , while the cheletropic product is the most stable product with energy of around -154 kJ mol <sup>-1</sup> . Therefore, if we provide enough energy for the reaction to overcome its activation barrier, the '''cheletropic product''' will be the major product as it is the '''thermodynamic product''' of the reaction.

=== Extension ===

[[File:YZ20215 E3 extension.png|x400px|400px|thumb|centre|Scheme 4 The reaction of sulfur dioxide with another diene in xylylene]]

In this reaction, the other diene of xylylene, also in cis conformation, could also reaction with sulfur dioxide to form both the endo and the exo products, and the activation energies and reaction energies of these two reactions are investigated as shown below.

{| class="wikitable"
|+ Table 19. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.102071
| style="text-align: center;" |267.987431
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.105054
| style="text-align: center;" |275.819298
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.065615
| style="text-align: center;" |172.272196
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.067307
| style="text-align: center;" |176.714542
|}

{| class="wikitable"
|+ Table 20. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |113.6657804
| style="text-align: center;" |17.9505454
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |121.4976474
| style="text-align: center;" |22.3928914
|}

These two reaction, are endothermic reactions, with product being higher in energy than that of the reactants. The activation barrier is also around 30 kJ mol <sup>-1</sup> higher than that of the DA reaction occurring at the other diene, therefore, these two reactions are both '''thermodynamically and kinetically unfavourable'''.

=== Files ===

Optimised LOG File for Endo TS: [[File:Yz20215 E3 DA endo TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 E3 DA TS exo TS PM6.log]]

Optimised LOG File for Cheletropic TS: [[File:YZ20215 E3 CHE TS.LOG]]

'''Extension'''

Optimised LOG File for Endo TS: [[File:Yz20215 ext ENDO TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 ext exo TS.log]]

= Conclusion =

During the time span of this Transition State Computational Lab, three different pericyclic reactions were investigated.

The reactions were investigated by using PM6 and B3LYP/6-31G(d) methods in GaussView to optimise the reactants, transition states, and the products.

Other information were also extracted from the optimised molecule LOG. files: including vibration frequency calculations and IRC (Intrinsic Reaction Coordinate); bond lengths of the TS, reactants and products; the energies of different species; and the molecular orbitals.

These data were used to analyse the Transition states and the reactions, including confirmation of the TS by presence of one imaginary frequency in vibration frequencies, the activation barrier and energy change of the reaction from the energies of different species, and the MOs to determine the electron demand of a certain Diels-Alder reaction (inverse or normal electron demand).

In addition, the data confirmed that the reactions followed several existing rules and theories: Woodward-Hoffmann rules in Exercise 1, Frontier Molecular Orbital Theory, etc..

These computational methods could be applied to investigate many other pericyclic reactions, where various aspects of data could be obtained and analysed as like shown in this lab.

= References =

<references />

Rep:YZ20215TS

2018-02-27T23:05:49Z

Yz20215: /* Extension */

Rep:YZ20215TS

2018-02-27T23:05:24Z

Yz20215: /* Extension */

== Introduction ==

===Transition State ===
To investigate a reaction, it is crucial to firstly locate the Transition State of the reaction. The transition state of a reaction, on a 2D reaction coordinate, will be the highest point of energy connecting reactants and the products. In addition, it should also have the characteristics as shown below:

<math>\frac{\partial V}{\partial q_i}</math>= 0

<math>\frac{\partial^2 V}{\partial q_i^2}</math> < 0

Where as being a stationary point, its first derivative is equal to 0, while its second derivative should be negative as being the highest point on the reaction profile.

On a 3D PES (Potential Energy Surface), it is more difficult to determine the transition state, as it will be one saddle point among many other existing saddle points, however, being the maximum point on the minimum energy path, its first derivative and second derivative will both be equal to zero.

<math>\frac{\partial V}{\partial q_i}</math>= 0

<math>\frac{\partial^2 V}{\partial q_i^2}</math> = 0

=== Computational Methods ===

In this report, three different pericylic reactions were investigated using computational methods, including the PM6 and the B3LYP/6-31G(d) Methods.

PM6, with its full name being Parameterization Method 6, is a semi-empirical method. This method is based on the Hartree-Fock Model, and the model works by minimising the total molecular potential energy by varying the expansion coefficients, c<sub>μi</sub>, which is the coefficient in the equation of LCAO (Linear Combination of Atomic Orbitals).

This method is not perfect as it is based on the wrong assumption of accounting electrons as being largely independent of each other.<ref>Ot, W. J. (1990). Computational quantum chemistry. Journal of Molecular Structure: THEOCHEM (Vol. 207). </ref>

In reality, this is not true and the electrons will repulse each other due to their negative charge. Therefore, this method needs to be parameterised, which means the results fitted by a set of parameters, to product results that agree the most with experimental data.

While the other method, B3LYP, representing Becke, three-parameter, Lee-Yang-Parr, is based on Density Fucntional Theory (DFT), which is an incorporation of partly exact exchange from Hartree–Fock theory as well as exchange-correlation energy from other sources. It has an exchange-correlation functional as shown below:

<math>E_{\rm xc}^{\rm B3LYP} = E_{\rm x}^{\rm LDA} + a_0 (E_{\rm x}^{\rm HF} - E_{\rm x}^{\rm LDA}) + a_{\rm x} (E_{\rm x}^{\rm GGA} - E_{\rm x}^{\rm LDA}) + E_{\rm c}^{\rm LDA} + a_{\rm c} (E_{\rm c}^{\rm GGA} - E_{\rm c}^{\rm LDA}),</math>

where <math>a_0=0.20 \,\;</math>, <math>a_{\rm x}=0.72\,\;</math>, and <math>a_{\rm c}=0.81\,\;</math>. <ref>{{ cite journal |author1=K. Kim |author2=K. D. Jordan | title = Comparison of Density Functional and MP2 Calculations on the Water Monomer and Dimer | journal = J. Phys. Chem. | volume = 98 | issue = 40 | pages = 10089–10094 | year = 1994 | doi = 10.1021/j100091a024 }}</ref><ref>{{ cite journal |author1=P.J. Stephens |author2=F. J. Devlin |author3=C. F. Chabalowski |author4=M. J. Frisch | title = ''Ab Initio'' Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields | journal = J. Phys. Chem. | volume = 98 | pages = 11623–11627 | year = 1994 | doi = 10.1021/j100096a001 | issue = 45 }}</ref>

6-31G is a basis set of basis function among many others including 3-21G, etc.

=== Optimisation Methods ===

In this lab, three methods were used to optimise the TSs, with difficulty increasing from Method 1 to Method 3. Method 1 is the easiest and fastest one, but it is based on existing knowledge of the Transition State. Method 2, compared with Method 1, is more reliable as well as relatively fast, but it also has the limitation of requirement on knowledge of TS. Method 3 takes the most time to run, however, it does not have the limitation of the first two methods.

In this report, three pericylic reactions were investigated with all the Transition States being run with Method 3 and will be shown below.

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 1(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 1(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 1(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 2. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
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<uploadedFileContents>YZ20215 E1 ETHYLENE MO.LOG</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YZ20215 E1 TS PM6 MO.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
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<uploadedFileContents>YZ20215 E1 TS PM6 MO.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YZ20215 E1 CYCLOHEXENE MO.LOG</uploadedFileContents>
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</jmol>
|-
| style="text-align: center;" |HOMO
|<jmol>
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<uploadedFileContents>YZ20215 E1 CYCLOHEXENE MO.LOG</uploadedFileContents>
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</jmol>
|}

==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 3. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 cyclohexadiene min.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 dioxole min B3LYP.log</uploadedFileContents>
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|<jmol>
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<color>white</color>
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<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 product ENDO B3LYP MIN.LOG</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents> Yz20215 E2 product EXO B3LYP MIN.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 TS endo TS.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 TS exo TS.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
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<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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|-
| style="text-align: center;" |HOMO
|<jmol>
<jmolApplet>
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<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
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|<jmol>
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<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
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|<jmol>
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<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 4(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 4(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Therefore, in normal electron demand DA reactions, the orbitals of the electron-rich diene will be higher, therefore, favourable interaction occurs between the HOMO of diene and the LUMO of dienophile; while for inverse electron demand reactions, the LUMO of diene will interact with the HOMO of the dienophile.

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

In this reaction, due to the presence of a heterocyclic reactant, 1,3-dioxole, it is postulated that the reaction could possibly have an inverse electron demand, therefore, energy calculations were done and their single point energies determined in the following section to confirm the postulation.

==== Single point energies ====

{| class="wikitable"
|+ Table 11. Single point energies of reactants
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy of HOMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy of LUMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy difference between this HOMO and the LUMO of the other reactant/ a.u.'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |-0.20554
| style="text-align: center;" |-0.01711
| style="text-align: center;" |0.24349
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-0.19594
| style="text-align: center;" |0.03795
| style="text-align: center;" |0.17883
|}

In this reaction, the energy difference between the HOMO of the dienophile with the LUMO of diene is smaller than that of the other pair, therefore, they will give to a larger overlap of orbitals and more favourable interaciton.

Therefore, we can conclude from the data above that the reaction has an inverse electron demand. This is due to the presence of two oxygen atoms donating their lone pairs, making the dienophile electron rich.

=== Energy analysis ===

{| class="wikitable"
|+ Table 12. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 13. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 14. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
!<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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</jmol>
!<jmol>
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<color>white</color>
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<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
</jmolApplet>
</jmol>
| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure 5. Secondary orbital interactions in both Endo and Exo TS]]
|}

=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

[[File:Yz20215 E3 scheme.png|x400px|400px|thumb|centre|Scheme 3 Diels-Alder and Cheletropic reaction between Xylylene and Sulfur dioxide]]

The reaction between xylylene and sulfur dioxide was investigated.

The reaction between the reactants could occur either via a Diels-Alder reaction or cheletropic reaction as shown above in Scheme 3. For the Diels-Alder reaction between two, the product could be formed in an Endo or an Exo conformation.

In this exercise, the reactants, Transition States and products were optimised using PM6 Method using GaussView software. Also, the energies of different species were obtained to determine the activation energy and the energy change of reaction with reaction energy profile plotted. Therefore, the most thermodynamically and the most kinetically favoured product was determined.

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 15. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 16; </script>
<uploadedFileContents>Yz20215 E3 DA endo TS.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
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<script>frame 16; </script>
<uploadedFileContents>Yz20215 E3 DA TS exo TS PM6.log</uploadedFileContents>
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<script>frame 16; </script>
<uploadedFileContents>YZ20215 E3 CHE TS.LOG</uploadedFileContents>
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=== IRC calculations ===

{| class="wikitable"
|+ Table 16. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

Looking at IRC of these three reactions, we could see that the activation barrier of the reaction is quite small, this is due to one of the reactants, xylylene, being very unstable and high in energy.

This is because, according to Huckle's Rule, it has only 8 π electrons, which is (4n) instead of (4n+2), therefore, it is antiaromatic. However, due to structure constraint, both of the dienes are cis in xylylene, which is favourable as no energy expense on converting into trans conformation.

During the reaction, the xylyene part will react with the sulfur dioxide molecule to form a bicyclic ring, containing a benzene ring, which is aromatic and stable. Therefore, making it favourable to form the products.

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 17. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.021698
| style="text-align: center;" |56.9681033
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.021454
| style="text-align: center;" |56.3274813
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |-0.000002
| style="text-align: center;" |-0.0052510004
|}

{| class="wikitable"
|+ Table 18. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |83.4410224
| style="text-align: center;" |-97.3535473
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |87.4239054
| style="text-align: center;" |-97.9941693
|-
| style="text-align: center;" |Cheletropic
| style="text-align: center;" |105.7656504
| style="text-align: center;" |-154.3269016
|}

The energies of the reactants, Transition States, and different products were obtained from the optimised LOG. files in GaussView, and the reaction profile is plotted showing their relative energies with the proceeding of the three reactions.

All TS and product energies are normalised with respect to reactant energy (reactant energy=0). The reaction profile is shown below.

=== Reaction Profiles ===

[[File:Yz20215 E3 reaction profile.png|x700px|700px|thumb|centre|Figure 6. Reaction profile of three different reaction paths]]

In this profile, we could see that the '''endo TS''' is the lowest in energy, therefore will be formed faster compared with other two, and will be the '''kinetic product''' of the reaction. The Exo TS has slightly higher but close energy, while the cheletropic TS has the largest activation barrier.

However, if we compare the energies of the products, we could see that the Endo and the Exo products are very close in energy at approximately -98 kJ mol <sup>-1</sup> , while the cheletropic product is the most stable product with energy of around -154 kJ mol <sup>-1</sup> . Therefore, if we provide enough energy for the reaction to overcome its activation barrier, the '''cheletropic product''' will be the major product as it is the '''thermodynamic product''' of the reaction.

=== Extension ===

[[File:YZ20215 E3 extension.png|x400px|400px|thumb|centre|Scheme 4 The reaction of sulfur dioxide with another diene in xylylene]]

In this reaction, the other diene of xylylene, also in cis conformation, could also reaction with sulfur dioxide to form both the endo and the exo products, and the activation energies and reaction energies of these two reactions are investigated as shown below.

{| class="wikitable"
|+ Table 19. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.102071
| style="text-align: center;" |267.987431
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.105054
| style="text-align: center;" |275.819298
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.065615
| style="text-align: center;" |172.272196
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.067307
| style="text-align: center;" |176.714542
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |113.6657804
| style="text-align: center;" |17.9505454
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |121.4976474
| style="text-align: center;" |22.3928914
|}

These two reaction, are endothermic reactions, with product being higher in energy than that of the reactants. The activation barrier is also around 30 kJ mol <sup>-1</sup> higher than that of the DA reaction occurring at the other diene, therefore, these two reactions are both '''thermodynamically and kinetically unfavourable'''.

=== Files ===

Optimised LOG File for Endo TS: [[File:Yz20215 E3 DA endo TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 E3 DA TS exo TS PM6.log]]

Optimised LOG File for Cheletropic TS: [[File:YZ20215 E3 CHE TS.LOG]]

'''Extension'''

Optimised LOG File for Endo TS: [[File:Yz20215 ext ENDO TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 ext exo TS.log]]

= Conclusion =

During the time span of this Transition State Computational Lab, three different pericyclic reactions were investigated.

The reactions were investigated by using PM6 and B3LYP/6-31G(d) methods in GaussView to optimise the reactants, transition states, and the products.

Other information were also extracted from the optimised molecule LOG. files: including vibration frequency calculations and IRC (Intrinsic Reaction Coordinate); bond lengths of the TS, reactants and products; the energies of different species; and the molecular orbitals.

These data were used to analyse the Transition states and the reactions, including confirmation of the TS by presence of one imaginary frequency in vibration frequencies, the activation barrier and energy change of the reaction from the energies of different species, and the MOs to determine the electron demand of a certain Diels-Alder reaction (inverse or normal electron demand).

In addition, the data confirmed that the reactions followed several existing rules and theories: Woodward-Hoffmann rules in Exercise 1, Frontier Molecular Orbital Theory, etc..

These computational methods could be applied to investigate many other pericyclic reactions, where various aspects of data could be obtained and analysed as like shown in this lab.

Rep:YZ20215TS

2018-02-27T23:04:58Z

Yz20215: /* Reaction Profiles */

== Introduction ==

===Transition State ===
To investigate a reaction, it is crucial to firstly locate the Transition State of the reaction. The transition state of a reaction, on a 2D reaction coordinate, will be the highest point of energy connecting reactants and the products. In addition, it should also have the characteristics as shown below:

<math>\frac{\partial V}{\partial q_i}</math>= 0

<math>\frac{\partial^2 V}{\partial q_i^2}</math> < 0

Where as being a stationary point, its first derivative is equal to 0, while its second derivative should be negative as being the highest point on the reaction profile.

On a 3D PES (Potential Energy Surface), it is more difficult to determine the transition state, as it will be one saddle point among many other existing saddle points, however, being the maximum point on the minimum energy path, its first derivative and second derivative will both be equal to zero.

<math>\frac{\partial V}{\partial q_i}</math>= 0

<math>\frac{\partial^2 V}{\partial q_i^2}</math> = 0

=== Computational Methods ===

In this report, three different pericylic reactions were investigated using computational methods, including the PM6 and the B3LYP/6-31G(d) Methods.

PM6, with its full name being Parameterization Method 6, is a semi-empirical method. This method is based on the Hartree-Fock Model, and the model works by minimising the total molecular potential energy by varying the expansion coefficients, c<sub>μi</sub>, which is the coefficient in the equation of LCAO (Linear Combination of Atomic Orbitals).

This method is not perfect as it is based on the wrong assumption of accounting electrons as being largely independent of each other.<ref>Ot, W. J. (1990). Computational quantum chemistry. Journal of Molecular Structure: THEOCHEM (Vol. 207). </ref>

In reality, this is not true and the electrons will repulse each other due to their negative charge. Therefore, this method needs to be parameterised, which means the results fitted by a set of parameters, to product results that agree the most with experimental data.

While the other method, B3LYP, representing Becke, three-parameter, Lee-Yang-Parr, is based on Density Fucntional Theory (DFT), which is an incorporation of partly exact exchange from Hartree–Fock theory as well as exchange-correlation energy from other sources. It has an exchange-correlation functional as shown below:

<math>E_{\rm xc}^{\rm B3LYP} = E_{\rm x}^{\rm LDA} + a_0 (E_{\rm x}^{\rm HF} - E_{\rm x}^{\rm LDA}) + a_{\rm x} (E_{\rm x}^{\rm GGA} - E_{\rm x}^{\rm LDA}) + E_{\rm c}^{\rm LDA} + a_{\rm c} (E_{\rm c}^{\rm GGA} - E_{\rm c}^{\rm LDA}),</math>

where <math>a_0=0.20 \,\;</math>, <math>a_{\rm x}=0.72\,\;</math>, and <math>a_{\rm c}=0.81\,\;</math>. <ref>{{ cite journal |author1=K. Kim |author2=K. D. Jordan | title = Comparison of Density Functional and MP2 Calculations on the Water Monomer and Dimer | journal = J. Phys. Chem. | volume = 98 | issue = 40 | pages = 10089–10094 | year = 1994 | doi = 10.1021/j100091a024 }}</ref><ref>{{ cite journal |author1=P.J. Stephens |author2=F. J. Devlin |author3=C. F. Chabalowski |author4=M. J. Frisch | title = ''Ab Initio'' Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields | journal = J. Phys. Chem. | volume = 98 | pages = 11623–11627 | year = 1994 | doi = 10.1021/j100096a001 | issue = 45 }}</ref>

6-31G is a basis set of basis function among many others including 3-21G, etc.

=== Optimisation Methods ===

In this lab, three methods were used to optimise the TSs, with difficulty increasing from Method 1 to Method 3. Method 1 is the easiest and fastest one, but it is based on existing knowledge of the Transition State. Method 2, compared with Method 1, is more reliable as well as relatively fast, but it also has the limitation of requirement on knowledge of TS. Method 3 takes the most time to run, however, it does not have the limitation of the first two methods.

In this report, three pericylic reactions were investigated with all the Transition States being run with Method 3 and will be shown below.

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 1(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 1(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 1(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 2. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
|<jmol>
<jmolApplet>
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<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E1 BUTANDIENE MO.LOG</uploadedFileContents>
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|<jmol>
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<uploadedFileContents>YZ20215 E1 ETHYLENE MO.LOG</uploadedFileContents>
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|-
| style="text-align: center;" |HOMO
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==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 3. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 cyclohexadiene min.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 dioxole min B3LYP.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 product ENDO B3LYP MIN.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents> Yz20215 E2 product EXO B3LYP MIN.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 TS endo TS.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 TS exo TS.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
|<jmol>
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<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
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<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
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|<jmol>
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<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" |HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 4(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 4(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Therefore, in normal electron demand DA reactions, the orbitals of the electron-rich diene will be higher, therefore, favourable interaction occurs between the HOMO of diene and the LUMO of dienophile; while for inverse electron demand reactions, the LUMO of diene will interact with the HOMO of the dienophile.

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

In this reaction, due to the presence of a heterocyclic reactant, 1,3-dioxole, it is postulated that the reaction could possibly have an inverse electron demand, therefore, energy calculations were done and their single point energies determined in the following section to confirm the postulation.

==== Single point energies ====

{| class="wikitable"
|+ Table 11. Single point energies of reactants
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy of HOMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy of LUMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy difference between this HOMO and the LUMO of the other reactant/ a.u.'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |-0.20554
| style="text-align: center;" |-0.01711
| style="text-align: center;" |0.24349
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-0.19594
| style="text-align: center;" |0.03795
| style="text-align: center;" |0.17883
|}

In this reaction, the energy difference between the HOMO of the dienophile with the LUMO of diene is smaller than that of the other pair, therefore, they will give to a larger overlap of orbitals and more favourable interaciton.

Therefore, we can conclude from the data above that the reaction has an inverse electron demand. This is due to the presence of two oxygen atoms donating their lone pairs, making the dienophile electron rich.

=== Energy analysis ===

{| class="wikitable"
|+ Table 12. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 13. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 14. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
!<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
</jmolApplet>
</jmol>
| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure 5. Secondary orbital interactions in both Endo and Exo TS]]
|}

=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

[[File:Yz20215 E3 scheme.png|x400px|400px|thumb|centre|Scheme 3 Diels-Alder and Cheletropic reaction between Xylylene and Sulfur dioxide]]

The reaction between xylylene and sulfur dioxide was investigated.

The reaction between the reactants could occur either via a Diels-Alder reaction or cheletropic reaction as shown above in Scheme 3. For the Diels-Alder reaction between two, the product could be formed in an Endo or an Exo conformation.

In this exercise, the reactants, Transition States and products were optimised using PM6 Method using GaussView software. Also, the energies of different species were obtained to determine the activation energy and the energy change of reaction with reaction energy profile plotted. Therefore, the most thermodynamically and the most kinetically favoured product was determined.

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 15. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E3 DA endo TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E3 DA TS exo TS PM6.log</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>YZ20215 E3 CHE TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== IRC calculations ===

{| class="wikitable"
|+ Table 16. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

Looking at IRC of these three reactions, we could see that the activation barrier of the reaction is quite small, this is due to one of the reactants, xylylene, being very unstable and high in energy.

This is because, according to Huckle's Rule, it has only 8 π electrons, which is (4n) instead of (4n+2), therefore, it is antiaromatic. However, due to structure constraint, both of the dienes are cis in xylylene, which is favourable as no energy expense on converting into trans conformation.

During the reaction, the xylyene part will react with the sulfur dioxide molecule to form a bicyclic ring, containing a benzene ring, which is aromatic and stable. Therefore, making it favourable to form the products.

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 17. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.021698
| style="text-align: center;" |56.9681033
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.021454
| style="text-align: center;" |56.3274813
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |-0.000002
| style="text-align: center;" |-0.0052510004
|}

{| class="wikitable"
|+ Table 18. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |83.4410224
| style="text-align: center;" |-97.3535473
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |87.4239054
| style="text-align: center;" |-97.9941693
|-
| style="text-align: center;" |Cheletropic
| style="text-align: center;" |105.7656504
| style="text-align: center;" |-154.3269016
|}

The energies of the reactants, Transition States, and different products were obtained from the optimised LOG. files in GaussView, and the reaction profile is plotted showing their relative energies with the proceeding of the three reactions.

All TS and product energies are normalised with respect to reactant energy (reactant energy=0). The reaction profile is shown below.

=== Reaction Profiles ===

[[File:Yz20215 E3 reaction profile.png|x700px|700px|thumb|centre|Figure 6. Reaction profile of three different reaction paths]]

In this profile, we could see that the '''endo TS''' is the lowest in energy, therefore will be formed faster compared with other two, and will be the '''kinetic product''' of the reaction. The Exo TS has slightly higher but close energy, while the cheletropic TS has the largest activation barrier.

However, if we compare the energies of the products, we could see that the Endo and the Exo products are very close in energy at approximately -98 kJ mol <sup>-1</sup> , while the cheletropic product is the most stable product with energy of around -154 kJ mol <sup>-1</sup> . Therefore, if we provide enough energy for the reaction to overcome its activation barrier, the '''cheletropic product''' will be the major product as it is the '''thermodynamic product''' of the reaction.

=== Extension ===

[[File:YZ20215 E3 extension.png|x400px|400px|thumb|centre|Scheme 4 The reaction of sulfur dioxide with another diene in xylylene]]

In this reaction, the other diene of xylylene, also in cis conformation, could also reaction with sulfur dioxide to form both the endo and the exo products, and the activation energies and reaction energies of these two reactions are investigated as shown below.

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.102071
| style="text-align: center;" |267.987431
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.105054
| style="text-align: center;" |275.819298
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.065615
| style="text-align: center;" |172.272196
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.067307
| style="text-align: center;" |176.714542
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |113.6657804
| style="text-align: center;" |17.9505454
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |121.4976474
| style="text-align: center;" |22.3928914
|}

These two reaction, are endothermic reactions, with product being higher in energy than that of the reactants. The activation barrier is also around 30 kJ mol <sup>-1</sup> higher than that of the DA reaction occurring at the other diene, therefore, these two reactions are both '''thermodynamically and kinetically unfavourable'''.

=== Files ===

Optimised LOG File for Endo TS: [[File:Yz20215 E3 DA endo TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 E3 DA TS exo TS PM6.log]]

Optimised LOG File for Cheletropic TS: [[File:YZ20215 E3 CHE TS.LOG]]

'''Extension'''

Optimised LOG File for Endo TS: [[File:Yz20215 ext ENDO TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 ext exo TS.log]]

= Conclusion =

During the time span of this Transition State Computational Lab, three different pericyclic reactions were investigated.

The reactions were investigated by using PM6 and B3LYP/6-31G(d) methods in GaussView to optimise the reactants, transition states, and the products.

Other information were also extracted from the optimised molecule LOG. files: including vibration frequency calculations and IRC (Intrinsic Reaction Coordinate); bond lengths of the TS, reactants and products; the energies of different species; and the molecular orbitals.

These data were used to analyse the Transition states and the reactions, including confirmation of the TS by presence of one imaginary frequency in vibration frequencies, the activation barrier and energy change of the reaction from the energies of different species, and the MOs to determine the electron demand of a certain Diels-Alder reaction (inverse or normal electron demand).

In addition, the data confirmed that the reactions followed several existing rules and theories: Woodward-Hoffmann rules in Exercise 1, Frontier Molecular Orbital Theory, etc..

These computational methods could be applied to investigate many other pericyclic reactions, where various aspects of data could be obtained and analysed as like shown in this lab.

Rep:YZ20215TS

2018-02-27T23:03:58Z

Yz20215: /* Activation and Reaction Energy calculations */

== Introduction ==

===Transition State ===
To investigate a reaction, it is crucial to firstly locate the Transition State of the reaction. The transition state of a reaction, on a 2D reaction coordinate, will be the highest point of energy connecting reactants and the products. In addition, it should also have the characteristics as shown below:

<math>\frac{\partial V}{\partial q_i}</math>= 0

<math>\frac{\partial^2 V}{\partial q_i^2}</math> < 0

Where as being a stationary point, its first derivative is equal to 0, while its second derivative should be negative as being the highest point on the reaction profile.

On a 3D PES (Potential Energy Surface), it is more difficult to determine the transition state, as it will be one saddle point among many other existing saddle points, however, being the maximum point on the minimum energy path, its first derivative and second derivative will both be equal to zero.

<math>\frac{\partial V}{\partial q_i}</math>= 0

<math>\frac{\partial^2 V}{\partial q_i^2}</math> = 0

=== Computational Methods ===

In this report, three different pericylic reactions were investigated using computational methods, including the PM6 and the B3LYP/6-31G(d) Methods.

PM6, with its full name being Parameterization Method 6, is a semi-empirical method. This method is based on the Hartree-Fock Model, and the model works by minimising the total molecular potential energy by varying the expansion coefficients, c<sub>μi</sub>, which is the coefficient in the equation of LCAO (Linear Combination of Atomic Orbitals).

This method is not perfect as it is based on the wrong assumption of accounting electrons as being largely independent of each other.<ref>Ot, W. J. (1990). Computational quantum chemistry. Journal of Molecular Structure: THEOCHEM (Vol. 207). </ref>

In reality, this is not true and the electrons will repulse each other due to their negative charge. Therefore, this method needs to be parameterised, which means the results fitted by a set of parameters, to product results that agree the most with experimental data.

While the other method, B3LYP, representing Becke, three-parameter, Lee-Yang-Parr, is based on Density Fucntional Theory (DFT), which is an incorporation of partly exact exchange from Hartree–Fock theory as well as exchange-correlation energy from other sources. It has an exchange-correlation functional as shown below:

<math>E_{\rm xc}^{\rm B3LYP} = E_{\rm x}^{\rm LDA} + a_0 (E_{\rm x}^{\rm HF} - E_{\rm x}^{\rm LDA}) + a_{\rm x} (E_{\rm x}^{\rm GGA} - E_{\rm x}^{\rm LDA}) + E_{\rm c}^{\rm LDA} + a_{\rm c} (E_{\rm c}^{\rm GGA} - E_{\rm c}^{\rm LDA}),</math>

where <math>a_0=0.20 \,\;</math>, <math>a_{\rm x}=0.72\,\;</math>, and <math>a_{\rm c}=0.81\,\;</math>. <ref>{{ cite journal |author1=K. Kim |author2=K. D. Jordan | title = Comparison of Density Functional and MP2 Calculations on the Water Monomer and Dimer | journal = J. Phys. Chem. | volume = 98 | issue = 40 | pages = 10089–10094 | year = 1994 | doi = 10.1021/j100091a024 }}</ref><ref>{{ cite journal |author1=P.J. Stephens |author2=F. J. Devlin |author3=C. F. Chabalowski |author4=M. J. Frisch | title = ''Ab Initio'' Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields | journal = J. Phys. Chem. | volume = 98 | pages = 11623–11627 | year = 1994 | doi = 10.1021/j100096a001 | issue = 45 }}</ref>

6-31G is a basis set of basis function among many others including 3-21G, etc.

=== Optimisation Methods ===

In this lab, three methods were used to optimise the TSs, with difficulty increasing from Method 1 to Method 3. Method 1 is the easiest and fastest one, but it is based on existing knowledge of the Transition State. Method 2, compared with Method 1, is more reliable as well as relatively fast, but it also has the limitation of requirement on knowledge of TS. Method 3 takes the most time to run, however, it does not have the limitation of the first two methods.

In this report, three pericylic reactions were investigated with all the Transition States being run with Method 3 and will be shown below.

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 1(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 1(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 1(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 2. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 3. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 4(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 4(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Therefore, in normal electron demand DA reactions, the orbitals of the electron-rich diene will be higher, therefore, favourable interaction occurs between the HOMO of diene and the LUMO of dienophile; while for inverse electron demand reactions, the LUMO of diene will interact with the HOMO of the dienophile.

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

In this reaction, due to the presence of a heterocyclic reactant, 1,3-dioxole, it is postulated that the reaction could possibly have an inverse electron demand, therefore, energy calculations were done and their single point energies determined in the following section to confirm the postulation.

==== Single point energies ====

{| class="wikitable"
|+ Table 11. Single point energies of reactants
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy of HOMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy of LUMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy difference between this HOMO and the LUMO of the other reactant/ a.u.'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |-0.20554
| style="text-align: center;" |-0.01711
| style="text-align: center;" |0.24349
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-0.19594
| style="text-align: center;" |0.03795
| style="text-align: center;" |0.17883
|}

In this reaction, the energy difference between the HOMO of the dienophile with the LUMO of diene is smaller than that of the other pair, therefore, they will give to a larger overlap of orbitals and more favourable interaciton.

Therefore, we can conclude from the data above that the reaction has an inverse electron demand. This is due to the presence of two oxygen atoms donating their lone pairs, making the dienophile electron rich.

=== Energy analysis ===

{| class="wikitable"
|+ Table 12. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 13. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 14. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
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| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure 5. Secondary orbital interactions in both Endo and Exo TS]]
|}

=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

[[File:Yz20215 E3 scheme.png|x400px|400px|thumb|centre|Scheme 3 Diels-Alder and Cheletropic reaction between Xylylene and Sulfur dioxide]]

The reaction between xylylene and sulfur dioxide was investigated.

The reaction between the reactants could occur either via a Diels-Alder reaction or cheletropic reaction as shown above in Scheme 3. For the Diels-Alder reaction between two, the product could be formed in an Endo or an Exo conformation.

In this exercise, the reactants, Transition States and products were optimised using PM6 Method using GaussView software. Also, the energies of different species were obtained to determine the activation energy and the energy change of reaction with reaction energy profile plotted. Therefore, the most thermodynamically and the most kinetically favoured product was determined.

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 15. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
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=== IRC calculations ===

{| class="wikitable"
|+ Table 16. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

Looking at IRC of these three reactions, we could see that the activation barrier of the reaction is quite small, this is due to one of the reactants, xylylene, being very unstable and high in energy.

This is because, according to Huckle's Rule, it has only 8 π electrons, which is (4n) instead of (4n+2), therefore, it is antiaromatic. However, due to structure constraint, both of the dienes are cis in xylylene, which is favourable as no energy expense on converting into trans conformation.

During the reaction, the xylyene part will react with the sulfur dioxide molecule to form a bicyclic ring, containing a benzene ring, which is aromatic and stable. Therefore, making it favourable to form the products.

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 17. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.021698
| style="text-align: center;" |56.9681033
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.021454
| style="text-align: center;" |56.3274813
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |-0.000002
| style="text-align: center;" |-0.0052510004
|}

{| class="wikitable"
|+ Table 18. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |83.4410224
| style="text-align: center;" |-97.3535473
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |87.4239054
| style="text-align: center;" |-97.9941693
|-
| style="text-align: center;" |Cheletropic
| style="text-align: center;" |105.7656504
| style="text-align: center;" |-154.3269016
|}

The energies of the reactants, Transition States, and different products were obtained from the optimised LOG. files in GaussView, and the reaction profile is plotted showing their relative energies with the proceeding of the three reactions.

All TS and product energies are normalised with respect to reactant energy (reactant energy=0). The reaction profile is shown below.

=== Reaction Profiles ===

[[File:Yz20215 E3 reaction profile.png|x700px|700px|thumb|centre|Figure Reaction profile of three different reaction paths]]

In this profile, we could see that the '''endo TS''' is the lowest in energy, therefore will be formed faster compared with other two, and will be the '''kinetic product''' of the reaction. The Exo TS has slightly higher but close energy, while the cheletropic TS has the largest activation barrier.

However, if we compare the energies of the products, we could see that the Endo and the Exo products are very close in energy at approximately -98 kJ mol <sup>-1</sup> , while the cheletropic product is the most stable product with energy of around -154 kJ mol <sup>-1</sup> . Therefore, if we provide enough energy for the reaction to overcome its activation barrier, the '''cheletropic product''' will be the major product as it is the '''thermodynamic product''' of the reaction.

=== Extension ===

[[File:YZ20215 E3 extension.png|x400px|400px|thumb|centre|Scheme 4 The reaction of sulfur dioxide with another diene in xylylene]]

In this reaction, the other diene of xylylene, also in cis conformation, could also reaction with sulfur dioxide to form both the endo and the exo products, and the activation energies and reaction energies of these two reactions are investigated as shown below.

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.102071
| style="text-align: center;" |267.987431
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.105054
| style="text-align: center;" |275.819298
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.065615
| style="text-align: center;" |172.272196
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.067307
| style="text-align: center;" |176.714542
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |113.6657804
| style="text-align: center;" |17.9505454
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |121.4976474
| style="text-align: center;" |22.3928914
|}

These two reaction, are endothermic reactions, with product being higher in energy than that of the reactants. The activation barrier is also around 30 kJ mol <sup>-1</sup> higher than that of the DA reaction occurring at the other diene, therefore, these two reactions are both '''thermodynamically and kinetically unfavourable'''.

=== Files ===

Optimised LOG File for Endo TS: [[File:Yz20215 E3 DA endo TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 E3 DA TS exo TS PM6.log]]

Optimised LOG File for Cheletropic TS: [[File:YZ20215 E3 CHE TS.LOG]]

'''Extension'''

Optimised LOG File for Endo TS: [[File:Yz20215 ext ENDO TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 ext exo TS.log]]

= Conclusion =

During the time span of this Transition State Computational Lab, three different pericyclic reactions were investigated.

The reactions were investigated by using PM6 and B3LYP/6-31G(d) methods in GaussView to optimise the reactants, transition states, and the products.

Other information were also extracted from the optimised molecule LOG. files: including vibration frequency calculations and IRC (Intrinsic Reaction Coordinate); bond lengths of the TS, reactants and products; the energies of different species; and the molecular orbitals.

These data were used to analyse the Transition states and the reactions, including confirmation of the TS by presence of one imaginary frequency in vibration frequencies, the activation barrier and energy change of the reaction from the energies of different species, and the MOs to determine the electron demand of a certain Diels-Alder reaction (inverse or normal electron demand).

In addition, the data confirmed that the reactions followed several existing rules and theories: Woodward-Hoffmann rules in Exercise 1, Frontier Molecular Orbital Theory, etc..

These computational methods could be applied to investigate many other pericyclic reactions, where various aspects of data could be obtained and analysed as like shown in this lab.

Rep:YZ20215TS

2018-02-27T23:03:32Z

Yz20215: /* IRC calculations */

== Introduction ==

===Transition State ===
To investigate a reaction, it is crucial to firstly locate the Transition State of the reaction. The transition state of a reaction, on a 2D reaction coordinate, will be the highest point of energy connecting reactants and the products. In addition, it should also have the characteristics as shown below:

<math>\frac{\partial V}{\partial q_i}</math>= 0

<math>\frac{\partial^2 V}{\partial q_i^2}</math> < 0

Where as being a stationary point, its first derivative is equal to 0, while its second derivative should be negative as being the highest point on the reaction profile.

On a 3D PES (Potential Energy Surface), it is more difficult to determine the transition state, as it will be one saddle point among many other existing saddle points, however, being the maximum point on the minimum energy path, its first derivative and second derivative will both be equal to zero.

<math>\frac{\partial V}{\partial q_i}</math>= 0

<math>\frac{\partial^2 V}{\partial q_i^2}</math> = 0

=== Computational Methods ===

In this report, three different pericylic reactions were investigated using computational methods, including the PM6 and the B3LYP/6-31G(d) Methods.

PM6, with its full name being Parameterization Method 6, is a semi-empirical method. This method is based on the Hartree-Fock Model, and the model works by minimising the total molecular potential energy by varying the expansion coefficients, c<sub>μi</sub>, which is the coefficient in the equation of LCAO (Linear Combination of Atomic Orbitals).

This method is not perfect as it is based on the wrong assumption of accounting electrons as being largely independent of each other.<ref>Ot, W. J. (1990). Computational quantum chemistry. Journal of Molecular Structure: THEOCHEM (Vol. 207). </ref>

In reality, this is not true and the electrons will repulse each other due to their negative charge. Therefore, this method needs to be parameterised, which means the results fitted by a set of parameters, to product results that agree the most with experimental data.

While the other method, B3LYP, representing Becke, three-parameter, Lee-Yang-Parr, is based on Density Fucntional Theory (DFT), which is an incorporation of partly exact exchange from Hartree–Fock theory as well as exchange-correlation energy from other sources. It has an exchange-correlation functional as shown below:

<math>E_{\rm xc}^{\rm B3LYP} = E_{\rm x}^{\rm LDA} + a_0 (E_{\rm x}^{\rm HF} - E_{\rm x}^{\rm LDA}) + a_{\rm x} (E_{\rm x}^{\rm GGA} - E_{\rm x}^{\rm LDA}) + E_{\rm c}^{\rm LDA} + a_{\rm c} (E_{\rm c}^{\rm GGA} - E_{\rm c}^{\rm LDA}),</math>

where <math>a_0=0.20 \,\;</math>, <math>a_{\rm x}=0.72\,\;</math>, and <math>a_{\rm c}=0.81\,\;</math>. <ref>{{ cite journal |author1=K. Kim |author2=K. D. Jordan | title = Comparison of Density Functional and MP2 Calculations on the Water Monomer and Dimer | journal = J. Phys. Chem. | volume = 98 | issue = 40 | pages = 10089–10094 | year = 1994 | doi = 10.1021/j100091a024 }}</ref><ref>{{ cite journal |author1=P.J. Stephens |author2=F. J. Devlin |author3=C. F. Chabalowski |author4=M. J. Frisch | title = ''Ab Initio'' Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields | journal = J. Phys. Chem. | volume = 98 | pages = 11623–11627 | year = 1994 | doi = 10.1021/j100096a001 | issue = 45 }}</ref>

6-31G is a basis set of basis function among many others including 3-21G, etc.

=== Optimisation Methods ===

In this lab, three methods were used to optimise the TSs, with difficulty increasing from Method 1 to Method 3. Method 1 is the easiest and fastest one, but it is based on existing knowledge of the Transition State. Method 2, compared with Method 1, is more reliable as well as relatively fast, but it also has the limitation of requirement on knowledge of TS. Method 3 takes the most time to run, however, it does not have the limitation of the first two methods.

In this report, three pericylic reactions were investigated with all the Transition States being run with Method 3 and will be shown below.

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 1(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 1(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 1(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 2. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 3. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 4(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 4(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Therefore, in normal electron demand DA reactions, the orbitals of the electron-rich diene will be higher, therefore, favourable interaction occurs between the HOMO of diene and the LUMO of dienophile; while for inverse electron demand reactions, the LUMO of diene will interact with the HOMO of the dienophile.

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

In this reaction, due to the presence of a heterocyclic reactant, 1,3-dioxole, it is postulated that the reaction could possibly have an inverse electron demand, therefore, energy calculations were done and their single point energies determined in the following section to confirm the postulation.

==== Single point energies ====

{| class="wikitable"
|+ Table 11. Single point energies of reactants
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy of HOMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy of LUMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy difference between this HOMO and the LUMO of the other reactant/ a.u.'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |-0.20554
| style="text-align: center;" |-0.01711
| style="text-align: center;" |0.24349
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-0.19594
| style="text-align: center;" |0.03795
| style="text-align: center;" |0.17883
|}

In this reaction, the energy difference between the HOMO of the dienophile with the LUMO of diene is smaller than that of the other pair, therefore, they will give to a larger overlap of orbitals and more favourable interaciton.

Therefore, we can conclude from the data above that the reaction has an inverse electron demand. This is due to the presence of two oxygen atoms donating their lone pairs, making the dienophile electron rich.

=== Energy analysis ===

{| class="wikitable"
|+ Table 12. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 13. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 14. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
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</jmol>
| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure 5. Secondary orbital interactions in both Endo and Exo TS]]
|}

=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

[[File:Yz20215 E3 scheme.png|x400px|400px|thumb|centre|Scheme 3 Diels-Alder and Cheletropic reaction between Xylylene and Sulfur dioxide]]

The reaction between xylylene and sulfur dioxide was investigated.

The reaction between the reactants could occur either via a Diels-Alder reaction or cheletropic reaction as shown above in Scheme 3. For the Diels-Alder reaction between two, the product could be formed in an Endo or an Exo conformation.

In this exercise, the reactants, Transition States and products were optimised using PM6 Method using GaussView software. Also, the energies of different species were obtained to determine the activation energy and the energy change of reaction with reaction energy profile plotted. Therefore, the most thermodynamically and the most kinetically favoured product was determined.

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 15. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
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=== IRC calculations ===

{| class="wikitable"
|+ Table 16. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

Looking at IRC of these three reactions, we could see that the activation barrier of the reaction is quite small, this is due to one of the reactants, xylylene, being very unstable and high in energy.

This is because, according to Huckle's Rule, it has only 8 π electrons, which is (4n) instead of (4n+2), therefore, it is antiaromatic. However, due to structure constraint, both of the dienes are cis in xylylene, which is favourable as no energy expense on converting into trans conformation.

During the reaction, the xylyene part will react with the sulfur dioxide molecule to form a bicyclic ring, containing a benzene ring, which is aromatic and stable. Therefore, making it favourable to form the products.

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.021698
| style="text-align: center;" |56.9681033
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.021454
| style="text-align: center;" |56.3274813
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |-0.000002
| style="text-align: center;" |-0.0052510004
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |83.4410224
| style="text-align: center;" |-97.3535473
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |87.4239054
| style="text-align: center;" |-97.9941693
|-
| style="text-align: center;" |Cheletropic
| style="text-align: center;" |105.7656504
| style="text-align: center;" |-154.3269016
|}

The energies of the reactants, Transition States, and different products were obtained from the optimised LOG. files in GaussView, and the reaction profile is plotted showing their relative energies with the proceeding of the three reactions.

All TS and product energies are normalised with respect to reactant energy (reactant energy=0). The reaction profile is shown below.

=== Reaction Profiles ===

[[File:Yz20215 E3 reaction profile.png|x700px|700px|thumb|centre|Figure Reaction profile of three different reaction paths]]

In this profile, we could see that the '''endo TS''' is the lowest in energy, therefore will be formed faster compared with other two, and will be the '''kinetic product''' of the reaction. The Exo TS has slightly higher but close energy, while the cheletropic TS has the largest activation barrier.

However, if we compare the energies of the products, we could see that the Endo and the Exo products are very close in energy at approximately -98 kJ mol <sup>-1</sup> , while the cheletropic product is the most stable product with energy of around -154 kJ mol <sup>-1</sup> . Therefore, if we provide enough energy for the reaction to overcome its activation barrier, the '''cheletropic product''' will be the major product as it is the '''thermodynamic product''' of the reaction.

=== Extension ===

[[File:YZ20215 E3 extension.png|x400px|400px|thumb|centre|Scheme 4 The reaction of sulfur dioxide with another diene in xylylene]]

In this reaction, the other diene of xylylene, also in cis conformation, could also reaction with sulfur dioxide to form both the endo and the exo products, and the activation energies and reaction energies of these two reactions are investigated as shown below.

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.102071
| style="text-align: center;" |267.987431
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.105054
| style="text-align: center;" |275.819298
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.065615
| style="text-align: center;" |172.272196
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.067307
| style="text-align: center;" |176.714542
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |113.6657804
| style="text-align: center;" |17.9505454
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |121.4976474
| style="text-align: center;" |22.3928914
|}

These two reaction, are endothermic reactions, with product being higher in energy than that of the reactants. The activation barrier is also around 30 kJ mol <sup>-1</sup> higher than that of the DA reaction occurring at the other diene, therefore, these two reactions are both '''thermodynamically and kinetically unfavourable'''.

=== Files ===

Optimised LOG File for Endo TS: [[File:Yz20215 E3 DA endo TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 E3 DA TS exo TS PM6.log]]

Optimised LOG File for Cheletropic TS: [[File:YZ20215 E3 CHE TS.LOG]]

'''Extension'''

Optimised LOG File for Endo TS: [[File:Yz20215 ext ENDO TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 ext exo TS.log]]

= Conclusion =

During the time span of this Transition State Computational Lab, three different pericyclic reactions were investigated.

The reactions were investigated by using PM6 and B3LYP/6-31G(d) methods in GaussView to optimise the reactants, transition states, and the products.

Other information were also extracted from the optimised molecule LOG. files: including vibration frequency calculations and IRC (Intrinsic Reaction Coordinate); bond lengths of the TS, reactants and products; the energies of different species; and the molecular orbitals.

These data were used to analyse the Transition states and the reactions, including confirmation of the TS by presence of one imaginary frequency in vibration frequencies, the activation barrier and energy change of the reaction from the energies of different species, and the MOs to determine the electron demand of a certain Diels-Alder reaction (inverse or normal electron demand).

In addition, the data confirmed that the reactions followed several existing rules and theories: Woodward-Hoffmann rules in Exercise 1, Frontier Molecular Orbital Theory, etc..

These computational methods could be applied to investigate many other pericyclic reactions, where various aspects of data could be obtained and analysed as like shown in this lab.

Rep:YZ20215TS

2018-02-27T23:03:04Z

Yz20215: /* Optimisation of Transitions States using PM6 Method */

== Introduction ==

===Transition State ===
To investigate a reaction, it is crucial to firstly locate the Transition State of the reaction. The transition state of a reaction, on a 2D reaction coordinate, will be the highest point of energy connecting reactants and the products. In addition, it should also have the characteristics as shown below:

<math>\frac{\partial V}{\partial q_i}</math>= 0

<math>\frac{\partial^2 V}{\partial q_i^2}</math> < 0

Where as being a stationary point, its first derivative is equal to 0, while its second derivative should be negative as being the highest point on the reaction profile.

On a 3D PES (Potential Energy Surface), it is more difficult to determine the transition state, as it will be one saddle point among many other existing saddle points, however, being the maximum point on the minimum energy path, its first derivative and second derivative will both be equal to zero.

<math>\frac{\partial V}{\partial q_i}</math>= 0

<math>\frac{\partial^2 V}{\partial q_i^2}</math> = 0

=== Computational Methods ===

In this report, three different pericylic reactions were investigated using computational methods, including the PM6 and the B3LYP/6-31G(d) Methods.

PM6, with its full name being Parameterization Method 6, is a semi-empirical method. This method is based on the Hartree-Fock Model, and the model works by minimising the total molecular potential energy by varying the expansion coefficients, c<sub>μi</sub>, which is the coefficient in the equation of LCAO (Linear Combination of Atomic Orbitals).

This method is not perfect as it is based on the wrong assumption of accounting electrons as being largely independent of each other.<ref>Ot, W. J. (1990). Computational quantum chemistry. Journal of Molecular Structure: THEOCHEM (Vol. 207). </ref>

In reality, this is not true and the electrons will repulse each other due to their negative charge. Therefore, this method needs to be parameterised, which means the results fitted by a set of parameters, to product results that agree the most with experimental data.

While the other method, B3LYP, representing Becke, three-parameter, Lee-Yang-Parr, is based on Density Fucntional Theory (DFT), which is an incorporation of partly exact exchange from Hartree–Fock theory as well as exchange-correlation energy from other sources. It has an exchange-correlation functional as shown below:

<math>E_{\rm xc}^{\rm B3LYP} = E_{\rm x}^{\rm LDA} + a_0 (E_{\rm x}^{\rm HF} - E_{\rm x}^{\rm LDA}) + a_{\rm x} (E_{\rm x}^{\rm GGA} - E_{\rm x}^{\rm LDA}) + E_{\rm c}^{\rm LDA} + a_{\rm c} (E_{\rm c}^{\rm GGA} - E_{\rm c}^{\rm LDA}),</math>

where <math>a_0=0.20 \,\;</math>, <math>a_{\rm x}=0.72\,\;</math>, and <math>a_{\rm c}=0.81\,\;</math>. <ref>{{ cite journal |author1=K. Kim |author2=K. D. Jordan | title = Comparison of Density Functional and MP2 Calculations on the Water Monomer and Dimer | journal = J. Phys. Chem. | volume = 98 | issue = 40 | pages = 10089–10094 | year = 1994 | doi = 10.1021/j100091a024 }}</ref><ref>{{ cite journal |author1=P.J. Stephens |author2=F. J. Devlin |author3=C. F. Chabalowski |author4=M. J. Frisch | title = ''Ab Initio'' Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields | journal = J. Phys. Chem. | volume = 98 | pages = 11623–11627 | year = 1994 | doi = 10.1021/j100096a001 | issue = 45 }}</ref>

6-31G is a basis set of basis function among many others including 3-21G, etc.

=== Optimisation Methods ===

In this lab, three methods were used to optimise the TSs, with difficulty increasing from Method 1 to Method 3. Method 1 is the easiest and fastest one, but it is based on existing knowledge of the Transition State. Method 2, compared with Method 1, is more reliable as well as relatively fast, but it also has the limitation of requirement on knowledge of TS. Method 3 takes the most time to run, however, it does not have the limitation of the first two methods.

In this report, three pericylic reactions were investigated with all the Transition States being run with Method 3 and will be shown below.

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 1(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 1(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 1(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 2. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 3. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 cyclohexadiene min.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 dioxole min B3LYP.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 product ENDO B3LYP MIN.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents> Yz20215 E2 product EXO B3LYP MIN.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 TS endo TS.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 TS exo TS.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
|<jmol>
<jmolApplet>
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<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
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|<jmol>
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<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
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|<jmol>
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<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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|<jmol>
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<color>white</color>
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<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" |HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 4(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 4(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Therefore, in normal electron demand DA reactions, the orbitals of the electron-rich diene will be higher, therefore, favourable interaction occurs between the HOMO of diene and the LUMO of dienophile; while for inverse electron demand reactions, the LUMO of diene will interact with the HOMO of the dienophile.

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

In this reaction, due to the presence of a heterocyclic reactant, 1,3-dioxole, it is postulated that the reaction could possibly have an inverse electron demand, therefore, energy calculations were done and their single point energies determined in the following section to confirm the postulation.

==== Single point energies ====

{| class="wikitable"
|+ Table 11. Single point energies of reactants
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy of HOMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy of LUMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy difference between this HOMO and the LUMO of the other reactant/ a.u.'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |-0.20554
| style="text-align: center;" |-0.01711
| style="text-align: center;" |0.24349
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-0.19594
| style="text-align: center;" |0.03795
| style="text-align: center;" |0.17883
|}

In this reaction, the energy difference between the HOMO of the dienophile with the LUMO of diene is smaller than that of the other pair, therefore, they will give to a larger overlap of orbitals and more favourable interaciton.

Therefore, we can conclude from the data above that the reaction has an inverse electron demand. This is due to the presence of two oxygen atoms donating their lone pairs, making the dienophile electron rich.

=== Energy analysis ===

{| class="wikitable"
|+ Table 12. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 13. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 14. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
!<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
</jmolApplet>
</jmol>
| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure 5. Secondary orbital interactions in both Endo and Exo TS]]
|}

=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

[[File:Yz20215 E3 scheme.png|x400px|400px|thumb|centre|Scheme 3 Diels-Alder and Cheletropic reaction between Xylylene and Sulfur dioxide]]

The reaction between xylylene and sulfur dioxide was investigated.

The reaction between the reactants could occur either via a Diels-Alder reaction or cheletropic reaction as shown above in Scheme 3. For the Diels-Alder reaction between two, the product could be formed in an Endo or an Exo conformation.

In this exercise, the reactants, Transition States and products were optimised using PM6 Method using GaussView software. Also, the energies of different species were obtained to determine the activation energy and the energy change of reaction with reaction energy profile plotted. Therefore, the most thermodynamically and the most kinetically favoured product was determined.

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 15. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E3 DA endo TS.LOG</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
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<script>frame 16; </script>
<uploadedFileContents>Yz20215 E3 DA TS exo TS PM6.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
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<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>YZ20215 E3 CHE TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== IRC calculations ===

{| class="wikitable"
|+ Table 15. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

Looking at IRC of these three reactions, we could see that the activation barrier of the reaction is quite small, this is due to one of the reactants, xylylene, being very unstable and high in energy.

This is because, according to Huckle's Rule, it has only 8 π electrons, which is (4n) instead of (4n+2), therefore, it is antiaromatic. However, due to structure constraint, both of the dienes are cis in xylylene, which is favourable as no energy expense on converting into trans conformation.

During the reaction, the xylyene part will react with the sulfur dioxide molecule to form a bicyclic ring, containing a benzene ring, which is aromatic and stable. Therefore, making it favourable to form the products.

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.021698
| style="text-align: center;" |56.9681033
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.021454
| style="text-align: center;" |56.3274813
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |-0.000002
| style="text-align: center;" |-0.0052510004
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |83.4410224
| style="text-align: center;" |-97.3535473
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |87.4239054
| style="text-align: center;" |-97.9941693
|-
| style="text-align: center;" |Cheletropic
| style="text-align: center;" |105.7656504
| style="text-align: center;" |-154.3269016
|}

The energies of the reactants, Transition States, and different products were obtained from the optimised LOG. files in GaussView, and the reaction profile is plotted showing their relative energies with the proceeding of the three reactions.

All TS and product energies are normalised with respect to reactant energy (reactant energy=0). The reaction profile is shown below.

=== Reaction Profiles ===

[[File:Yz20215 E3 reaction profile.png|x700px|700px|thumb|centre|Figure Reaction profile of three different reaction paths]]

In this profile, we could see that the '''endo TS''' is the lowest in energy, therefore will be formed faster compared with other two, and will be the '''kinetic product''' of the reaction. The Exo TS has slightly higher but close energy, while the cheletropic TS has the largest activation barrier.

However, if we compare the energies of the products, we could see that the Endo and the Exo products are very close in energy at approximately -98 kJ mol <sup>-1</sup> , while the cheletropic product is the most stable product with energy of around -154 kJ mol <sup>-1</sup> . Therefore, if we provide enough energy for the reaction to overcome its activation barrier, the '''cheletropic product''' will be the major product as it is the '''thermodynamic product''' of the reaction.

=== Extension ===

[[File:YZ20215 E3 extension.png|x400px|400px|thumb|centre|Scheme 4 The reaction of sulfur dioxide with another diene in xylylene]]

In this reaction, the other diene of xylylene, also in cis conformation, could also reaction with sulfur dioxide to form both the endo and the exo products, and the activation energies and reaction energies of these two reactions are investigated as shown below.

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.102071
| style="text-align: center;" |267.987431
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.105054
| style="text-align: center;" |275.819298
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.065615
| style="text-align: center;" |172.272196
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.067307
| style="text-align: center;" |176.714542
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |113.6657804
| style="text-align: center;" |17.9505454
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |121.4976474
| style="text-align: center;" |22.3928914
|}

These two reaction, are endothermic reactions, with product being higher in energy than that of the reactants. The activation barrier is also around 30 kJ mol <sup>-1</sup> higher than that of the DA reaction occurring at the other diene, therefore, these two reactions are both '''thermodynamically and kinetically unfavourable'''.

=== Files ===

Optimised LOG File for Endo TS: [[File:Yz20215 E3 DA endo TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 E3 DA TS exo TS PM6.log]]

Optimised LOG File for Cheletropic TS: [[File:YZ20215 E3 CHE TS.LOG]]

'''Extension'''

Optimised LOG File for Endo TS: [[File:Yz20215 ext ENDO TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 ext exo TS.log]]

= Conclusion =

During the time span of this Transition State Computational Lab, three different pericyclic reactions were investigated.

The reactions were investigated by using PM6 and B3LYP/6-31G(d) methods in GaussView to optimise the reactants, transition states, and the products.

Other information were also extracted from the optimised molecule LOG. files: including vibration frequency calculations and IRC (Intrinsic Reaction Coordinate); bond lengths of the TS, reactants and products; the energies of different species; and the molecular orbitals.

These data were used to analyse the Transition states and the reactions, including confirmation of the TS by presence of one imaginary frequency in vibration frequencies, the activation barrier and energy change of the reaction from the energies of different species, and the MOs to determine the electron demand of a certain Diels-Alder reaction (inverse or normal electron demand).

In addition, the data confirmed that the reactions followed several existing rules and theories: Woodward-Hoffmann rules in Exercise 1, Frontier Molecular Orbital Theory, etc..

These computational methods could be applied to investigate many other pericyclic reactions, where various aspects of data could be obtained and analysed as like shown in this lab.

Rep:YZ20215TS

2018-02-27T23:02:39Z

Yz20215: /* Secondary Orbital Interaction */

== Introduction ==

===Transition State ===
To investigate a reaction, it is crucial to firstly locate the Transition State of the reaction. The transition state of a reaction, on a 2D reaction coordinate, will be the highest point of energy connecting reactants and the products. In addition, it should also have the characteristics as shown below:

<math>\frac{\partial V}{\partial q_i}</math>= 0

<math>\frac{\partial^2 V}{\partial q_i^2}</math> < 0

Where as being a stationary point, its first derivative is equal to 0, while its second derivative should be negative as being the highest point on the reaction profile.

On a 3D PES (Potential Energy Surface), it is more difficult to determine the transition state, as it will be one saddle point among many other existing saddle points, however, being the maximum point on the minimum energy path, its first derivative and second derivative will both be equal to zero.

<math>\frac{\partial V}{\partial q_i}</math>= 0

<math>\frac{\partial^2 V}{\partial q_i^2}</math> = 0

=== Computational Methods ===

In this report, three different pericylic reactions were investigated using computational methods, including the PM6 and the B3LYP/6-31G(d) Methods.

PM6, with its full name being Parameterization Method 6, is a semi-empirical method. This method is based on the Hartree-Fock Model, and the model works by minimising the total molecular potential energy by varying the expansion coefficients, c<sub>μi</sub>, which is the coefficient in the equation of LCAO (Linear Combination of Atomic Orbitals).

This method is not perfect as it is based on the wrong assumption of accounting electrons as being largely independent of each other.<ref>Ot, W. J. (1990). Computational quantum chemistry. Journal of Molecular Structure: THEOCHEM (Vol. 207). </ref>

In reality, this is not true and the electrons will repulse each other due to their negative charge. Therefore, this method needs to be parameterised, which means the results fitted by a set of parameters, to product results that agree the most with experimental data.

While the other method, B3LYP, representing Becke, three-parameter, Lee-Yang-Parr, is based on Density Fucntional Theory (DFT), which is an incorporation of partly exact exchange from Hartree–Fock theory as well as exchange-correlation energy from other sources. It has an exchange-correlation functional as shown below:

<math>E_{\rm xc}^{\rm B3LYP} = E_{\rm x}^{\rm LDA} + a_0 (E_{\rm x}^{\rm HF} - E_{\rm x}^{\rm LDA}) + a_{\rm x} (E_{\rm x}^{\rm GGA} - E_{\rm x}^{\rm LDA}) + E_{\rm c}^{\rm LDA} + a_{\rm c} (E_{\rm c}^{\rm GGA} - E_{\rm c}^{\rm LDA}),</math>

where <math>a_0=0.20 \,\;</math>, <math>a_{\rm x}=0.72\,\;</math>, and <math>a_{\rm c}=0.81\,\;</math>. <ref>{{ cite journal |author1=K. Kim |author2=K. D. Jordan | title = Comparison of Density Functional and MP2 Calculations on the Water Monomer and Dimer | journal = J. Phys. Chem. | volume = 98 | issue = 40 | pages = 10089–10094 | year = 1994 | doi = 10.1021/j100091a024 }}</ref><ref>{{ cite journal |author1=P.J. Stephens |author2=F. J. Devlin |author3=C. F. Chabalowski |author4=M. J. Frisch | title = ''Ab Initio'' Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields | journal = J. Phys. Chem. | volume = 98 | pages = 11623–11627 | year = 1994 | doi = 10.1021/j100096a001 | issue = 45 }}</ref>

6-31G is a basis set of basis function among many others including 3-21G, etc.

=== Optimisation Methods ===

In this lab, three methods were used to optimise the TSs, with difficulty increasing from Method 1 to Method 3. Method 1 is the easiest and fastest one, but it is based on existing knowledge of the Transition State. Method 2, compared with Method 1, is more reliable as well as relatively fast, but it also has the limitation of requirement on knowledge of TS. Method 3 takes the most time to run, however, it does not have the limitation of the first two methods.

In this report, three pericylic reactions were investigated with all the Transition States being run with Method 3 and will be shown below.

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 1(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 1(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 1(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 2. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
|<jmol>
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|-
| style="text-align: center;" |HOMO
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==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 3. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 4(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 4(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Therefore, in normal electron demand DA reactions, the orbitals of the electron-rich diene will be higher, therefore, favourable interaction occurs between the HOMO of diene and the LUMO of dienophile; while for inverse electron demand reactions, the LUMO of diene will interact with the HOMO of the dienophile.

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

In this reaction, due to the presence of a heterocyclic reactant, 1,3-dioxole, it is postulated that the reaction could possibly have an inverse electron demand, therefore, energy calculations were done and their single point energies determined in the following section to confirm the postulation.

==== Single point energies ====

{| class="wikitable"
|+ Table 11. Single point energies of reactants
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy of HOMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy of LUMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy difference between this HOMO and the LUMO of the other reactant/ a.u.'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |-0.20554
| style="text-align: center;" |-0.01711
| style="text-align: center;" |0.24349
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-0.19594
| style="text-align: center;" |0.03795
| style="text-align: center;" |0.17883
|}

In this reaction, the energy difference between the HOMO of the dienophile with the LUMO of diene is smaller than that of the other pair, therefore, they will give to a larger overlap of orbitals and more favourable interaciton.

Therefore, we can conclude from the data above that the reaction has an inverse electron demand. This is due to the presence of two oxygen atoms donating their lone pairs, making the dienophile electron rich.

=== Energy analysis ===

{| class="wikitable"
|+ Table 12. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 13. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 14. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
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| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure 5. Secondary orbital interactions in both Endo and Exo TS]]
|}

=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

[[File:Yz20215 E3 scheme.png|x400px|400px|thumb|centre|Scheme 3 Diels-Alder and Cheletropic reaction between Xylylene and Sulfur dioxide]]

The reaction between xylylene and sulfur dioxide was investigated.

The reaction between the reactants could occur either via a Diels-Alder reaction or cheletropic reaction as shown above in Scheme 3. For the Diels-Alder reaction between two, the product could be formed in an Endo or an Exo conformation.

In this exercise, the reactants, Transition States and products were optimised using PM6 Method using GaussView software. Also, the energies of different species were obtained to determine the activation energy and the energy change of reaction with reaction energy profile plotted. Therefore, the most thermodynamically and the most kinetically favoured product was determined.

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 14. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
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=== IRC calculations ===

{| class="wikitable"
|+ Table 15. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

Looking at IRC of these three reactions, we could see that the activation barrier of the reaction is quite small, this is due to one of the reactants, xylylene, being very unstable and high in energy.

This is because, according to Huckle's Rule, it has only 8 π electrons, which is (4n) instead of (4n+2), therefore, it is antiaromatic. However, due to structure constraint, both of the dienes are cis in xylylene, which is favourable as no energy expense on converting into trans conformation.

During the reaction, the xylyene part will react with the sulfur dioxide molecule to form a bicyclic ring, containing a benzene ring, which is aromatic and stable. Therefore, making it favourable to form the products.

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.021698
| style="text-align: center;" |56.9681033
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.021454
| style="text-align: center;" |56.3274813
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |-0.000002
| style="text-align: center;" |-0.0052510004
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |83.4410224
| style="text-align: center;" |-97.3535473
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |87.4239054
| style="text-align: center;" |-97.9941693
|-
| style="text-align: center;" |Cheletropic
| style="text-align: center;" |105.7656504
| style="text-align: center;" |-154.3269016
|}

The energies of the reactants, Transition States, and different products were obtained from the optimised LOG. files in GaussView, and the reaction profile is plotted showing their relative energies with the proceeding of the three reactions.

All TS and product energies are normalised with respect to reactant energy (reactant energy=0). The reaction profile is shown below.

=== Reaction Profiles ===

[[File:Yz20215 E3 reaction profile.png|x700px|700px|thumb|centre|Figure Reaction profile of three different reaction paths]]

In this profile, we could see that the '''endo TS''' is the lowest in energy, therefore will be formed faster compared with other two, and will be the '''kinetic product''' of the reaction. The Exo TS has slightly higher but close energy, while the cheletropic TS has the largest activation barrier.

However, if we compare the energies of the products, we could see that the Endo and the Exo products are very close in energy at approximately -98 kJ mol <sup>-1</sup> , while the cheletropic product is the most stable product with energy of around -154 kJ mol <sup>-1</sup> . Therefore, if we provide enough energy for the reaction to overcome its activation barrier, the '''cheletropic product''' will be the major product as it is the '''thermodynamic product''' of the reaction.

=== Extension ===

[[File:YZ20215 E3 extension.png|x400px|400px|thumb|centre|Scheme 4 The reaction of sulfur dioxide with another diene in xylylene]]

In this reaction, the other diene of xylylene, also in cis conformation, could also reaction with sulfur dioxide to form both the endo and the exo products, and the activation energies and reaction energies of these two reactions are investigated as shown below.

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.102071
| style="text-align: center;" |267.987431
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.105054
| style="text-align: center;" |275.819298
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.065615
| style="text-align: center;" |172.272196
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.067307
| style="text-align: center;" |176.714542
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |113.6657804
| style="text-align: center;" |17.9505454
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |121.4976474
| style="text-align: center;" |22.3928914
|}

These two reaction, are endothermic reactions, with product being higher in energy than that of the reactants. The activation barrier is also around 30 kJ mol <sup>-1</sup> higher than that of the DA reaction occurring at the other diene, therefore, these two reactions are both '''thermodynamically and kinetically unfavourable'''.

=== Files ===

Optimised LOG File for Endo TS: [[File:Yz20215 E3 DA endo TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 E3 DA TS exo TS PM6.log]]

Optimised LOG File for Cheletropic TS: [[File:YZ20215 E3 CHE TS.LOG]]

'''Extension'''

Optimised LOG File for Endo TS: [[File:Yz20215 ext ENDO TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 ext exo TS.log]]

= Conclusion =

During the time span of this Transition State Computational Lab, three different pericyclic reactions were investigated.

The reactions were investigated by using PM6 and B3LYP/6-31G(d) methods in GaussView to optimise the reactants, transition states, and the products.

Other information were also extracted from the optimised molecule LOG. files: including vibration frequency calculations and IRC (Intrinsic Reaction Coordinate); bond lengths of the TS, reactants and products; the energies of different species; and the molecular orbitals.

These data were used to analyse the Transition states and the reactions, including confirmation of the TS by presence of one imaginary frequency in vibration frequencies, the activation barrier and energy change of the reaction from the energies of different species, and the MOs to determine the electron demand of a certain Diels-Alder reaction (inverse or normal electron demand).

In addition, the data confirmed that the reactions followed several existing rules and theories: Woodward-Hoffmann rules in Exercise 1, Frontier Molecular Orbital Theory, etc..

These computational methods could be applied to investigate many other pericyclic reactions, where various aspects of data could be obtained and analysed as like shown in this lab.

Rep:YZ20215TS

2018-02-27T23:01:38Z

Yz20215: /* MO analysis */

== Introduction ==

===Transition State ===
To investigate a reaction, it is crucial to firstly locate the Transition State of the reaction. The transition state of a reaction, on a 2D reaction coordinate, will be the highest point of energy connecting reactants and the products. In addition, it should also have the characteristics as shown below:

<math>\frac{\partial V}{\partial q_i}</math>= 0

<math>\frac{\partial^2 V}{\partial q_i^2}</math> < 0

Where as being a stationary point, its first derivative is equal to 0, while its second derivative should be negative as being the highest point on the reaction profile.

On a 3D PES (Potential Energy Surface), it is more difficult to determine the transition state, as it will be one saddle point among many other existing saddle points, however, being the maximum point on the minimum energy path, its first derivative and second derivative will both be equal to zero.

<math>\frac{\partial V}{\partial q_i}</math>= 0

<math>\frac{\partial^2 V}{\partial q_i^2}</math> = 0

=== Computational Methods ===

In this report, three different pericylic reactions were investigated using computational methods, including the PM6 and the B3LYP/6-31G(d) Methods.

PM6, with its full name being Parameterization Method 6, is a semi-empirical method. This method is based on the Hartree-Fock Model, and the model works by minimising the total molecular potential energy by varying the expansion coefficients, c<sub>μi</sub>, which is the coefficient in the equation of LCAO (Linear Combination of Atomic Orbitals).

This method is not perfect as it is based on the wrong assumption of accounting electrons as being largely independent of each other.<ref>Ot, W. J. (1990). Computational quantum chemistry. Journal of Molecular Structure: THEOCHEM (Vol. 207). </ref>

In reality, this is not true and the electrons will repulse each other due to their negative charge. Therefore, this method needs to be parameterised, which means the results fitted by a set of parameters, to product results that agree the most with experimental data.

While the other method, B3LYP, representing Becke, three-parameter, Lee-Yang-Parr, is based on Density Fucntional Theory (DFT), which is an incorporation of partly exact exchange from Hartree–Fock theory as well as exchange-correlation energy from other sources. It has an exchange-correlation functional as shown below:

<math>E_{\rm xc}^{\rm B3LYP} = E_{\rm x}^{\rm LDA} + a_0 (E_{\rm x}^{\rm HF} - E_{\rm x}^{\rm LDA}) + a_{\rm x} (E_{\rm x}^{\rm GGA} - E_{\rm x}^{\rm LDA}) + E_{\rm c}^{\rm LDA} + a_{\rm c} (E_{\rm c}^{\rm GGA} - E_{\rm c}^{\rm LDA}),</math>

where <math>a_0=0.20 \,\;</math>, <math>a_{\rm x}=0.72\,\;</math>, and <math>a_{\rm c}=0.81\,\;</math>. <ref>{{ cite journal |author1=K. Kim |author2=K. D. Jordan | title = Comparison of Density Functional and MP2 Calculations on the Water Monomer and Dimer | journal = J. Phys. Chem. | volume = 98 | issue = 40 | pages = 10089–10094 | year = 1994 | doi = 10.1021/j100091a024 }}</ref><ref>{{ cite journal |author1=P.J. Stephens |author2=F. J. Devlin |author3=C. F. Chabalowski |author4=M. J. Frisch | title = ''Ab Initio'' Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields | journal = J. Phys. Chem. | volume = 98 | pages = 11623–11627 | year = 1994 | doi = 10.1021/j100096a001 | issue = 45 }}</ref>

6-31G is a basis set of basis function among many others including 3-21G, etc.

=== Optimisation Methods ===

In this lab, three methods were used to optimise the TSs, with difficulty increasing from Method 1 to Method 3. Method 1 is the easiest and fastest one, but it is based on existing knowledge of the Transition State. Method 2, compared with Method 1, is more reliable as well as relatively fast, but it also has the limitation of requirement on knowledge of TS. Method 3 takes the most time to run, however, it does not have the limitation of the first two methods.

In this report, three pericylic reactions were investigated with all the Transition States being run with Method 3 and will be shown below.

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 1(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 1(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 1(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 2. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 3. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 4(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 4(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Therefore, in normal electron demand DA reactions, the orbitals of the electron-rich diene will be higher, therefore, favourable interaction occurs between the HOMO of diene and the LUMO of dienophile; while for inverse electron demand reactions, the LUMO of diene will interact with the HOMO of the dienophile.

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

In this reaction, due to the presence of a heterocyclic reactant, 1,3-dioxole, it is postulated that the reaction could possibly have an inverse electron demand, therefore, energy calculations were done and their single point energies determined in the following section to confirm the postulation.

==== Single point energies ====

{| class="wikitable"
|+ Table 11. Single point energies of reactants
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy of HOMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy of LUMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy difference between this HOMO and the LUMO of the other reactant/ a.u.'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |-0.20554
| style="text-align: center;" |-0.01711
| style="text-align: center;" |0.24349
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-0.19594
| style="text-align: center;" |0.03795
| style="text-align: center;" |0.17883
|}

In this reaction, the energy difference between the HOMO of the dienophile with the LUMO of diene is smaller than that of the other pair, therefore, they will give to a larger overlap of orbitals and more favourable interaciton.

Therefore, we can conclude from the data above that the reaction has an inverse electron demand. This is due to the presence of two oxygen atoms donating their lone pairs, making the dienophile electron rich.

=== Energy analysis ===

{| class="wikitable"
|+ Table 12. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 13. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 14. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
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| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure Secondary orbital interactions in both Endo and Exo TS]]
|}

=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

[[File:Yz20215 E3 scheme.png|x400px|400px|thumb|centre|Scheme 3 Diels-Alder and Cheletropic reaction between Xylylene and Sulfur dioxide]]

The reaction between xylylene and sulfur dioxide was investigated.

The reaction between the reactants could occur either via a Diels-Alder reaction or cheletropic reaction as shown above in Scheme 3. For the Diels-Alder reaction between two, the product could be formed in an Endo or an Exo conformation.

In this exercise, the reactants, Transition States and products were optimised using PM6 Method using GaussView software. Also, the energies of different species were obtained to determine the activation energy and the energy change of reaction with reaction energy profile plotted. Therefore, the most thermodynamically and the most kinetically favoured product was determined.

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 14. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
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=== IRC calculations ===

{| class="wikitable"
|+ Table 15. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

Looking at IRC of these three reactions, we could see that the activation barrier of the reaction is quite small, this is due to one of the reactants, xylylene, being very unstable and high in energy.

This is because, according to Huckle's Rule, it has only 8 π electrons, which is (4n) instead of (4n+2), therefore, it is antiaromatic. However, due to structure constraint, both of the dienes are cis in xylylene, which is favourable as no energy expense on converting into trans conformation.

During the reaction, the xylyene part will react with the sulfur dioxide molecule to form a bicyclic ring, containing a benzene ring, which is aromatic and stable. Therefore, making it favourable to form the products.

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.021698
| style="text-align: center;" |56.9681033
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.021454
| style="text-align: center;" |56.3274813
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |-0.000002
| style="text-align: center;" |-0.0052510004
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |83.4410224
| style="text-align: center;" |-97.3535473
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |87.4239054
| style="text-align: center;" |-97.9941693
|-
| style="text-align: center;" |Cheletropic
| style="text-align: center;" |105.7656504
| style="text-align: center;" |-154.3269016
|}

The energies of the reactants, Transition States, and different products were obtained from the optimised LOG. files in GaussView, and the reaction profile is plotted showing their relative energies with the proceeding of the three reactions.

All TS and product energies are normalised with respect to reactant energy (reactant energy=0). The reaction profile is shown below.

=== Reaction Profiles ===

[[File:Yz20215 E3 reaction profile.png|x700px|700px|thumb|centre|Figure Reaction profile of three different reaction paths]]

In this profile, we could see that the '''endo TS''' is the lowest in energy, therefore will be formed faster compared with other two, and will be the '''kinetic product''' of the reaction. The Exo TS has slightly higher but close energy, while the cheletropic TS has the largest activation barrier.

However, if we compare the energies of the products, we could see that the Endo and the Exo products are very close in energy at approximately -98 kJ mol <sup>-1</sup> , while the cheletropic product is the most stable product with energy of around -154 kJ mol <sup>-1</sup> . Therefore, if we provide enough energy for the reaction to overcome its activation barrier, the '''cheletropic product''' will be the major product as it is the '''thermodynamic product''' of the reaction.

=== Extension ===

[[File:YZ20215 E3 extension.png|x400px|400px|thumb|centre|Scheme 4 The reaction of sulfur dioxide with another diene in xylylene]]

In this reaction, the other diene of xylylene, also in cis conformation, could also reaction with sulfur dioxide to form both the endo and the exo products, and the activation energies and reaction energies of these two reactions are investigated as shown below.

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.102071
| style="text-align: center;" |267.987431
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.105054
| style="text-align: center;" |275.819298
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.065615
| style="text-align: center;" |172.272196
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.067307
| style="text-align: center;" |176.714542
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |113.6657804
| style="text-align: center;" |17.9505454
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |121.4976474
| style="text-align: center;" |22.3928914
|}

These two reaction, are endothermic reactions, with product being higher in energy than that of the reactants. The activation barrier is also around 30 kJ mol <sup>-1</sup> higher than that of the DA reaction occurring at the other diene, therefore, these two reactions are both '''thermodynamically and kinetically unfavourable'''.

=== Files ===

Optimised LOG File for Endo TS: [[File:Yz20215 E3 DA endo TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 E3 DA TS exo TS PM6.log]]

Optimised LOG File for Cheletropic TS: [[File:YZ20215 E3 CHE TS.LOG]]

'''Extension'''

Optimised LOG File for Endo TS: [[File:Yz20215 ext ENDO TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 ext exo TS.log]]

= Conclusion =

During the time span of this Transition State Computational Lab, three different pericyclic reactions were investigated.

The reactions were investigated by using PM6 and B3LYP/6-31G(d) methods in GaussView to optimise the reactants, transition states, and the products.

Other information were also extracted from the optimised molecule LOG. files: including vibration frequency calculations and IRC (Intrinsic Reaction Coordinate); bond lengths of the TS, reactants and products; the energies of different species; and the molecular orbitals.

These data were used to analyse the Transition states and the reactions, including confirmation of the TS by presence of one imaginary frequency in vibration frequencies, the activation barrier and energy change of the reaction from the energies of different species, and the MOs to determine the electron demand of a certain Diels-Alder reaction (inverse or normal electron demand).

In addition, the data confirmed that the reactions followed several existing rules and theories: Woodward-Hoffmann rules in Exercise 1, Frontier Molecular Orbital Theory, etc..

These computational methods could be applied to investigate many other pericyclic reactions, where various aspects of data could be obtained and analysed as like shown in this lab.

Rep:YZ20215TS

2018-02-27T22:59:56Z

Yz20215: /* Vibrations */

== Introduction ==

===Transition State ===
To investigate a reaction, it is crucial to firstly locate the Transition State of the reaction. The transition state of a reaction, on a 2D reaction coordinate, will be the highest point of energy connecting reactants and the products. In addition, it should also have the characteristics as shown below:

<math>\frac{\partial V}{\partial q_i}</math>= 0

<math>\frac{\partial^2 V}{\partial q_i^2}</math> < 0

Where as being a stationary point, its first derivative is equal to 0, while its second derivative should be negative as being the highest point on the reaction profile.

On a 3D PES (Potential Energy Surface), it is more difficult to determine the transition state, as it will be one saddle point among many other existing saddle points, however, being the maximum point on the minimum energy path, its first derivative and second derivative will both be equal to zero.

<math>\frac{\partial V}{\partial q_i}</math>= 0

<math>\frac{\partial^2 V}{\partial q_i^2}</math> = 0

=== Computational Methods ===

In this report, three different pericylic reactions were investigated using computational methods, including the PM6 and the B3LYP/6-31G(d) Methods.

PM6, with its full name being Parameterization Method 6, is a semi-empirical method. This method is based on the Hartree-Fock Model, and the model works by minimising the total molecular potential energy by varying the expansion coefficients, c<sub>μi</sub>, which is the coefficient in the equation of LCAO (Linear Combination of Atomic Orbitals).

This method is not perfect as it is based on the wrong assumption of accounting electrons as being largely independent of each other.<ref>Ot, W. J. (1990). Computational quantum chemistry. Journal of Molecular Structure: THEOCHEM (Vol. 207). </ref>

In reality, this is not true and the electrons will repulse each other due to their negative charge. Therefore, this method needs to be parameterised, which means the results fitted by a set of parameters, to product results that agree the most with experimental data.

While the other method, B3LYP, representing Becke, three-parameter, Lee-Yang-Parr, is based on Density Fucntional Theory (DFT), which is an incorporation of partly exact exchange from Hartree–Fock theory as well as exchange-correlation energy from other sources. It has an exchange-correlation functional as shown below:

<math>E_{\rm xc}^{\rm B3LYP} = E_{\rm x}^{\rm LDA} + a_0 (E_{\rm x}^{\rm HF} - E_{\rm x}^{\rm LDA}) + a_{\rm x} (E_{\rm x}^{\rm GGA} - E_{\rm x}^{\rm LDA}) + E_{\rm c}^{\rm LDA} + a_{\rm c} (E_{\rm c}^{\rm GGA} - E_{\rm c}^{\rm LDA}),</math>

where <math>a_0=0.20 \,\;</math>, <math>a_{\rm x}=0.72\,\;</math>, and <math>a_{\rm c}=0.81\,\;</math>. <ref>{{ cite journal |author1=K. Kim |author2=K. D. Jordan | title = Comparison of Density Functional and MP2 Calculations on the Water Monomer and Dimer | journal = J. Phys. Chem. | volume = 98 | issue = 40 | pages = 10089–10094 | year = 1994 | doi = 10.1021/j100091a024 }}</ref><ref>{{ cite journal |author1=P.J. Stephens |author2=F. J. Devlin |author3=C. F. Chabalowski |author4=M. J. Frisch | title = ''Ab Initio'' Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields | journal = J. Phys. Chem. | volume = 98 | pages = 11623–11627 | year = 1994 | doi = 10.1021/j100096a001 | issue = 45 }}</ref>

6-31G is a basis set of basis function among many others including 3-21G, etc.

=== Optimisation Methods ===

In this lab, three methods were used to optimise the TSs, with difficulty increasing from Method 1 to Method 3. Method 1 is the easiest and fastest one, but it is based on existing knowledge of the Transition State. Method 2, compared with Method 1, is more reliable as well as relatively fast, but it also has the limitation of requirement on knowledge of TS. Method 3 takes the most time to run, however, it does not have the limitation of the first two methods.

In this report, three pericylic reactions were investigated with all the Transition States being run with Method 3 and will be shown below.

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 1(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 1(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 1(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 2. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 3. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 cyclohexadiene min.LOG</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 dioxole min B3LYP.log</uploadedFileContents>
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|<jmol>
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<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 product ENDO B3LYP MIN.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
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<script>frame 16; </script>
<uploadedFileContents> Yz20215 E2 product EXO B3LYP MIN.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 TS endo TS.log</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 TS exo TS.log</uploadedFileContents>
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</jmol>
|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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|}

{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 5(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 5(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Therefore, in normal electron demand DA reactions, the orbitals of the electron-rich diene will be higher, therefore, favourable interaction occurs between the HOMO of diene and the LUMO of dienophile; while for inverse electron demand reactions, the LUMO of diene will interact with the HOMO of the dienophile.

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

In this reaction, due to the presence of a heterocyclic reactant, 1,3-dioxole, it is postulated that the reaction could possibly have an inverse electron demand, therefore, energy calculations were done and their single point energies determined in the following section to confirm the postulation.

==== Single point energies ====

{| class="wikitable"
|+ Table 11. Single point energies of reactants
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy of HOMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy of LUMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy difference between this HOMO and the LUMO of the other reactant/ a.u.'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |-0.20554
| style="text-align: center;" |-0.01711
| style="text-align: center;" |0.24349
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-0.19594
| style="text-align: center;" |0.03795
| style="text-align: center;" |0.17883
|}

In this reaction, the energy difference between the HOMO of the dienophile with the LUMO of diene is smaller than that of the other pair, therefore, they will give to a larger overlap of orbitals and more favourable interaciton.

Therefore, we can conclude from the data above that the reaction has an inverse electron demand. This is due to the presence of two oxygen atoms donating their lone pairs, making the dienophile electron rich.

=== Energy analysis ===

{| class="wikitable"
|+ Table 12. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 13. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 14. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
!<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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!<jmol>
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</jmolApplet>
</jmol>
| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure Secondary orbital interactions in both Endo and Exo TS]]
|}

=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

[[File:Yz20215 E3 scheme.png|x400px|400px|thumb|centre|Scheme 3 Diels-Alder and Cheletropic reaction between Xylylene and Sulfur dioxide]]

The reaction between xylylene and sulfur dioxide was investigated.

The reaction between the reactants could occur either via a Diels-Alder reaction or cheletropic reaction as shown above in Scheme 3. For the Diels-Alder reaction between two, the product could be formed in an Endo or an Exo conformation.

In this exercise, the reactants, Transition States and products were optimised using PM6 Method using GaussView software. Also, the energies of different species were obtained to determine the activation energy and the energy change of reaction with reaction energy profile plotted. Therefore, the most thermodynamically and the most kinetically favoured product was determined.

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 14. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E3 DA endo TS.LOG</uploadedFileContents>
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|<jmol>
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<script>frame 16; </script>
<uploadedFileContents>YZ20215 E3 CHE TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== IRC calculations ===

{| class="wikitable"
|+ Table 15. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

Looking at IRC of these three reactions, we could see that the activation barrier of the reaction is quite small, this is due to one of the reactants, xylylene, being very unstable and high in energy.

This is because, according to Huckle's Rule, it has only 8 π electrons, which is (4n) instead of (4n+2), therefore, it is antiaromatic. However, due to structure constraint, both of the dienes are cis in xylylene, which is favourable as no energy expense on converting into trans conformation.

During the reaction, the xylyene part will react with the sulfur dioxide molecule to form a bicyclic ring, containing a benzene ring, which is aromatic and stable. Therefore, making it favourable to form the products.

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.021698
| style="text-align: center;" |56.9681033
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.021454
| style="text-align: center;" |56.3274813
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |-0.000002
| style="text-align: center;" |-0.0052510004
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |83.4410224
| style="text-align: center;" |-97.3535473
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |87.4239054
| style="text-align: center;" |-97.9941693
|-
| style="text-align: center;" |Cheletropic
| style="text-align: center;" |105.7656504
| style="text-align: center;" |-154.3269016
|}

The energies of the reactants, Transition States, and different products were obtained from the optimised LOG. files in GaussView, and the reaction profile is plotted showing their relative energies with the proceeding of the three reactions.

All TS and product energies are normalised with respect to reactant energy (reactant energy=0). The reaction profile is shown below.

=== Reaction Profiles ===

[[File:Yz20215 E3 reaction profile.png|x700px|700px|thumb|centre|Figure Reaction profile of three different reaction paths]]

In this profile, we could see that the '''endo TS''' is the lowest in energy, therefore will be formed faster compared with other two, and will be the '''kinetic product''' of the reaction. The Exo TS has slightly higher but close energy, while the cheletropic TS has the largest activation barrier.

However, if we compare the energies of the products, we could see that the Endo and the Exo products are very close in energy at approximately -98 kJ mol <sup>-1</sup> , while the cheletropic product is the most stable product with energy of around -154 kJ mol <sup>-1</sup> . Therefore, if we provide enough energy for the reaction to overcome its activation barrier, the '''cheletropic product''' will be the major product as it is the '''thermodynamic product''' of the reaction.

=== Extension ===

[[File:YZ20215 E3 extension.png|x400px|400px|thumb|centre|Scheme 4 The reaction of sulfur dioxide with another diene in xylylene]]

In this reaction, the other diene of xylylene, also in cis conformation, could also reaction with sulfur dioxide to form both the endo and the exo products, and the activation energies and reaction energies of these two reactions are investigated as shown below.

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.102071
| style="text-align: center;" |267.987431
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.105054
| style="text-align: center;" |275.819298
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.065615
| style="text-align: center;" |172.272196
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.067307
| style="text-align: center;" |176.714542
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |113.6657804
| style="text-align: center;" |17.9505454
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |121.4976474
| style="text-align: center;" |22.3928914
|}

These two reaction, are endothermic reactions, with product being higher in energy than that of the reactants. The activation barrier is also around 30 kJ mol <sup>-1</sup> higher than that of the DA reaction occurring at the other diene, therefore, these two reactions are both '''thermodynamically and kinetically unfavourable'''.

=== Files ===

Optimised LOG File for Endo TS: [[File:Yz20215 E3 DA endo TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 E3 DA TS exo TS PM6.log]]

Optimised LOG File for Cheletropic TS: [[File:YZ20215 E3 CHE TS.LOG]]

'''Extension'''

Optimised LOG File for Endo TS: [[File:Yz20215 ext ENDO TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 ext exo TS.log]]

= Conclusion =

During the time span of this Transition State Computational Lab, three different pericyclic reactions were investigated.

The reactions were investigated by using PM6 and B3LYP/6-31G(d) methods in GaussView to optimise the reactants, transition states, and the products.

Other information were also extracted from the optimised molecule LOG. files: including vibration frequency calculations and IRC (Intrinsic Reaction Coordinate); bond lengths of the TS, reactants and products; the energies of different species; and the molecular orbitals.

These data were used to analyse the Transition states and the reactions, including confirmation of the TS by presence of one imaginary frequency in vibration frequencies, the activation barrier and energy change of the reaction from the energies of different species, and the MOs to determine the electron demand of a certain Diels-Alder reaction (inverse or normal electron demand).

In addition, the data confirmed that the reactions followed several existing rules and theories: Woodward-Hoffmann rules in Exercise 1, Frontier Molecular Orbital Theory, etc..

These computational methods could be applied to investigate many other pericyclic reactions, where various aspects of data could be obtained and analysed as like shown in this lab.

Rep:YZ20215TS

2018-02-27T22:59:30Z

Yz20215: /* MO analysis */

== Introduction ==

===Transition State ===
To investigate a reaction, it is crucial to firstly locate the Transition State of the reaction. The transition state of a reaction, on a 2D reaction coordinate, will be the highest point of energy connecting reactants and the products. In addition, it should also have the characteristics as shown below:

<math>\frac{\partial V}{\partial q_i}</math>= 0

<math>\frac{\partial^2 V}{\partial q_i^2}</math> < 0

Where as being a stationary point, its first derivative is equal to 0, while its second derivative should be negative as being the highest point on the reaction profile.

On a 3D PES (Potential Energy Surface), it is more difficult to determine the transition state, as it will be one saddle point among many other existing saddle points, however, being the maximum point on the minimum energy path, its first derivative and second derivative will both be equal to zero.

<math>\frac{\partial V}{\partial q_i}</math>= 0

<math>\frac{\partial^2 V}{\partial q_i^2}</math> = 0

=== Computational Methods ===

In this report, three different pericylic reactions were investigated using computational methods, including the PM6 and the B3LYP/6-31G(d) Methods.

PM6, with its full name being Parameterization Method 6, is a semi-empirical method. This method is based on the Hartree-Fock Model, and the model works by minimising the total molecular potential energy by varying the expansion coefficients, c<sub>μi</sub>, which is the coefficient in the equation of LCAO (Linear Combination of Atomic Orbitals).

This method is not perfect as it is based on the wrong assumption of accounting electrons as being largely independent of each other.<ref>Ot, W. J. (1990). Computational quantum chemistry. Journal of Molecular Structure: THEOCHEM (Vol. 207). </ref>

In reality, this is not true and the electrons will repulse each other due to their negative charge. Therefore, this method needs to be parameterised, which means the results fitted by a set of parameters, to product results that agree the most with experimental data.

While the other method, B3LYP, representing Becke, three-parameter, Lee-Yang-Parr, is based on Density Fucntional Theory (DFT), which is an incorporation of partly exact exchange from Hartree–Fock theory as well as exchange-correlation energy from other sources. It has an exchange-correlation functional as shown below:

<math>E_{\rm xc}^{\rm B3LYP} = E_{\rm x}^{\rm LDA} + a_0 (E_{\rm x}^{\rm HF} - E_{\rm x}^{\rm LDA}) + a_{\rm x} (E_{\rm x}^{\rm GGA} - E_{\rm x}^{\rm LDA}) + E_{\rm c}^{\rm LDA} + a_{\rm c} (E_{\rm c}^{\rm GGA} - E_{\rm c}^{\rm LDA}),</math>

where <math>a_0=0.20 \,\;</math>, <math>a_{\rm x}=0.72\,\;</math>, and <math>a_{\rm c}=0.81\,\;</math>. <ref>{{ cite journal |author1=K. Kim |author2=K. D. Jordan | title = Comparison of Density Functional and MP2 Calculations on the Water Monomer and Dimer | journal = J. Phys. Chem. | volume = 98 | issue = 40 | pages = 10089–10094 | year = 1994 | doi = 10.1021/j100091a024 }}</ref><ref>{{ cite journal |author1=P.J. Stephens |author2=F. J. Devlin |author3=C. F. Chabalowski |author4=M. J. Frisch | title = ''Ab Initio'' Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields | journal = J. Phys. Chem. | volume = 98 | pages = 11623–11627 | year = 1994 | doi = 10.1021/j100096a001 | issue = 45 }}</ref>

6-31G is a basis set of basis function among many others including 3-21G, etc.

=== Optimisation Methods ===

In this lab, three methods were used to optimise the TSs, with difficulty increasing from Method 1 to Method 3. Method 1 is the easiest and fastest one, but it is based on existing knowledge of the Transition State. Method 2, compared with Method 1, is more reliable as well as relatively fast, but it also has the limitation of requirement on knowledge of TS. Method 3 takes the most time to run, however, it does not have the limitation of the first two methods.

In this report, three pericylic reactions were investigated with all the Transition States being run with Method 3 and will be shown below.

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 1(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 1(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 1(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 2. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E1 BUTANDIENE MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YZ20215 E1 ETHYLENE MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YZ20215 E1 TS PM6 MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YZ20215 E1 TS PM6 MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YZ20215 E1 CYCLOHEXENE MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" |HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E1 BUTANDIENE MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YZ20215 E1 ETHYLENE MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YZ20215 E1 TS PM6 MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YZ20215 E1 TS PM6 MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YZ20215 E1 CYCLOHEXENE MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 4. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 cyclohexadiene min.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 dioxole min B3LYP.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 product ENDO B3LYP MIN.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents> Yz20215 E2 product EXO B3LYP MIN.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 TS endo TS.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 TS exo TS.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" |HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 5(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 5(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Therefore, in normal electron demand DA reactions, the orbitals of the electron-rich diene will be higher, therefore, favourable interaction occurs between the HOMO of diene and the LUMO of dienophile; while for inverse electron demand reactions, the LUMO of diene will interact with the HOMO of the dienophile.

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

In this reaction, due to the presence of a heterocyclic reactant, 1,3-dioxole, it is postulated that the reaction could possibly have an inverse electron demand, therefore, energy calculations were done and their single point energies determined in the following section to confirm the postulation.

==== Single point energies ====

{| class="wikitable"
|+ Table 11. Single point energies of reactants
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy of HOMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy of LUMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy difference between this HOMO and the LUMO of the other reactant/ a.u.'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |-0.20554
| style="text-align: center;" |-0.01711
| style="text-align: center;" |0.24349
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-0.19594
| style="text-align: center;" |0.03795
| style="text-align: center;" |0.17883
|}

In this reaction, the energy difference between the HOMO of the dienophile with the LUMO of diene is smaller than that of the other pair, therefore, they will give to a larger overlap of orbitals and more favourable interaciton.

Therefore, we can conclude from the data above that the reaction has an inverse electron demand. This is due to the presence of two oxygen atoms donating their lone pairs, making the dienophile electron rich.

=== Energy analysis ===

{| class="wikitable"
|+ Table 12. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 13. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 14. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
!<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>yz20215 E2 TS exo TS MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
</jmolApplet>
</jmol>
| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure Secondary orbital interactions in both Endo and Exo TS]]
|}

=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

[[File:Yz20215 E3 scheme.png|x400px|400px|thumb|centre|Scheme 3 Diels-Alder and Cheletropic reaction between Xylylene and Sulfur dioxide]]

The reaction between xylylene and sulfur dioxide was investigated.

The reaction between the reactants could occur either via a Diels-Alder reaction or cheletropic reaction as shown above in Scheme 3. For the Diels-Alder reaction between two, the product could be formed in an Endo or an Exo conformation.

In this exercise, the reactants, Transition States and products were optimised using PM6 Method using GaussView software. Also, the energies of different species were obtained to determine the activation energy and the energy change of reaction with reaction energy profile plotted. Therefore, the most thermodynamically and the most kinetically favoured product was determined.

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 14. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E3 DA endo TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E3 DA TS exo TS PM6.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>YZ20215 E3 CHE TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== IRC calculations ===

{| class="wikitable"
|+ Table 15. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

Looking at IRC of these three reactions, we could see that the activation barrier of the reaction is quite small, this is due to one of the reactants, xylylene, being very unstable and high in energy.

This is because, according to Huckle's Rule, it has only 8 π electrons, which is (4n) instead of (4n+2), therefore, it is antiaromatic. However, due to structure constraint, both of the dienes are cis in xylylene, which is favourable as no energy expense on converting into trans conformation.

During the reaction, the xylyene part will react with the sulfur dioxide molecule to form a bicyclic ring, containing a benzene ring, which is aromatic and stable. Therefore, making it favourable to form the products.

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.021698
| style="text-align: center;" |56.9681033
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.021454
| style="text-align: center;" |56.3274813
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |-0.000002
| style="text-align: center;" |-0.0052510004
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |83.4410224
| style="text-align: center;" |-97.3535473
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |87.4239054
| style="text-align: center;" |-97.9941693
|-
| style="text-align: center;" |Cheletropic
| style="text-align: center;" |105.7656504
| style="text-align: center;" |-154.3269016
|}

The energies of the reactants, Transition States, and different products were obtained from the optimised LOG. files in GaussView, and the reaction profile is plotted showing their relative energies with the proceeding of the three reactions.

All TS and product energies are normalised with respect to reactant energy (reactant energy=0). The reaction profile is shown below.

=== Reaction Profiles ===

[[File:Yz20215 E3 reaction profile.png|x700px|700px|thumb|centre|Figure Reaction profile of three different reaction paths]]

In this profile, we could see that the '''endo TS''' is the lowest in energy, therefore will be formed faster compared with other two, and will be the '''kinetic product''' of the reaction. The Exo TS has slightly higher but close energy, while the cheletropic TS has the largest activation barrier.

However, if we compare the energies of the products, we could see that the Endo and the Exo products are very close in energy at approximately -98 kJ mol <sup>-1</sup> , while the cheletropic product is the most stable product with energy of around -154 kJ mol <sup>-1</sup> . Therefore, if we provide enough energy for the reaction to overcome its activation barrier, the '''cheletropic product''' will be the major product as it is the '''thermodynamic product''' of the reaction.

=== Extension ===

[[File:YZ20215 E3 extension.png|x400px|400px|thumb|centre|Scheme 4 The reaction of sulfur dioxide with another diene in xylylene]]

In this reaction, the other diene of xylylene, also in cis conformation, could also reaction with sulfur dioxide to form both the endo and the exo products, and the activation energies and reaction energies of these two reactions are investigated as shown below.

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.102071
| style="text-align: center;" |267.987431
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.105054
| style="text-align: center;" |275.819298
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.065615
| style="text-align: center;" |172.272196
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.067307
| style="text-align: center;" |176.714542
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |113.6657804
| style="text-align: center;" |17.9505454
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |121.4976474
| style="text-align: center;" |22.3928914
|}

These two reaction, are endothermic reactions, with product being higher in energy than that of the reactants. The activation barrier is also around 30 kJ mol <sup>-1</sup> higher than that of the DA reaction occurring at the other diene, therefore, these two reactions are both '''thermodynamically and kinetically unfavourable'''.

=== Files ===

Optimised LOG File for Endo TS: [[File:Yz20215 E3 DA endo TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 E3 DA TS exo TS PM6.log]]

Optimised LOG File for Cheletropic TS: [[File:YZ20215 E3 CHE TS.LOG]]

'''Extension'''

Optimised LOG File for Endo TS: [[File:Yz20215 ext ENDO TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 ext exo TS.log]]

= Conclusion =

During the time span of this Transition State Computational Lab, three different pericyclic reactions were investigated.

The reactions were investigated by using PM6 and B3LYP/6-31G(d) methods in GaussView to optimise the reactants, transition states, and the products.

Other information were also extracted from the optimised molecule LOG. files: including vibration frequency calculations and IRC (Intrinsic Reaction Coordinate); bond lengths of the TS, reactants and products; the energies of different species; and the molecular orbitals.

These data were used to analyse the Transition states and the reactions, including confirmation of the TS by presence of one imaginary frequency in vibration frequencies, the activation barrier and energy change of the reaction from the energies of different species, and the MOs to determine the electron demand of a certain Diels-Alder reaction (inverse or normal electron demand).

In addition, the data confirmed that the reactions followed several existing rules and theories: Woodward-Hoffmann rules in Exercise 1, Frontier Molecular Orbital Theory, etc..

These computational methods could be applied to investigate many other pericyclic reactions, where various aspects of data could be obtained and analysed as like shown in this lab.

Rep:YZ20215TS

2018-02-27T22:59:08Z

Yz20215: /* Confirmation of correst TS using frequency calculation and IRC */

== Introduction ==

===Transition State ===
To investigate a reaction, it is crucial to firstly locate the Transition State of the reaction. The transition state of a reaction, on a 2D reaction coordinate, will be the highest point of energy connecting reactants and the products. In addition, it should also have the characteristics as shown below:

<math>\frac{\partial V}{\partial q_i}</math>= 0

<math>\frac{\partial^2 V}{\partial q_i^2}</math> < 0

Where as being a stationary point, its first derivative is equal to 0, while its second derivative should be negative as being the highest point on the reaction profile.

On a 3D PES (Potential Energy Surface), it is more difficult to determine the transition state, as it will be one saddle point among many other existing saddle points, however, being the maximum point on the minimum energy path, its first derivative and second derivative will both be equal to zero.

<math>\frac{\partial V}{\partial q_i}</math>= 0

<math>\frac{\partial^2 V}{\partial q_i^2}</math> = 0

=== Computational Methods ===

In this report, three different pericylic reactions were investigated using computational methods, including the PM6 and the B3LYP/6-31G(d) Methods.

PM6, with its full name being Parameterization Method 6, is a semi-empirical method. This method is based on the Hartree-Fock Model, and the model works by minimising the total molecular potential energy by varying the expansion coefficients, c<sub>μi</sub>, which is the coefficient in the equation of LCAO (Linear Combination of Atomic Orbitals).

This method is not perfect as it is based on the wrong assumption of accounting electrons as being largely independent of each other.<ref>Ot, W. J. (1990). Computational quantum chemistry. Journal of Molecular Structure: THEOCHEM (Vol. 207). </ref>

In reality, this is not true and the electrons will repulse each other due to their negative charge. Therefore, this method needs to be parameterised, which means the results fitted by a set of parameters, to product results that agree the most with experimental data.

While the other method, B3LYP, representing Becke, three-parameter, Lee-Yang-Parr, is based on Density Fucntional Theory (DFT), which is an incorporation of partly exact exchange from Hartree–Fock theory as well as exchange-correlation energy from other sources. It has an exchange-correlation functional as shown below:

<math>E_{\rm xc}^{\rm B3LYP} = E_{\rm x}^{\rm LDA} + a_0 (E_{\rm x}^{\rm HF} - E_{\rm x}^{\rm LDA}) + a_{\rm x} (E_{\rm x}^{\rm GGA} - E_{\rm x}^{\rm LDA}) + E_{\rm c}^{\rm LDA} + a_{\rm c} (E_{\rm c}^{\rm GGA} - E_{\rm c}^{\rm LDA}),</math>

where <math>a_0=0.20 \,\;</math>, <math>a_{\rm x}=0.72\,\;</math>, and <math>a_{\rm c}=0.81\,\;</math>. <ref>{{ cite journal |author1=K. Kim |author2=K. D. Jordan | title = Comparison of Density Functional and MP2 Calculations on the Water Monomer and Dimer | journal = J. Phys. Chem. | volume = 98 | issue = 40 | pages = 10089–10094 | year = 1994 | doi = 10.1021/j100091a024 }}</ref><ref>{{ cite journal |author1=P.J. Stephens |author2=F. J. Devlin |author3=C. F. Chabalowski |author4=M. J. Frisch | title = ''Ab Initio'' Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields | journal = J. Phys. Chem. | volume = 98 | pages = 11623–11627 | year = 1994 | doi = 10.1021/j100096a001 | issue = 45 }}</ref>

6-31G is a basis set of basis function among many others including 3-21G, etc.

=== Optimisation Methods ===

In this lab, three methods were used to optimise the TSs, with difficulty increasing from Method 1 to Method 3. Method 1 is the easiest and fastest one, but it is based on existing knowledge of the Transition State. Method 2, compared with Method 1, is more reliable as well as relatively fast, but it also has the limitation of requirement on knowledge of TS. Method 3 takes the most time to run, however, it does not have the limitation of the first two methods.

In this report, three pericylic reactions were investigated with all the Transition States being run with Method 3 and will be shown below.

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 1(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 1(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 1(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 3. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 4. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
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| style="text-align: center;" |Vibration Frequencies
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| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 5(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 5(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Therefore, in normal electron demand DA reactions, the orbitals of the electron-rich diene will be higher, therefore, favourable interaction occurs between the HOMO of diene and the LUMO of dienophile; while for inverse electron demand reactions, the LUMO of diene will interact with the HOMO of the dienophile.

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

In this reaction, due to the presence of a heterocyclic reactant, 1,3-dioxole, it is postulated that the reaction could possibly have an inverse electron demand, therefore, energy calculations were done and their single point energies determined in the following section to confirm the postulation.

==== Single point energies ====

{| class="wikitable"
|+ Table 11. Single point energies of reactants
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy of HOMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy of LUMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy difference between this HOMO and the LUMO of the other reactant/ a.u.'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |-0.20554
| style="text-align: center;" |-0.01711
| style="text-align: center;" |0.24349
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-0.19594
| style="text-align: center;" |0.03795
| style="text-align: center;" |0.17883
|}

In this reaction, the energy difference between the HOMO of the dienophile with the LUMO of diene is smaller than that of the other pair, therefore, they will give to a larger overlap of orbitals and more favourable interaciton.

Therefore, we can conclude from the data above that the reaction has an inverse electron demand. This is due to the presence of two oxygen atoms donating their lone pairs, making the dienophile electron rich.

=== Energy analysis ===

{| class="wikitable"
|+ Table 12. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 13. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 14. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
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| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure Secondary orbital interactions in both Endo and Exo TS]]
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=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

[[File:Yz20215 E3 scheme.png|x400px|400px|thumb|centre|Scheme 3 Diels-Alder and Cheletropic reaction between Xylylene and Sulfur dioxide]]

The reaction between xylylene and sulfur dioxide was investigated.

The reaction between the reactants could occur either via a Diels-Alder reaction or cheletropic reaction as shown above in Scheme 3. For the Diels-Alder reaction between two, the product could be formed in an Endo or an Exo conformation.

In this exercise, the reactants, Transition States and products were optimised using PM6 Method using GaussView software. Also, the energies of different species were obtained to determine the activation energy and the energy change of reaction with reaction energy profile plotted. Therefore, the most thermodynamically and the most kinetically favoured product was determined.

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 14. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
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=== IRC calculations ===

{| class="wikitable"
|+ Table 15. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

Looking at IRC of these three reactions, we could see that the activation barrier of the reaction is quite small, this is due to one of the reactants, xylylene, being very unstable and high in energy.

This is because, according to Huckle's Rule, it has only 8 π electrons, which is (4n) instead of (4n+2), therefore, it is antiaromatic. However, due to structure constraint, both of the dienes are cis in xylylene, which is favourable as no energy expense on converting into trans conformation.

During the reaction, the xylyene part will react with the sulfur dioxide molecule to form a bicyclic ring, containing a benzene ring, which is aromatic and stable. Therefore, making it favourable to form the products.

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.021698
| style="text-align: center;" |56.9681033
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.021454
| style="text-align: center;" |56.3274813
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |-0.000002
| style="text-align: center;" |-0.0052510004
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |83.4410224
| style="text-align: center;" |-97.3535473
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |87.4239054
| style="text-align: center;" |-97.9941693
|-
| style="text-align: center;" |Cheletropic
| style="text-align: center;" |105.7656504
| style="text-align: center;" |-154.3269016
|}

The energies of the reactants, Transition States, and different products were obtained from the optimised LOG. files in GaussView, and the reaction profile is plotted showing their relative energies with the proceeding of the three reactions.

All TS and product energies are normalised with respect to reactant energy (reactant energy=0). The reaction profile is shown below.

=== Reaction Profiles ===

[[File:Yz20215 E3 reaction profile.png|x700px|700px|thumb|centre|Figure Reaction profile of three different reaction paths]]

In this profile, we could see that the '''endo TS''' is the lowest in energy, therefore will be formed faster compared with other two, and will be the '''kinetic product''' of the reaction. The Exo TS has slightly higher but close energy, while the cheletropic TS has the largest activation barrier.

However, if we compare the energies of the products, we could see that the Endo and the Exo products are very close in energy at approximately -98 kJ mol <sup>-1</sup> , while the cheletropic product is the most stable product with energy of around -154 kJ mol <sup>-1</sup> . Therefore, if we provide enough energy for the reaction to overcome its activation barrier, the '''cheletropic product''' will be the major product as it is the '''thermodynamic product''' of the reaction.

=== Extension ===

[[File:YZ20215 E3 extension.png|x400px|400px|thumb|centre|Scheme 4 The reaction of sulfur dioxide with another diene in xylylene]]

In this reaction, the other diene of xylylene, also in cis conformation, could also reaction with sulfur dioxide to form both the endo and the exo products, and the activation energies and reaction energies of these two reactions are investigated as shown below.

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.102071
| style="text-align: center;" |267.987431
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.105054
| style="text-align: center;" |275.819298
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.065615
| style="text-align: center;" |172.272196
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.067307
| style="text-align: center;" |176.714542
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |113.6657804
| style="text-align: center;" |17.9505454
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |121.4976474
| style="text-align: center;" |22.3928914
|}

These two reaction, are endothermic reactions, with product being higher in energy than that of the reactants. The activation barrier is also around 30 kJ mol <sup>-1</sup> higher than that of the DA reaction occurring at the other diene, therefore, these two reactions are both '''thermodynamically and kinetically unfavourable'''.

=== Files ===

Optimised LOG File for Endo TS: [[File:Yz20215 E3 DA endo TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 E3 DA TS exo TS PM6.log]]

Optimised LOG File for Cheletropic TS: [[File:YZ20215 E3 CHE TS.LOG]]

'''Extension'''

Optimised LOG File for Endo TS: [[File:Yz20215 ext ENDO TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 ext exo TS.log]]

= Conclusion =

During the time span of this Transition State Computational Lab, three different pericyclic reactions were investigated.

The reactions were investigated by using PM6 and B3LYP/6-31G(d) methods in GaussView to optimise the reactants, transition states, and the products.

Other information were also extracted from the optimised molecule LOG. files: including vibration frequency calculations and IRC (Intrinsic Reaction Coordinate); bond lengths of the TS, reactants and products; the energies of different species; and the molecular orbitals.

These data were used to analyse the Transition states and the reactions, including confirmation of the TS by presence of one imaginary frequency in vibration frequencies, the activation barrier and energy change of the reaction from the energies of different species, and the MOs to determine the electron demand of a certain Diels-Alder reaction (inverse or normal electron demand).

In addition, the data confirmed that the reactions followed several existing rules and theories: Woodward-Hoffmann rules in Exercise 1, Frontier Molecular Orbital Theory, etc..

These computational methods could be applied to investigate many other pericyclic reactions, where various aspects of data could be obtained and analysed as like shown in this lab.

Rep:YZ20215TS

2018-02-27T22:58:24Z

Yz20215: /* Introduction */

== Introduction ==

===Transition State ===
To investigate a reaction, it is crucial to firstly locate the Transition State of the reaction. The transition state of a reaction, on a 2D reaction coordinate, will be the highest point of energy connecting reactants and the products. In addition, it should also have the characteristics as shown below:

<math>\frac{\partial V}{\partial q_i}</math>= 0

<math>\frac{\partial^2 V}{\partial q_i^2}</math> < 0

Where as being a stationary point, its first derivative is equal to 0, while its second derivative should be negative as being the highest point on the reaction profile.

On a 3D PES (Potential Energy Surface), it is more difficult to determine the transition state, as it will be one saddle point among many other existing saddle points, however, being the maximum point on the minimum energy path, its first derivative and second derivative will both be equal to zero.

<math>\frac{\partial V}{\partial q_i}</math>= 0

<math>\frac{\partial^2 V}{\partial q_i^2}</math> = 0

=== Computational Methods ===

In this report, three different pericylic reactions were investigated using computational methods, including the PM6 and the B3LYP/6-31G(d) Methods.

PM6, with its full name being Parameterization Method 6, is a semi-empirical method. This method is based on the Hartree-Fock Model, and the model works by minimising the total molecular potential energy by varying the expansion coefficients, c<sub>μi</sub>, which is the coefficient in the equation of LCAO (Linear Combination of Atomic Orbitals).

This method is not perfect as it is based on the wrong assumption of accounting electrons as being largely independent of each other.<ref>Ot, W. J. (1990). Computational quantum chemistry. Journal of Molecular Structure: THEOCHEM (Vol. 207). </ref>

In reality, this is not true and the electrons will repulse each other due to their negative charge. Therefore, this method needs to be parameterised, which means the results fitted by a set of parameters, to product results that agree the most with experimental data.

While the other method, B3LYP, representing Becke, three-parameter, Lee-Yang-Parr, is based on Density Fucntional Theory (DFT), which is an incorporation of partly exact exchange from Hartree–Fock theory as well as exchange-correlation energy from other sources. It has an exchange-correlation functional as shown below:

<math>E_{\rm xc}^{\rm B3LYP} = E_{\rm x}^{\rm LDA} + a_0 (E_{\rm x}^{\rm HF} - E_{\rm x}^{\rm LDA}) + a_{\rm x} (E_{\rm x}^{\rm GGA} - E_{\rm x}^{\rm LDA}) + E_{\rm c}^{\rm LDA} + a_{\rm c} (E_{\rm c}^{\rm GGA} - E_{\rm c}^{\rm LDA}),</math>

where <math>a_0=0.20 \,\;</math>, <math>a_{\rm x}=0.72\,\;</math>, and <math>a_{\rm c}=0.81\,\;</math>. <ref>{{ cite journal |author1=K. Kim |author2=K. D. Jordan | title = Comparison of Density Functional and MP2 Calculations on the Water Monomer and Dimer | journal = J. Phys. Chem. | volume = 98 | issue = 40 | pages = 10089–10094 | year = 1994 | doi = 10.1021/j100091a024 }}</ref><ref>{{ cite journal |author1=P.J. Stephens |author2=F. J. Devlin |author3=C. F. Chabalowski |author4=M. J. Frisch | title = ''Ab Initio'' Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields | journal = J. Phys. Chem. | volume = 98 | pages = 11623–11627 | year = 1994 | doi = 10.1021/j100096a001 | issue = 45 }}</ref>

6-31G is a basis set of basis function among many others including 3-21G, etc.

=== Optimisation Methods ===

In this lab, three methods were used to optimise the TSs, with difficulty increasing from Method 1 to Method 3. Method 1 is the easiest and fastest one, but it is based on existing knowledge of the Transition State. Method 2, compared with Method 1, is more reliable as well as relatively fast, but it also has the limitation of requirement on knowledge of TS. Method 3 takes the most time to run, however, it does not have the limitation of the first two methods.

In this report, three pericylic reactions were investigated with all the Transition States being run with Method 3 and will be shown below.

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 2(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 2(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 2(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 3. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
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|<jmol>
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|-
| style="text-align: center;" |HOMO
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==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 4. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 cyclohexadiene min.LOG</uploadedFileContents>
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|<jmol>
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<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 dioxole min B3LYP.log</uploadedFileContents>
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<script>frame 16; </script>
<uploadedFileContents> Yz20215 E2 product EXO B3LYP MIN.LOG</uploadedFileContents>
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 TS endo TS.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 TS exo TS.log</uploadedFileContents>
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
|<jmol>
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<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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|}

{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 5(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 5(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Therefore, in normal electron demand DA reactions, the orbitals of the electron-rich diene will be higher, therefore, favourable interaction occurs between the HOMO of diene and the LUMO of dienophile; while for inverse electron demand reactions, the LUMO of diene will interact with the HOMO of the dienophile.

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

In this reaction, due to the presence of a heterocyclic reactant, 1,3-dioxole, it is postulated that the reaction could possibly have an inverse electron demand, therefore, energy calculations were done and their single point energies determined in the following section to confirm the postulation.

==== Single point energies ====

{| class="wikitable"
|+ Table 11. Single point energies of reactants
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy of HOMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy of LUMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy difference between this HOMO and the LUMO of the other reactant/ a.u.'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |-0.20554
| style="text-align: center;" |-0.01711
| style="text-align: center;" |0.24349
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-0.19594
| style="text-align: center;" |0.03795
| style="text-align: center;" |0.17883
|}

In this reaction, the energy difference between the HOMO of the dienophile with the LUMO of diene is smaller than that of the other pair, therefore, they will give to a larger overlap of orbitals and more favourable interaciton.

Therefore, we can conclude from the data above that the reaction has an inverse electron demand. This is due to the presence of two oxygen atoms donating their lone pairs, making the dienophile electron rich.

=== Energy analysis ===

{| class="wikitable"
|+ Table 12. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 13. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 14. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
!<jmol>
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<uploadedFileContents>yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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</jmolApplet>
</jmol>
| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure Secondary orbital interactions in both Endo and Exo TS]]
|}

=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

[[File:Yz20215 E3 scheme.png|x400px|400px|thumb|centre|Scheme 3 Diels-Alder and Cheletropic reaction between Xylylene and Sulfur dioxide]]

The reaction between xylylene and sulfur dioxide was investigated.

The reaction between the reactants could occur either via a Diels-Alder reaction or cheletropic reaction as shown above in Scheme 3. For the Diels-Alder reaction between two, the product could be formed in an Endo or an Exo conformation.

In this exercise, the reactants, Transition States and products were optimised using PM6 Method using GaussView software. Also, the energies of different species were obtained to determine the activation energy and the energy change of reaction with reaction energy profile plotted. Therefore, the most thermodynamically and the most kinetically favoured product was determined.

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 14. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E3 DA endo TS.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 16; </script>
<uploadedFileContents>Yz20215 E3 DA TS exo TS PM6.log</uploadedFileContents>
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<script>frame 16; </script>
<uploadedFileContents>YZ20215 E3 CHE TS.LOG</uploadedFileContents>
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|}

=== IRC calculations ===

{| class="wikitable"
|+ Table 15. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

Looking at IRC of these three reactions, we could see that the activation barrier of the reaction is quite small, this is due to one of the reactants, xylylene, being very unstable and high in energy.

This is because, according to Huckle's Rule, it has only 8 π electrons, which is (4n) instead of (4n+2), therefore, it is antiaromatic. However, due to structure constraint, both of the dienes are cis in xylylene, which is favourable as no energy expense on converting into trans conformation.

During the reaction, the xylyene part will react with the sulfur dioxide molecule to form a bicyclic ring, containing a benzene ring, which is aromatic and stable. Therefore, making it favourable to form the products.

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.021698
| style="text-align: center;" |56.9681033
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.021454
| style="text-align: center;" |56.3274813
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |-0.000002
| style="text-align: center;" |-0.0052510004
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |83.4410224
| style="text-align: center;" |-97.3535473
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |87.4239054
| style="text-align: center;" |-97.9941693
|-
| style="text-align: center;" |Cheletropic
| style="text-align: center;" |105.7656504
| style="text-align: center;" |-154.3269016
|}

The energies of the reactants, Transition States, and different products were obtained from the optimised LOG. files in GaussView, and the reaction profile is plotted showing their relative energies with the proceeding of the three reactions.

All TS and product energies are normalised with respect to reactant energy (reactant energy=0). The reaction profile is shown below.

=== Reaction Profiles ===

[[File:Yz20215 E3 reaction profile.png|x700px|700px|thumb|centre|Figure Reaction profile of three different reaction paths]]

In this profile, we could see that the '''endo TS''' is the lowest in energy, therefore will be formed faster compared with other two, and will be the '''kinetic product''' of the reaction. The Exo TS has slightly higher but close energy, while the cheletropic TS has the largest activation barrier.

However, if we compare the energies of the products, we could see that the Endo and the Exo products are very close in energy at approximately -98 kJ mol <sup>-1</sup> , while the cheletropic product is the most stable product with energy of around -154 kJ mol <sup>-1</sup> . Therefore, if we provide enough energy for the reaction to overcome its activation barrier, the '''cheletropic product''' will be the major product as it is the '''thermodynamic product''' of the reaction.

=== Extension ===

[[File:YZ20215 E3 extension.png|x400px|400px|thumb|centre|Scheme 4 The reaction of sulfur dioxide with another diene in xylylene]]

In this reaction, the other diene of xylylene, also in cis conformation, could also reaction with sulfur dioxide to form both the endo and the exo products, and the activation energies and reaction energies of these two reactions are investigated as shown below.

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.102071
| style="text-align: center;" |267.987431
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.105054
| style="text-align: center;" |275.819298
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.065615
| style="text-align: center;" |172.272196
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.067307
| style="text-align: center;" |176.714542
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |113.6657804
| style="text-align: center;" |17.9505454
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |121.4976474
| style="text-align: center;" |22.3928914
|}

These two reaction, are endothermic reactions, with product being higher in energy than that of the reactants. The activation barrier is also around 30 kJ mol <sup>-1</sup> higher than that of the DA reaction occurring at the other diene, therefore, these two reactions are both '''thermodynamically and kinetically unfavourable'''.

=== Files ===

Optimised LOG File for Endo TS: [[File:Yz20215 E3 DA endo TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 E3 DA TS exo TS PM6.log]]

Optimised LOG File for Cheletropic TS: [[File:YZ20215 E3 CHE TS.LOG]]

'''Extension'''

Optimised LOG File for Endo TS: [[File:Yz20215 ext ENDO TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 ext exo TS.log]]

= Conclusion =

During the time span of this Transition State Computational Lab, three different pericyclic reactions were investigated.

The reactions were investigated by using PM6 and B3LYP/6-31G(d) methods in GaussView to optimise the reactants, transition states, and the products.

Other information were also extracted from the optimised molecule LOG. files: including vibration frequency calculations and IRC (Intrinsic Reaction Coordinate); bond lengths of the TS, reactants and products; the energies of different species; and the molecular orbitals.

These data were used to analyse the Transition states and the reactions, including confirmation of the TS by presence of one imaginary frequency in vibration frequencies, the activation barrier and energy change of the reaction from the energies of different species, and the MOs to determine the electron demand of a certain Diels-Alder reaction (inverse or normal electron demand).

In addition, the data confirmed that the reactions followed several existing rules and theories: Woodward-Hoffmann rules in Exercise 1, Frontier Molecular Orbital Theory, etc..

These computational methods could be applied to investigate many other pericyclic reactions, where various aspects of data could be obtained and analysed as like shown in this lab.

Rep:YZ20215TS

2018-02-27T22:14:21Z

Yz20215: /* Introduction */

== Introduction ==

To investigate a reaction, it is crucial to firstly locate the Transition State of the reaction. The transition state of a reaction, on a 2D reaction coordinate, will be the highest point of energy connecting reactants and the products. It is also a stationary point, with its first derivative <math>\frac{\partial V}{\partial q_i}</math>equal to 0, while second derivative,<math>\frac{\partial^2 V}{\partial q_i^2}</math>, being On a 3D PES (Potential Energy Surface), it is more difficult to determine

=== Computational Methods ===

In this report, three different pericylic reactions were investigated using computational methods, including the PM6 and the B3LYP Methods.

PM6, with its full name being Parameterization Method 6, is a semi-empirical method. This method is based on the Hartree-Fock Model, and the model works by minimising the total molecular potential energy by varying the expansion coefficients, c

=== Optimisation Methods ===

In this lab, three methods

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 2(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 2(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 2(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 3. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E1 BUTANDIENE MO.LOG</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YZ20215 E1 ETHYLENE MO.LOG</uploadedFileContents>
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|<jmol>
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<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YZ20215 E1 TS PM6 MO.LOG</uploadedFileContents>
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|<jmol>
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<uploadedFileContents>YZ20215 E1 TS PM6 MO.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>YZ20215 E1 CYCLOHEXENE MO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" |HOMO
|<jmol>
<jmolApplet>
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<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E1 BUTANDIENE MO.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
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<uploadedFileContents>YZ20215 E1 ETHYLENE MO.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
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<uploadedFileContents>YZ20215 E1 CYCLOHEXENE MO.LOG</uploadedFileContents>
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==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 4. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 cyclohexadiene min.LOG</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 dioxole min B3LYP.log</uploadedFileContents>
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|<jmol>
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<script>frame 16; </script>
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|<jmol>
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<script>frame 16; </script>
<uploadedFileContents> Yz20215 E2 product EXO B3LYP MIN.LOG</uploadedFileContents>
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 TS endo TS.log</uploadedFileContents>
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|<jmol>
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<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 TS exo TS.log</uploadedFileContents>
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
|<jmol>
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|<jmol>
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<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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</jmol>
|-
| style="text-align: center;" |HOMO
|<jmol>
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<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
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<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
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|<jmol>
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<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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|<jmol>
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<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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|}

{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 5(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 5(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Therefore, in normal electron demand DA reactions, the orbitals of the electron-rich diene will be higher, therefore, favourable interaction occurs between the HOMO of diene and the LUMO of dienophile; while for inverse electron demand reactions, the LUMO of diene will interact with the HOMO of the dienophile.

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

In this reaction, due to the presence of a heterocyclic reactant, 1,3-dioxole, it is postulated that the reaction could possibly have an inverse electron demand, therefore, energy calculations were done and their single point energies determined in the following section to confirm the postulation.

==== Single point energies ====

{| class="wikitable"
|+ Table 11. Single point energies of reactants
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy of HOMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy of LUMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy difference between this HOMO and the LUMO of the other reactant/ a.u.'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |-0.20554
| style="text-align: center;" |-0.01711
| style="text-align: center;" |0.24349
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-0.19594
| style="text-align: center;" |0.03795
| style="text-align: center;" |0.17883
|}

In this reaction, the energy difference between the HOMO of the dienophile with the LUMO of diene is smaller than that of the other pair, therefore, they will give to a larger overlap of orbitals and more favourable interaciton.

Therefore, we can conclude from the data above that the reaction has an inverse electron demand. This is due to the presence of two oxygen atoms donating their lone pairs, making the dienophile electron rich.

=== Energy analysis ===

{| class="wikitable"
|+ Table 12. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 13. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 14. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
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<uploadedFileContents>yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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!<jmol>
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</jmolApplet>
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| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure Secondary orbital interactions in both Endo and Exo TS]]
|}

=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

[[File:Yz20215 E3 scheme.png|x400px|400px|thumb|centre|Scheme 3 Diels-Alder and Cheletropic reaction between Xylylene and Sulfur dioxide]]

The reaction between xylylene and sulfur dioxide was investigated.

The reaction between the reactants could occur either via a Diels-Alder reaction or cheletropic reaction as shown above in Scheme 3. For the Diels-Alder reaction between two, the product could be formed in an Endo or an Exo conformation.

In this exercise, the reactants, Transition States and products were optimised using PM6 Method using GaussView software. Also, the energies of different species were obtained to determine the activation energy and the energy change of reaction with reaction energy profile plotted. Therefore, the most thermodynamically and the most kinetically favoured product was determined.

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 14. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E3 DA endo TS.LOG</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
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<script>frame 16; </script>
<uploadedFileContents>Yz20215 E3 DA TS exo TS PM6.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
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<script>frame 16; </script>
<uploadedFileContents>YZ20215 E3 CHE TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== IRC calculations ===

{| class="wikitable"
|+ Table 15. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

Looking at IRC of these three reactions, we could see that the activation barrier of the reaction is quite small, this is due to one of the reactants, xylylene, being very unstable and high in energy.

This is because, according to Huckle's Rule, it has only 8 π electrons, which is (4n) instead of (4n+2), therefore, it is antiaromatic. However, due to structure constraint, both of the dienes are cis in xylylene, which is favourable as no energy expense on converting into trans conformation.

During the reaction, the xylyene part will react with the sulfur dioxide molecule to form a bicyclic ring, containing a benzene ring, which is aromatic and stable. Therefore, making it favourable to form the products.

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.021698
| style="text-align: center;" |56.9681033
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.021454
| style="text-align: center;" |56.3274813
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |-0.000002
| style="text-align: center;" |-0.0052510004
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |83.4410224
| style="text-align: center;" |-97.3535473
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |87.4239054
| style="text-align: center;" |-97.9941693
|-
| style="text-align: center;" |Cheletropic
| style="text-align: center;" |105.7656504
| style="text-align: center;" |-154.3269016
|}

The energies of the reactants, Transition States, and different products were obtained from the optimised LOG. files in GaussView, and the reaction profile is plotted showing their relative energies with the proceeding of the three reactions.

All TS and product energies are normalised with respect to reactant energy (reactant energy=0). The reaction profile is shown below.

=== Reaction Profiles ===

[[File:Yz20215 E3 reaction profile.png|x700px|700px|thumb|centre|Figure Reaction profile of three different reaction paths]]

In this profile, we could see that the '''endo TS''' is the lowest in energy, therefore will be formed faster compared with other two, and will be the '''kinetic product''' of the reaction. The Exo TS has slightly higher but close energy, while the cheletropic TS has the largest activation barrier.

However, if we compare the energies of the products, we could see that the Endo and the Exo products are very close in energy at approximately -98 kJ mol <sup>-1</sup> , while the cheletropic product is the most stable product with energy of around -154 kJ mol <sup>-1</sup> . Therefore, if we provide enough energy for the reaction to overcome its activation barrier, the '''cheletropic product''' will be the major product as it is the '''thermodynamic product''' of the reaction.

=== Extension ===

[[File:YZ20215 E3 extension.png|x400px|400px|thumb|centre|Scheme 4 The reaction of sulfur dioxide with another diene in xylylene]]

In this reaction, the other diene of xylylene, also in cis conformation, could also reaction with sulfur dioxide to form both the endo and the exo products, and the activation energies and reaction energies of these two reactions are investigated as shown below.

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.102071
| style="text-align: center;" |267.987431
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.105054
| style="text-align: center;" |275.819298
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.065615
| style="text-align: center;" |172.272196
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.067307
| style="text-align: center;" |176.714542
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |113.6657804
| style="text-align: center;" |17.9505454
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |121.4976474
| style="text-align: center;" |22.3928914
|}

These two reaction, are endothermic reactions, with product being higher in energy than that of the reactants. The activation barrier is also around 30 kJ mol <sup>-1</sup> higher than that of the DA reaction occurring at the other diene, therefore, these two reactions are both '''thermodynamically and kinetically unfavourable'''.

=== Files ===

Optimised LOG File for Endo TS: [[File:Yz20215 E3 DA endo TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 E3 DA TS exo TS PM6.log]]

Optimised LOG File for Cheletropic TS: [[File:YZ20215 E3 CHE TS.LOG]]

'''Extension'''

Optimised LOG File for Endo TS: [[File:Yz20215 ext ENDO TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 ext exo TS.log]]

= Conclusion =

During the time span of this Transition State Computational Lab, three different pericyclic reactions were investigated.

The reactions were investigated by using PM6 and B3LYP/6-31G(d) methods in GaussView to optimise the reactants, transition states, and the products.

Other information were also extracted from the optimised molecule LOG. files: including vibration frequency calculations and IRC (Intrinsic Reaction Coordinate); bond lengths of the TS, reactants and products; the energies of different species; and the molecular orbitals.

These data were used to analyse the Transition states and the reactions, including confirmation of the TS by presence of one imaginary frequency in vibration frequencies, the activation barrier and energy change of the reaction from the energies of different species, and the MOs to determine the electron demand of a certain Diels-Alder reaction (inverse or normal electron demand).

In addition, the data confirmed that the reactions followed several existing rules and theories: Woodward-Hoffmann rules in Exercise 1, Frontier Molecular Orbital Theory, etc..

These computational methods could be applied to investigate many other pericyclic reactions, where various aspects of data could be obtained and analysed as like shown in this lab.

Rep:YZ20215TS

2018-02-27T19:38:14Z

Yz20215: /* Files */

== Introduction ==

To investigate a reaction, it is crucial to firstly locate the Transition State of the reaction, because

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 2(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 2(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 2(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 3. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 4. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 5(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 5(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Therefore, in normal electron demand DA reactions, the orbitals of the electron-rich diene will be higher, therefore, favourable interaction occurs between the HOMO of diene and the LUMO of dienophile; while for inverse electron demand reactions, the LUMO of diene will interact with the HOMO of the dienophile.

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

In this reaction, due to the presence of a heterocyclic reactant, 1,3-dioxole, it is postulated that the reaction could possibly have an inverse electron demand, therefore, energy calculations were done and their single point energies determined in the following section to confirm the postulation.

==== Single point energies ====

{| class="wikitable"
|+ Table 11. Single point energies of reactants
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy of HOMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy of LUMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy difference between this HOMO and the LUMO of the other reactant/ a.u.'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |-0.20554
| style="text-align: center;" |-0.01711
| style="text-align: center;" |0.24349
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-0.19594
| style="text-align: center;" |0.03795
| style="text-align: center;" |0.17883
|}

In this reaction, the energy difference between the HOMO of the dienophile with the LUMO of diene is smaller than that of the other pair, therefore, they will give to a larger overlap of orbitals and more favourable interaciton.

Therefore, we can conclude from the data above that the reaction has an inverse electron demand. This is due to the presence of two oxygen atoms donating their lone pairs, making the dienophile electron rich.

=== Energy analysis ===

{| class="wikitable"
|+ Table 12. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 13. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 14. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
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| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure Secondary orbital interactions in both Endo and Exo TS]]
|}

=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

[[File:Yz20215 E3 scheme.png|x400px|400px|thumb|centre|Scheme 3 Diels-Alder and Cheletropic reaction between Xylylene and Sulfur dioxide]]

The reaction between xylylene and sulfur dioxide was investigated.

The reaction between the reactants could occur either via a Diels-Alder reaction or cheletropic reaction as shown above in Scheme 3. For the Diels-Alder reaction between two, the product could be formed in an Endo or an Exo conformation.

In this exercise, the reactants, Transition States and products were optimised using PM6 Method using GaussView software. Also, the energies of different species were obtained to determine the activation energy and the energy change of reaction with reaction energy profile plotted. Therefore, the most thermodynamically and the most kinetically favoured product was determined.

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 14. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
|<jmol>
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<color>white</color>
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<script>frame 16; </script>
<uploadedFileContents>Yz20215 E3 DA endo TS.LOG</uploadedFileContents>
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|<jmol>
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=== IRC calculations ===

{| class="wikitable"
|+ Table 15. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

Looking at IRC of these three reactions, we could see that the activation barrier of the reaction is quite small, this is due to one of the reactants, xylylene, being very unstable and high in energy.

This is because, according to Huckle's Rule, it has only 8 π electrons, which is (4n) instead of (4n+2), therefore, it is antiaromatic. However, due to structure constraint, both of the dienes are cis in xylylene, which is favourable as no energy expense on converting into trans conformation.

During the reaction, the xylyene part will react with the sulfur dioxide molecule to form a bicyclic ring, containing a benzene ring, which is aromatic and stable. Therefore, making it favourable to form the products.

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.021698
| style="text-align: center;" |56.9681033
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.021454
| style="text-align: center;" |56.3274813
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |-0.000002
| style="text-align: center;" |-0.0052510004
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |83.4410224
| style="text-align: center;" |-97.3535473
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |87.4239054
| style="text-align: center;" |-97.9941693
|-
| style="text-align: center;" |Cheletropic
| style="text-align: center;" |105.7656504
| style="text-align: center;" |-154.3269016
|}

The energies of the reactants, Transition States, and different products were obtained from the optimised LOG. files in GaussView, and the reaction profile is plotted showing their relative energies with the proceeding of the three reactions.

All TS and product energies are normalised with respect to reactant energy (reactant energy=0). The reaction profile is shown below.

=== Reaction Profiles ===

[[File:Yz20215 E3 reaction profile.png|x700px|700px|thumb|centre|Figure Reaction profile of three different reaction paths]]

In this profile, we could see that the '''endo TS''' is the lowest in energy, therefore will be formed faster compared with other two, and will be the '''kinetic product''' of the reaction. The Exo TS has slightly higher but close energy, while the cheletropic TS has the largest activation barrier.

However, if we compare the energies of the products, we could see that the Endo and the Exo products are very close in energy at approximately -98 kJ mol <sup>-1</sup> , while the cheletropic product is the most stable product with energy of around -154 kJ mol <sup>-1</sup> . Therefore, if we provide enough energy for the reaction to overcome its activation barrier, the '''cheletropic product''' will be the major product as it is the '''thermodynamic product''' of the reaction.

=== Extension ===

[[File:YZ20215 E3 extension.png|x400px|400px|thumb|centre|Scheme 4 The reaction of sulfur dioxide with another diene in xylylene]]

In this reaction, the other diene of xylylene, also in cis conformation, could also reaction with sulfur dioxide to form both the endo and the exo products, and the activation energies and reaction energies of these two reactions are investigated as shown below.

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.102071
| style="text-align: center;" |267.987431
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.105054
| style="text-align: center;" |275.819298
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.065615
| style="text-align: center;" |172.272196
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.067307
| style="text-align: center;" |176.714542
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |113.6657804
| style="text-align: center;" |17.9505454
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |121.4976474
| style="text-align: center;" |22.3928914
|}

These two reaction, are endothermic reactions, with product being higher in energy than that of the reactants. The activation barrier is also around 30 kJ mol <sup>-1</sup> higher than that of the DA reaction occurring at the other diene, therefore, these two reactions are both '''thermodynamically and kinetically unfavourable'''.

=== Files ===

Optimised LOG File for Endo TS: [[File:Yz20215 E3 DA endo TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 E3 DA TS exo TS PM6.log]]

Optimised LOG File for Cheletropic TS: [[File:YZ20215 E3 CHE TS.LOG]]

'''Extension'''

Optimised LOG File for Endo TS: [[File:Yz20215 ext ENDO TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 ext exo TS.log]]

= Conclusion =

During the time span of this Transition State Computational Lab, three different pericyclic reactions were investigated.

The reactions were investigated by using PM6 and B3LYP/6-31G(d) methods in GaussView to optimise the reactants, transition states, and the products.

Other information were also extracted from the optimised molecule LOG. files: including vibration frequency calculations and IRC (Intrinsic Reaction Coordinate); bond lengths of the TS, reactants and products; the energies of different species; and the molecular orbitals.

These data were used to analyse the Transition states and the reactions, including confirmation of the TS by presence of one imaginary frequency in vibration frequencies, the activation barrier and energy change of the reaction from the energies of different species, and the MOs to determine the electron demand of a certain Diels-Alder reaction (inverse or normal electron demand).

In addition, the data confirmed that the reactions followed several existing rules and theories: Woodward-Hoffmann rules in Exercise 1, Frontier Molecular Orbital Theory, etc..

These computational methods could be applied to investigate many other pericyclic reactions, where various aspects of data could be obtained and analysed as like shown in this lab.

Rep:YZ20215TS

2018-02-27T19:37:07Z

Yz20215: /* Extension */

== Introduction ==

To investigate a reaction, it is crucial to firstly locate the Transition State of the reaction, because

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 2(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 2(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 2(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 3. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
|<jmol>
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|-
| style="text-align: center;" |HOMO
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==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 4. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 cyclohexadiene min.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 dioxole min B3LYP.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 product ENDO B3LYP MIN.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents> Yz20215 E2 product EXO B3LYP MIN.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 TS endo TS.log</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 TS exo TS.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
|<jmol>
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<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
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<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
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|<jmol>
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<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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|<jmol>
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<color>white</color>
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<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" |HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 5(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 5(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Therefore, in normal electron demand DA reactions, the orbitals of the electron-rich diene will be higher, therefore, favourable interaction occurs between the HOMO of diene and the LUMO of dienophile; while for inverse electron demand reactions, the LUMO of diene will interact with the HOMO of the dienophile.

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

In this reaction, due to the presence of a heterocyclic reactant, 1,3-dioxole, it is postulated that the reaction could possibly have an inverse electron demand, therefore, energy calculations were done and their single point energies determined in the following section to confirm the postulation.

==== Single point energies ====

{| class="wikitable"
|+ Table 11. Single point energies of reactants
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy of HOMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy of LUMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy difference between this HOMO and the LUMO of the other reactant/ a.u.'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |-0.20554
| style="text-align: center;" |-0.01711
| style="text-align: center;" |0.24349
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-0.19594
| style="text-align: center;" |0.03795
| style="text-align: center;" |0.17883
|}

In this reaction, the energy difference between the HOMO of the dienophile with the LUMO of diene is smaller than that of the other pair, therefore, they will give to a larger overlap of orbitals and more favourable interaciton.

Therefore, we can conclude from the data above that the reaction has an inverse electron demand. This is due to the presence of two oxygen atoms donating their lone pairs, making the dienophile electron rich.

=== Energy analysis ===

{| class="wikitable"
|+ Table 12. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 13. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 14. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
!<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
</jmolApplet>
</jmol>
| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure Secondary orbital interactions in both Endo and Exo TS]]
|}

=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

[[File:Yz20215 E3 scheme.png|x400px|400px|thumb|centre|Scheme 3 Diels-Alder and Cheletropic reaction between Xylylene and Sulfur dioxide]]

The reaction between xylylene and sulfur dioxide was investigated.

The reaction between the reactants could occur either via a Diels-Alder reaction or cheletropic reaction as shown above in Scheme 3. For the Diels-Alder reaction between two, the product could be formed in an Endo or an Exo conformation.

In this exercise, the reactants, Transition States and products were optimised using PM6 Method using GaussView software. Also, the energies of different species were obtained to determine the activation energy and the energy change of reaction with reaction energy profile plotted. Therefore, the most thermodynamically and the most kinetically favoured product was determined.

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 14. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E3 DA endo TS.LOG</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E3 DA TS exo TS PM6.log</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>YZ20215 E3 CHE TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== IRC calculations ===

{| class="wikitable"
|+ Table 15. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

Looking at IRC of these three reactions, we could see that the activation barrier of the reaction is quite small, this is due to one of the reactants, xylylene, being very unstable and high in energy.

This is because, according to Huckle's Rule, it has only 8 π electrons, which is (4n) instead of (4n+2), therefore, it is antiaromatic. However, due to structure constraint, both of the dienes are cis in xylylene, which is favourable as no energy expense on converting into trans conformation.

During the reaction, the xylyene part will react with the sulfur dioxide molecule to form a bicyclic ring, containing a benzene ring, which is aromatic and stable. Therefore, making it favourable to form the products.

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.021698
| style="text-align: center;" |56.9681033
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.021454
| style="text-align: center;" |56.3274813
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |-0.000002
| style="text-align: center;" |-0.0052510004
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |83.4410224
| style="text-align: center;" |-97.3535473
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |87.4239054
| style="text-align: center;" |-97.9941693
|-
| style="text-align: center;" |Cheletropic
| style="text-align: center;" |105.7656504
| style="text-align: center;" |-154.3269016
|}

The energies of the reactants, Transition States, and different products were obtained from the optimised LOG. files in GaussView, and the reaction profile is plotted showing their relative energies with the proceeding of the three reactions.

All TS and product energies are normalised with respect to reactant energy (reactant energy=0). The reaction profile is shown below.

=== Reaction Profiles ===

[[File:Yz20215 E3 reaction profile.png|x700px|700px|thumb|centre|Figure Reaction profile of three different reaction paths]]

In this profile, we could see that the '''endo TS''' is the lowest in energy, therefore will be formed faster compared with other two, and will be the '''kinetic product''' of the reaction. The Exo TS has slightly higher but close energy, while the cheletropic TS has the largest activation barrier.

However, if we compare the energies of the products, we could see that the Endo and the Exo products are very close in energy at approximately -98 kJ mol <sup>-1</sup> , while the cheletropic product is the most stable product with energy of around -154 kJ mol <sup>-1</sup> . Therefore, if we provide enough energy for the reaction to overcome its activation barrier, the '''cheletropic product''' will be the major product as it is the '''thermodynamic product''' of the reaction.

=== Extension ===

[[File:YZ20215 E3 extension.png|x400px|400px|thumb|centre|Scheme 4 The reaction of sulfur dioxide with another diene in xylylene]]

In this reaction, the other diene of xylylene, also in cis conformation, could also reaction with sulfur dioxide to form both the endo and the exo products, and the activation energies and reaction energies of these two reactions are investigated as shown below.

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.102071
| style="text-align: center;" |267.987431
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.105054
| style="text-align: center;" |275.819298
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.065615
| style="text-align: center;" |172.272196
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.067307
| style="text-align: center;" |176.714542
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |113.6657804
| style="text-align: center;" |17.9505454
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |121.4976474
| style="text-align: center;" |22.3928914
|}

These two reaction, are endothermic reactions, with product being higher in energy than that of the reactants. The activation barrier is also around 30 kJ mol <sup>-1</sup> higher than that of the DA reaction occurring at the other diene, therefore, these two reactions are both '''thermodynamically and kinetically unfavourable'''.

=== Files ===

Optimised LOG File for Endo TS: [[File:Yz20215 E3 DA endo TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 E3 DA TS exo TS PM6.log]]

Optimised LOG File for Cheletropic TS: [[File:YZ20215 E3 CHE TS.LOG]]

= Conclusion =

During the time span of this Transition State Computational Lab, three different pericyclic reactions were investigated.

The reactions were investigated by using PM6 and B3LYP/6-31G(d) methods in GaussView to optimise the reactants, transition states, and the products.

Other information were also extracted from the optimised molecule LOG. files: including vibration frequency calculations and IRC (Intrinsic Reaction Coordinate); bond lengths of the TS, reactants and products; the energies of different species; and the molecular orbitals.

These data were used to analyse the Transition states and the reactions, including confirmation of the TS by presence of one imaginary frequency in vibration frequencies, the activation barrier and energy change of the reaction from the energies of different species, and the MOs to determine the electron demand of a certain Diels-Alder reaction (inverse or normal electron demand).

In addition, the data confirmed that the reactions followed several existing rules and theories: Woodward-Hoffmann rules in Exercise 1, Frontier Molecular Orbital Theory, etc..

These computational methods could be applied to investigate many other pericyclic reactions, where various aspects of data could be obtained and analysed as like shown in this lab.

Rep:YZ20215TS

2018-02-27T19:32:51Z

Yz20215: /* Activation and Reaction Energy calculations */

== Introduction ==

To investigate a reaction, it is crucial to firstly locate the Transition State of the reaction, because

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 2(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 2(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 2(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 3. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
|<jmol>
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|-
| style="text-align: center;" |HOMO
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==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 4. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 5(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 5(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Therefore, in normal electron demand DA reactions, the orbitals of the electron-rich diene will be higher, therefore, favourable interaction occurs between the HOMO of diene and the LUMO of dienophile; while for inverse electron demand reactions, the LUMO of diene will interact with the HOMO of the dienophile.

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

In this reaction, due to the presence of a heterocyclic reactant, 1,3-dioxole, it is postulated that the reaction could possibly have an inverse electron demand, therefore, energy calculations were done and their single point energies determined in the following section to confirm the postulation.

==== Single point energies ====

{| class="wikitable"
|+ Table 11. Single point energies of reactants
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy of HOMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy of LUMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy difference between this HOMO and the LUMO of the other reactant/ a.u.'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |-0.20554
| style="text-align: center;" |-0.01711
| style="text-align: center;" |0.24349
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-0.19594
| style="text-align: center;" |0.03795
| style="text-align: center;" |0.17883
|}

In this reaction, the energy difference between the HOMO of the dienophile with the LUMO of diene is smaller than that of the other pair, therefore, they will give to a larger overlap of orbitals and more favourable interaciton.

Therefore, we can conclude from the data above that the reaction has an inverse electron demand. This is due to the presence of two oxygen atoms donating their lone pairs, making the dienophile electron rich.

=== Energy analysis ===

{| class="wikitable"
|+ Table 12. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 13. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 14. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
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| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure Secondary orbital interactions in both Endo and Exo TS]]
|}

=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

[[File:Yz20215 E3 scheme.png|x400px|400px|thumb|centre|Scheme 3 Diels-Alder and Cheletropic reaction between Xylylene and Sulfur dioxide]]

The reaction between xylylene and sulfur dioxide was investigated.

The reaction between the reactants could occur either via a Diels-Alder reaction or cheletropic reaction as shown above in Scheme 3. For the Diels-Alder reaction between two, the product could be formed in an Endo or an Exo conformation.

In this exercise, the reactants, Transition States and products were optimised using PM6 Method using GaussView software. Also, the energies of different species were obtained to determine the activation energy and the energy change of reaction with reaction energy profile plotted. Therefore, the most thermodynamically and the most kinetically favoured product was determined.

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 14. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
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=== IRC calculations ===

{| class="wikitable"
|+ Table 15. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

Looking at IRC of these three reactions, we could see that the activation barrier of the reaction is quite small, this is due to one of the reactants, xylylene, being very unstable and high in energy.

This is because, according to Huckle's Rule, it has only 8 π electrons, which is (4n) instead of (4n+2), therefore, it is antiaromatic. However, due to structure constraint, both of the dienes are cis in xylylene, which is favourable as no energy expense on converting into trans conformation.

During the reaction, the xylyene part will react with the sulfur dioxide molecule to form a bicyclic ring, containing a benzene ring, which is aromatic and stable. Therefore, making it favourable to form the products.

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using PM6 Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.021698
| style="text-align: center;" |56.9681033
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.021454
| style="text-align: center;" |56.3274813
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |-0.000002
| style="text-align: center;" |-0.0052510004
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |83.4410224
| style="text-align: center;" |-97.3535473
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |87.4239054
| style="text-align: center;" |-97.9941693
|-
| style="text-align: center;" |Cheletropic
| style="text-align: center;" |105.7656504
| style="text-align: center;" |-154.3269016
|}

The energies of the reactants, Transition States, and different products were obtained from the optimised LOG. files in GaussView, and the reaction profile is plotted showing their relative energies with the proceeding of the three reactions.

All TS and product energies are normalised with respect to reactant energy (reactant energy=0). The reaction profile is shown below.

=== Reaction Profiles ===

[[File:Yz20215 E3 reaction profile.png|x700px|700px|thumb|centre|Figure Reaction profile of three different reaction paths]]

In this profile, we could see that the '''endo TS''' is the lowest in energy, therefore will be formed faster compared with other two, and will be the '''kinetic product''' of the reaction. The Exo TS has slightly higher but close energy, while the cheletropic TS has the largest activation barrier.

However, if we compare the energies of the products, we could see that the Endo and the Exo products are very close in energy at approximately -98 kJ mol <sup>-1</sup> , while the cheletropic product is the most stable product with energy of around -154 kJ mol <sup>-1</sup> . Therefore, if we provide enough energy for the reaction to overcome its activation barrier, the '''cheletropic product''' will be the major product as it is the '''thermodynamic product''' of the reaction.

=== Extension ===

[[File:YZ20215 E3 extension.png|x400px|400px|thumb|centre|Scheme 4 The reaction of sulfur dioxide with another diene in xylylene]]

In this reaction, the other diene of xylylene, also in cis conformation, could also reaction with sulfur dioxide to form both the endo and the exo products, and the activation energies and reaction energies of these two reactions are investigated as shown below.

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.102071
| style="text-align: center;" |267.987431
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.105054
| style="text-align: center;" |275.819298
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.065615
| style="text-align: center;" |172.272196
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.067307
| style="text-align: center;" |176.714542
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |113.6657804
| style="text-align: center;" |17.9505454
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |121.4976474
| style="text-align: center;" |22.3928914
|}

=== Files ===

Optimised LOG File for Endo TS: [[File:Yz20215 E3 DA endo TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 E3 DA TS exo TS PM6.log]]

Optimised LOG File for Cheletropic TS: [[File:YZ20215 E3 CHE TS.LOG]]

= Conclusion =

During the time span of this Transition State Computational Lab, three different pericyclic reactions were investigated.

The reactions were investigated by using PM6 and B3LYP/6-31G(d) methods in GaussView to optimise the reactants, transition states, and the products.

Other information were also extracted from the optimised molecule LOG. files: including vibration frequency calculations and IRC (Intrinsic Reaction Coordinate); bond lengths of the TS, reactants and products; the energies of different species; and the molecular orbitals.

These data were used to analyse the Transition states and the reactions, including confirmation of the TS by presence of one imaginary frequency in vibration frequencies, the activation barrier and energy change of the reaction from the energies of different species, and the MOs to determine the electron demand of a certain Diels-Alder reaction (inverse or normal electron demand).

In addition, the data confirmed that the reactions followed several existing rules and theories: Woodward-Hoffmann rules in Exercise 1, Frontier Molecular Orbital Theory, etc..

These computational methods could be applied to investigate many other pericyclic reactions, where various aspects of data could be obtained and analysed as like shown in this lab.

File:Yz20215 ext ENDO TS.LOG

2018-02-27T19:31:52Z

Yz20215:

File:Yz20215 ext exo TS.log

2018-02-27T19:31:52Z

Yz20215:

Rep:YZ20215TS

2018-02-27T19:31:08Z

Yz20215: /* Extension */

== Introduction ==

To investigate a reaction, it is crucial to firstly locate the Transition State of the reaction, because

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 2(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 2(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 2(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 3. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
|<jmol>
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| style="text-align: center;" |HOMO
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==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 4. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 cyclohexadiene min.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 dioxole min B3LYP.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 product ENDO B3LYP MIN.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents> Yz20215 E2 product EXO B3LYP MIN.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 TS endo TS.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 TS exo TS.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
|<jmol>
<jmolApplet>
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<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
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|<jmol>
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<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
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|<jmol>
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<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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|<jmol>
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<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" |HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 5(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 5(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Therefore, in normal electron demand DA reactions, the orbitals of the electron-rich diene will be higher, therefore, favourable interaction occurs between the HOMO of diene and the LUMO of dienophile; while for inverse electron demand reactions, the LUMO of diene will interact with the HOMO of the dienophile.

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

In this reaction, due to the presence of a heterocyclic reactant, 1,3-dioxole, it is postulated that the reaction could possibly have an inverse electron demand, therefore, energy calculations were done and their single point energies determined in the following section to confirm the postulation.

==== Single point energies ====

{| class="wikitable"
|+ Table 11. Single point energies of reactants
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy of HOMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy of LUMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy difference between this HOMO and the LUMO of the other reactant/ a.u.'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |-0.20554
| style="text-align: center;" |-0.01711
| style="text-align: center;" |0.24349
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-0.19594
| style="text-align: center;" |0.03795
| style="text-align: center;" |0.17883
|}

In this reaction, the energy difference between the HOMO of the dienophile with the LUMO of diene is smaller than that of the other pair, therefore, they will give to a larger overlap of orbitals and more favourable interaciton.

Therefore, we can conclude from the data above that the reaction has an inverse electron demand. This is due to the presence of two oxygen atoms donating their lone pairs, making the dienophile electron rich.

=== Energy analysis ===

{| class="wikitable"
|+ Table 12. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 13. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 14. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
!<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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!<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
</jmolApplet>
</jmol>
| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure Secondary orbital interactions in both Endo and Exo TS]]
|}

=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

[[File:Yz20215 E3 scheme.png|x400px|400px|thumb|centre|Scheme 3 Diels-Alder and Cheletropic reaction between Xylylene and Sulfur dioxide]]

The reaction between xylylene and sulfur dioxide was investigated.

The reaction between the reactants could occur either via a Diels-Alder reaction or cheletropic reaction as shown above in Scheme 3. For the Diels-Alder reaction between two, the product could be formed in an Endo or an Exo conformation.

In this exercise, the reactants, Transition States and products were optimised using PM6 Method using GaussView software. Also, the energies of different species were obtained to determine the activation energy and the energy change of reaction with reaction energy profile plotted. Therefore, the most thermodynamically and the most kinetically favoured product was determined.

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 14. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E3 DA endo TS.LOG</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
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<script>frame 16; </script>
<uploadedFileContents>Yz20215 E3 DA TS exo TS PM6.log</uploadedFileContents>
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|<jmol>
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<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>YZ20215 E3 CHE TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== IRC calculations ===

{| class="wikitable"
|+ Table 15. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

Looking at IRC of these three reactions, we could see that the activation barrier of the reaction is quite small, this is due to one of the reactants, xylylene, being very unstable and high in energy.

This is because, according to Huckle's Rule, it has only 8 π electrons, which is (4n) instead of (4n+2), therefore, it is antiaromatic. However, due to structure constraint, both of the dienes are cis in xylylene, which is favourable as no energy expense on converting into trans conformation.

During the reaction, the xylyene part will react with the sulfur dioxide molecule to form a bicyclic ring, containing a benzene ring, which is aromatic and stable. Therefore, making it favourable to form the products.

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.021698
| style="text-align: center;" |56.9681033
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.021454
| style="text-align: center;" |56.3274813
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |-0.000002
| style="text-align: center;" |-0.0052510004
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |83.4410224
| style="text-align: center;" |-97.3535473
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |87.4239054
| style="text-align: center;" |-97.9941693
|-
| style="text-align: center;" |Cheletropic
| style="text-align: center;" |105.7656504
| style="text-align: center;" |-154.3269016
|}

The energies of the reactants, Transition States, and different products were obtained from the optimised LOG. files in GaussView, and the reaction profile is plotted showing their relative energies with the proceeding of the three reactions.

All TS and product energies are normalised with respect to reactant energy (reactant energy=0). The reaction profile is shown below.

=== Reaction Profiles ===

[[File:Yz20215 E3 reaction profile.png|x700px|700px|thumb|centre|Figure Reaction profile of three different reaction paths]]

In this profile, we could see that the '''endo TS''' is the lowest in energy, therefore will be formed faster compared with other two, and will be the '''kinetic product''' of the reaction. The Exo TS has slightly higher but close energy, while the cheletropic TS has the largest activation barrier.

However, if we compare the energies of the products, we could see that the Endo and the Exo products are very close in energy at approximately -98 kJ mol <sup>-1</sup> , while the cheletropic product is the most stable product with energy of around -154 kJ mol <sup>-1</sup> . Therefore, if we provide enough energy for the reaction to overcome its activation barrier, the '''cheletropic product''' will be the major product as it is the '''thermodynamic product''' of the reaction.

=== Extension ===

[[File:YZ20215 E3 extension.png|x400px|400px|thumb|centre|Scheme 4 The reaction of sulfur dioxide with another diene in xylylene]]

In this reaction, the other diene of xylylene, also in cis conformation, could also reaction with sulfur dioxide to form both the endo and the exo products, and the activation energies and reaction energies of these two reactions are investigated as shown below.

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.102071
| style="text-align: center;" |267.987431
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.105054
| style="text-align: center;" |275.819298
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.065615
| style="text-align: center;" |172.272196
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.067307
| style="text-align: center;" |176.714542
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |113.6657804
| style="text-align: center;" |17.9505454
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |121.4976474
| style="text-align: center;" |22.3928914
|}

=== Files ===

Optimised LOG File for Endo TS: [[File:Yz20215 E3 DA endo TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 E3 DA TS exo TS PM6.log]]

Optimised LOG File for Cheletropic TS: [[File:YZ20215 E3 CHE TS.LOG]]

= Conclusion =

During the time span of this Transition State Computational Lab, three different pericyclic reactions were investigated.

The reactions were investigated by using PM6 and B3LYP/6-31G(d) methods in GaussView to optimise the reactants, transition states, and the products.

Other information were also extracted from the optimised molecule LOG. files: including vibration frequency calculations and IRC (Intrinsic Reaction Coordinate); bond lengths of the TS, reactants and products; the energies of different species; and the molecular orbitals.

These data were used to analyse the Transition states and the reactions, including confirmation of the TS by presence of one imaginary frequency in vibration frequencies, the activation barrier and energy change of the reaction from the energies of different species, and the MOs to determine the electron demand of a certain Diels-Alder reaction (inverse or normal electron demand).

In addition, the data confirmed that the reactions followed several existing rules and theories: Woodward-Hoffmann rules in Exercise 1, Frontier Molecular Orbital Theory, etc..

These computational methods could be applied to investigate many other pericyclic reactions, where various aspects of data could be obtained and analysed as like shown in this lab.

Rep:YZ20215TS

2018-02-27T19:24:09Z

Yz20215: /* Reaction Profiles */

== Introduction ==

To investigate a reaction, it is crucial to firstly locate the Transition State of the reaction, because

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 2(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 2(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 2(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 3. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 4. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 5(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 5(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Therefore, in normal electron demand DA reactions, the orbitals of the electron-rich diene will be higher, therefore, favourable interaction occurs between the HOMO of diene and the LUMO of dienophile; while for inverse electron demand reactions, the LUMO of diene will interact with the HOMO of the dienophile.

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

In this reaction, due to the presence of a heterocyclic reactant, 1,3-dioxole, it is postulated that the reaction could possibly have an inverse electron demand, therefore, energy calculations were done and their single point energies determined in the following section to confirm the postulation.

==== Single point energies ====

{| class="wikitable"
|+ Table 11. Single point energies of reactants
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy of HOMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy of LUMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy difference between this HOMO and the LUMO of the other reactant/ a.u.'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |-0.20554
| style="text-align: center;" |-0.01711
| style="text-align: center;" |0.24349
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-0.19594
| style="text-align: center;" |0.03795
| style="text-align: center;" |0.17883
|}

In this reaction, the energy difference between the HOMO of the dienophile with the LUMO of diene is smaller than that of the other pair, therefore, they will give to a larger overlap of orbitals and more favourable interaciton.

Therefore, we can conclude from the data above that the reaction has an inverse electron demand. This is due to the presence of two oxygen atoms donating their lone pairs, making the dienophile electron rich.

=== Energy analysis ===

{| class="wikitable"
|+ Table 12. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 13. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 14. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
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| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure Secondary orbital interactions in both Endo and Exo TS]]
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=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

[[File:Yz20215 E3 scheme.png|x400px|400px|thumb|centre|Scheme 3 Diels-Alder and Cheletropic reaction between Xylylene and Sulfur dioxide]]

The reaction between xylylene and sulfur dioxide was investigated.

The reaction between the reactants could occur either via a Diels-Alder reaction or cheletropic reaction as shown above in Scheme 3. For the Diels-Alder reaction between two, the product could be formed in an Endo or an Exo conformation.

In this exercise, the reactants, Transition States and products were optimised using PM6 Method using GaussView software. Also, the energies of different species were obtained to determine the activation energy and the energy change of reaction with reaction energy profile plotted. Therefore, the most thermodynamically and the most kinetically favoured product was determined.

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 14. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
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=== IRC calculations ===

{| class="wikitable"
|+ Table 15. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

Looking at IRC of these three reactions, we could see that the activation barrier of the reaction is quite small, this is due to one of the reactants, xylylene, being very unstable and high in energy.

This is because, according to Huckle's Rule, it has only 8 π electrons, which is (4n) instead of (4n+2), therefore, it is antiaromatic. However, due to structure constraint, both of the dienes are cis in xylylene, which is favourable as no energy expense on converting into trans conformation.

During the reaction, the xylyene part will react with the sulfur dioxide molecule to form a bicyclic ring, containing a benzene ring, which is aromatic and stable. Therefore, making it favourable to form the products.

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.021698
| style="text-align: center;" |56.9681033
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.021454
| style="text-align: center;" |56.3274813
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |-0.000002
| style="text-align: center;" |-0.0052510004
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |83.4410224
| style="text-align: center;" |-97.3535473
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |87.4239054
| style="text-align: center;" |-97.9941693
|-
| style="text-align: center;" |Cheletropic
| style="text-align: center;" |105.7656504
| style="text-align: center;" |-154.3269016
|}

The energies of the reactants, Transition States, and different products were obtained from the optimised LOG. files in GaussView, and the reaction profile is plotted showing their relative energies with the proceeding of the three reactions.

All TS and product energies are normalised with respect to reactant energy (reactant energy=0). The reaction profile is shown below.

=== Reaction Profiles ===

[[File:Yz20215 E3 reaction profile.png|x700px|700px|thumb|centre|Figure Reaction profile of three different reaction paths]]

In this profile, we could see that the '''endo TS''' is the lowest in energy, therefore will be formed faster compared with other two, and will be the '''kinetic product''' of the reaction. The Exo TS has slightly higher but close energy, while the cheletropic TS has the largest activation barrier.

However, if we compare the energies of the products, we could see that the Endo and the Exo products are very close in energy at approximately -98 kJ mol <sup>-1</sup> , while the cheletropic product is the most stable product with energy of around -154 kJ mol <sup>-1</sup> . Therefore, if we provide enough energy for the reaction to overcome its activation barrier, the '''cheletropic product''' will be the major product as it is the '''thermodynamic product''' of the reaction.

=== Extension ===

[[File:YZ20215 E3 extension.png|x400px|400px|thumb|centre|Scheme 4 The reaction of sulfur dioxide with another diene in xylylene]]

In this reaction, the other diene of xylylene, also in cis conformation, could also reaction with sulfur dioxide to form both the endo and the exo products, and the activation energies and reaction energies of these two reactions are investigated as shown below.

=== Files ===

Optimised LOG File for Endo TS: [[File:Yz20215 E3 DA endo TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 E3 DA TS exo TS PM6.log]]

Optimised LOG File for Cheletropic TS: [[File:YZ20215 E3 CHE TS.LOG]]

= Conclusion =

During the time span of this Transition State Computational Lab, three different pericyclic reactions were investigated.

The reactions were investigated by using PM6 and B3LYP/6-31G(d) methods in GaussView to optimise the reactants, transition states, and the products.

Other information were also extracted from the optimised molecule LOG. files: including vibration frequency calculations and IRC (Intrinsic Reaction Coordinate); bond lengths of the TS, reactants and products; the energies of different species; and the molecular orbitals.

These data were used to analyse the Transition states and the reactions, including confirmation of the TS by presence of one imaginary frequency in vibration frequencies, the activation barrier and energy change of the reaction from the energies of different species, and the MOs to determine the electron demand of a certain Diels-Alder reaction (inverse or normal electron demand).

In addition, the data confirmed that the reactions followed several existing rules and theories: Woodward-Hoffmann rules in Exercise 1, Frontier Molecular Orbital Theory, etc..

These computational methods could be applied to investigate many other pericyclic reactions, where various aspects of data could be obtained and analysed as like shown in this lab.

File:YZ20215 E3 extension.png

2018-02-27T19:23:28Z

Yz20215:

Rep:YZ20215TS

2018-02-27T19:17:23Z

Yz20215: /* Introduction */

== Introduction ==

To investigate a reaction, it is crucial to firstly locate the Transition State of the reaction, because

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 2(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 2(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 2(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 3. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 4. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 cyclohexadiene min.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 dioxole min B3LYP.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 product ENDO B3LYP MIN.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents> Yz20215 E2 product EXO B3LYP MIN.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 TS endo TS.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 TS exo TS.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
|<jmol>
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|<jmol>
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<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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|-
| style="text-align: center;" |HOMO
|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
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|<jmol>
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<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
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|<jmol>
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<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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|}

{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 5(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 5(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Therefore, in normal electron demand DA reactions, the orbitals of the electron-rich diene will be higher, therefore, favourable interaction occurs between the HOMO of diene and the LUMO of dienophile; while for inverse electron demand reactions, the LUMO of diene will interact with the HOMO of the dienophile.

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

In this reaction, due to the presence of a heterocyclic reactant, 1,3-dioxole, it is postulated that the reaction could possibly have an inverse electron demand, therefore, energy calculations were done and their single point energies determined in the following section to confirm the postulation.

==== Single point energies ====

{| class="wikitable"
|+ Table 11. Single point energies of reactants
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy of HOMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy of LUMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy difference between this HOMO and the LUMO of the other reactant/ a.u.'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |-0.20554
| style="text-align: center;" |-0.01711
| style="text-align: center;" |0.24349
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-0.19594
| style="text-align: center;" |0.03795
| style="text-align: center;" |0.17883
|}

In this reaction, the energy difference between the HOMO of the dienophile with the LUMO of diene is smaller than that of the other pair, therefore, they will give to a larger overlap of orbitals and more favourable interaciton.

Therefore, we can conclude from the data above that the reaction has an inverse electron demand. This is due to the presence of two oxygen atoms donating their lone pairs, making the dienophile electron rich.

=== Energy analysis ===

{| class="wikitable"
|+ Table 12. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 13. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 14. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
!<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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!<jmol>
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</jmolApplet>
</jmol>
| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure Secondary orbital interactions in both Endo and Exo TS]]
|}

=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

[[File:Yz20215 E3 scheme.png|x400px|400px|thumb|centre|Scheme 3 Diels-Alder and Cheletropic reaction between Xylylene and Sulfur dioxide]]

The reaction between xylylene and sulfur dioxide was investigated.

The reaction between the reactants could occur either via a Diels-Alder reaction or cheletropic reaction as shown above in Scheme 3. For the Diels-Alder reaction between two, the product could be formed in an Endo or an Exo conformation.

In this exercise, the reactants, Transition States and products were optimised using PM6 Method using GaussView software. Also, the energies of different species were obtained to determine the activation energy and the energy change of reaction with reaction energy profile plotted. Therefore, the most thermodynamically and the most kinetically favoured product was determined.

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 14. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E3 DA endo TS.LOG</uploadedFileContents>
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|<jmol>
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<script>frame 16; </script>
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<script>frame 16; </script>
<uploadedFileContents>YZ20215 E3 CHE TS.LOG</uploadedFileContents>
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|}

=== IRC calculations ===

{| class="wikitable"
|+ Table 15. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

Looking at IRC of these three reactions, we could see that the activation barrier of the reaction is quite small, this is due to one of the reactants, xylylene, being very unstable and high in energy.

This is because, according to Huckle's Rule, it has only 8 π electrons, which is (4n) instead of (4n+2), therefore, it is antiaromatic. However, due to structure constraint, both of the dienes are cis in xylylene, which is favourable as no energy expense on converting into trans conformation.

During the reaction, the xylyene part will react with the sulfur dioxide molecule to form a bicyclic ring, containing a benzene ring, which is aromatic and stable. Therefore, making it favourable to form the products.

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.021698
| style="text-align: center;" |56.9681033
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.021454
| style="text-align: center;" |56.3274813
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |-0.000002
| style="text-align: center;" |-0.0052510004
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |83.4410224
| style="text-align: center;" |-97.3535473
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |87.4239054
| style="text-align: center;" |-97.9941693
|-
| style="text-align: center;" |Cheletropic
| style="text-align: center;" |105.7656504
| style="text-align: center;" |-154.3269016
|}

The energies of the reactants, Transition States, and different products were obtained from the optimised LOG. files in GaussView, and the reaction profile is plotted showing their relative energies with the proceeding of the three reactions.

All TS and product energies are normalised with respect to reactant energy (reactant energy=0). The reaction profile is shown below.

=== Reaction Profiles ===

[[File:Yz20215 E3 reaction profile.png|x700px|700px|thumb|centre|Figure Reaction profile of three different reaction paths]]

In this profile, we could see that the '''endo TS''' is the lowest in energy, therefore will be formed faster compared with other two, and will be the '''kinetic product''' of the reaction. The Exo TS has slightly higher but close energy, while the cheletropic TS has the largest activation barrier.

However, if we compare the energies of the products, we could see that the Endo and the Exo products are very close in energy at approximately -98 kJ mol <sup>-1</sup> , while the cheletropic product is the most stable product with energy of around -154 kJ mol <sup>-1</sup> . Therefore, if we provide enough energy for the reaction to overcome its activation barrier, the '''cheletropic product''' will be the major product as it is the '''thermodynamic product''' of the reaction.

=== Files ===

Optimised LOG File for Endo TS: [[File:Yz20215 E3 DA endo TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 E3 DA TS exo TS PM6.log]]

Optimised LOG File for Cheletropic TS: [[File:YZ20215 E3 CHE TS.LOG]]

= Conclusion =

During the time span of this Transition State Computational Lab, three different pericyclic reactions were investigated.

The reactions were investigated by using PM6 and B3LYP/6-31G(d) methods in GaussView to optimise the reactants, transition states, and the products.

Other information were also extracted from the optimised molecule LOG. files: including vibration frequency calculations and IRC (Intrinsic Reaction Coordinate); bond lengths of the TS, reactants and products; the energies of different species; and the molecular orbitals.

These data were used to analyse the Transition states and the reactions, including confirmation of the TS by presence of one imaginary frequency in vibration frequencies, the activation barrier and energy change of the reaction from the energies of different species, and the MOs to determine the electron demand of a certain Diels-Alder reaction (inverse or normal electron demand).

In addition, the data confirmed that the reactions followed several existing rules and theories: Woodward-Hoffmann rules in Exercise 1, Frontier Molecular Orbital Theory, etc..

These computational methods could be applied to investigate many other pericyclic reactions, where various aspects of data could be obtained and analysed as like shown in this lab.

Rep:YZ20215TS

2018-02-27T18:54:48Z

Yz20215: /* Excercise 3- Diels-Alder vs Cheletropic */

== Introduction ==

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 2(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 2(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 2(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 3. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 4. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 5(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 5(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Therefore, in normal electron demand DA reactions, the orbitals of the electron-rich diene will be higher, therefore, favourable interaction occurs between the HOMO of diene and the LUMO of dienophile; while for inverse electron demand reactions, the LUMO of diene will interact with the HOMO of the dienophile.

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

In this reaction, due to the presence of a heterocyclic reactant, 1,3-dioxole, it is postulated that the reaction could possibly have an inverse electron demand, therefore, energy calculations were done and their single point energies determined in the following section to confirm the postulation.

==== Single point energies ====

{| class="wikitable"
|+ Table 11. Single point energies of reactants
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy of HOMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy of LUMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy difference between this HOMO and the LUMO of the other reactant/ a.u.'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |-0.20554
| style="text-align: center;" |-0.01711
| style="text-align: center;" |0.24349
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-0.19594
| style="text-align: center;" |0.03795
| style="text-align: center;" |0.17883
|}

In this reaction, the energy difference between the HOMO of the dienophile with the LUMO of diene is smaller than that of the other pair, therefore, they will give to a larger overlap of orbitals and more favourable interaciton.

Therefore, we can conclude from the data above that the reaction has an inverse electron demand. This is due to the presence of two oxygen atoms donating their lone pairs, making the dienophile electron rich.

=== Energy analysis ===

{| class="wikitable"
|+ Table 12. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 13. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 14. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
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| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure Secondary orbital interactions in both Endo and Exo TS]]
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=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

[[File:Yz20215 E3 scheme.png|x400px|400px|thumb|centre|Scheme 3 Diels-Alder and Cheletropic reaction between Xylylene and Sulfur dioxide]]

The reaction between xylylene and sulfur dioxide was investigated.

The reaction between the reactants could occur either via a Diels-Alder reaction or cheletropic reaction as shown above in Scheme 3. For the Diels-Alder reaction between two, the product could be formed in an Endo or an Exo conformation.

In this exercise, the reactants, Transition States and products were optimised using PM6 Method using GaussView software. Also, the energies of different species were obtained to determine the activation energy and the energy change of reaction with reaction energy profile plotted. Therefore, the most thermodynamically and the most kinetically favoured product was determined.

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 14. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
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=== IRC calculations ===

{| class="wikitable"
|+ Table 15. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

Looking at IRC of these three reactions, we could see that the activation barrier of the reaction is quite small, this is due to one of the reactants, xylylene, being very unstable and high in energy.

This is because, according to Huckle's Rule, it has only 8 π electrons, which is (4n) instead of (4n+2), therefore, it is antiaromatic. However, due to structure constraint, both of the dienes are cis in xylylene, which is favourable as no energy expense on converting into trans conformation.

During the reaction, the xylyene part will react with the sulfur dioxide molecule to form a bicyclic ring, containing a benzene ring, which is aromatic and stable. Therefore, making it favourable to form the products.

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.021698
| style="text-align: center;" |56.9681033
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.021454
| style="text-align: center;" |56.3274813
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |-0.000002
| style="text-align: center;" |-0.0052510004
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |83.4410224
| style="text-align: center;" |-97.3535473
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |87.4239054
| style="text-align: center;" |-97.9941693
|-
| style="text-align: center;" |Cheletropic
| style="text-align: center;" |105.7656504
| style="text-align: center;" |-154.3269016
|}

The energies of the reactants, Transition States, and different products were obtained from the optimised LOG. files in GaussView, and the reaction profile is plotted showing their relative energies with the proceeding of the three reactions.

All TS and product energies are normalised with respect to reactant energy (reactant energy=0). The reaction profile is shown below.

=== Reaction Profiles ===

[[File:Yz20215 E3 reaction profile.png|x700px|700px|thumb|centre|Figure Reaction profile of three different reaction paths]]

In this profile, we could see that the '''endo TS''' is the lowest in energy, therefore will be formed faster compared with other two, and will be the '''kinetic product''' of the reaction. The Exo TS has slightly higher but close energy, while the cheletropic TS has the largest activation barrier.

However, if we compare the energies of the products, we could see that the Endo and the Exo products are very close in energy at approximately -98 kJ mol <sup>-1</sup> , while the cheletropic product is the most stable product with energy of around -154 kJ mol <sup>-1</sup> . Therefore, if we provide enough energy for the reaction to overcome its activation barrier, the '''cheletropic product''' will be the major product as it is the '''thermodynamic product''' of the reaction.

=== Files ===

Optimised LOG File for Endo TS: [[File:Yz20215 E3 DA endo TS.LOG ]]

Optimised LOG File for Exo TS: [[File:Yz20215 E3 DA TS exo TS PM6.log]]

Optimised LOG File for Cheletropic TS: [[File:YZ20215 E3 CHE TS.LOG]]

= Conclusion =

During the time span of this Transition State Computational Lab, three different pericyclic reactions were investigated.

The reactions were investigated by using PM6 and B3LYP/6-31G(d) methods in GaussView to optimise the reactants, transition states, and the products.

Other information were also extracted from the optimised molecule LOG. files: including vibration frequency calculations and IRC (Intrinsic Reaction Coordinate); bond lengths of the TS, reactants and products; the energies of different species; and the molecular orbitals.

These data were used to analyse the Transition states and the reactions, including confirmation of the TS by presence of one imaginary frequency in vibration frequencies, the activation barrier and energy change of the reaction from the energies of different species, and the MOs to determine the electron demand of a certain Diels-Alder reaction (inverse or normal electron demand).

In addition, the data confirmed that the reactions followed several existing rules and theories: Woodward-Hoffmann rules in Exercise 1, Frontier Molecular Orbital Theory, etc..

These computational methods could be applied to investigate many other pericyclic reactions, where various aspects of data could be obtained and analysed as like shown in this lab.

Rep:YZ20215TS

2018-02-27T18:50:47Z

Yz20215: /* Reaction Profiles */

== Introduction ==

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 2(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 2(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 2(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 3. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 4. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 cyclohexadiene min.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 dioxole min B3LYP.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 product ENDO B3LYP MIN.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents> Yz20215 E2 product EXO B3LYP MIN.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 TS endo TS.log</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 TS exo TS.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
|<jmol>
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<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
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|<jmol>
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<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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|<jmol>
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<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" |HOMO
|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 5(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 5(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Therefore, in normal electron demand DA reactions, the orbitals of the electron-rich diene will be higher, therefore, favourable interaction occurs between the HOMO of diene and the LUMO of dienophile; while for inverse electron demand reactions, the LUMO of diene will interact with the HOMO of the dienophile.

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

In this reaction, due to the presence of a heterocyclic reactant, 1,3-dioxole, it is postulated that the reaction could possibly have an inverse electron demand, therefore, energy calculations were done and their single point energies determined in the following section to confirm the postulation.

==== Single point energies ====

{| class="wikitable"
|+ Table 11. Single point energies of reactants
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy of HOMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy of LUMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy difference between this HOMO and the LUMO of the other reactant/ a.u.'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |-0.20554
| style="text-align: center;" |-0.01711
| style="text-align: center;" |0.24349
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-0.19594
| style="text-align: center;" |0.03795
| style="text-align: center;" |0.17883
|}

In this reaction, the energy difference between the HOMO of the dienophile with the LUMO of diene is smaller than that of the other pair, therefore, they will give to a larger overlap of orbitals and more favourable interaciton.

Therefore, we can conclude from the data above that the reaction has an inverse electron demand. This is due to the presence of two oxygen atoms donating their lone pairs, making the dienophile electron rich.

=== Energy analysis ===

{| class="wikitable"
|+ Table 12. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 13. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 14. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
!<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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!<jmol>
<jmolApplet>
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<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
</jmolApplet>
</jmol>
| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure Secondary orbital interactions in both Endo and Exo TS]]
|}

=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

[[File:Yz20215 E3 scheme.png|x400px|400px|thumb|centre|Scheme 3 Diels-Alder and Cheletropic reaction between Xylylene and Sulfur dioxide]]

The reaction between xylylene and sulfur dioxide was investigated.

The reaction between the reactants could occur either via a Diels-Alder reaction or cheletropic reaction as shown above in Scheme 3. For the Diels-Alder reaction between two, the product could be formed in an Endo or an Exo conformation.

In this exercise, the reactants, Transition States and products were optimised using PM6 Method using GaussView software. Also, the energies of different species were obtained to determine the activation energy and the energy change of reaction with reaction energy profile plotted. Therefore, the most thermodynamically and the most kinetically favoured product was determined.

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 14. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E3 DA endo TS.LOG</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
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<script>frame 16; </script>
<uploadedFileContents>Yz20215 E3 DA TS exo TS PM6.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>YZ20215 E3 CHE TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== IRC calculations ===

{| class="wikitable"
|+ Table 15. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

Looking at IRC of these three reactions, we could see that the activation barrier of the reaction is quite small, this is due to one of the reactants, xylylene, being very unstable and high in energy.

This is because, according to Huckle's Rule, it has only 8 π electrons, which is (4n) instead of (4n+2), therefore, it is antiaromatic. However, due to structure constraint, both of the dienes are cis in xylylene, which is favourable as no energy expense on converting into trans conformation.

During the reaction, the xylyene part will react with the sulfur dioxide molecule to form a bicyclic ring, containing a benzene ring, which is aromatic and stable. Therefore, making it favourable to form the products.

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.021698
| style="text-align: center;" |56.9681033
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.021454
| style="text-align: center;" |56.3274813
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |-0.000002
| style="text-align: center;" |-0.0052510004
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |83.4410224
| style="text-align: center;" |-97.3535473
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |87.4239054
| style="text-align: center;" |-97.9941693
|-
| style="text-align: center;" |Cheletropic
| style="text-align: center;" |105.7656504
| style="text-align: center;" |-154.3269016
|}

The energies of the reactants, Transition States, and different products were obtained from the optimised LOG. files in GaussView, and the reaction profile is plotted showing their relative energies with the proceeding of the three reactions.

All TS and product energies are normalised with respect to reactant energy (reactant energy=0). The reaction profile is shown below.

=== Reaction Profiles ===

[[File:Yz20215 E3 reaction profile.png|x700px|700px|thumb|centre|Figure Reaction profile of three different reaction paths]]

In this profile, we could see that the '''endo TS''' is the lowest in energy, therefore will be formed faster compared with other two, and will be the '''kinetic product''' of the reaction. The Exo TS has slightly higher but close energy, while the cheletropic TS has the largest activation barrier.

However, if we compare the energies of the products, we could see that the Endo and the Exo products are very close in energy at approximately -98 kJ mol <sup>-1</sup> , while the cheletropic product is the most stable product with energy of around -154 kJ mol <sup>-1</sup> . Therefore, if we provide enough energy for the reaction to overcome its activation barrier, the '''cheletropic product''' will be the major product as it is the '''thermodynamic product''' of the reaction.

=== Files ===

= Conclusion =

During the time span of this Transition State Computational Lab, three different pericyclic reactions were investigated.

The reactions were investigated by using PM6 and B3LYP/6-31G(d) methods in GaussView to optimise the reactants, transition states, and the products.

Other information were also extracted from the optimised molecule LOG. files: including vibration frequency calculations and IRC (Intrinsic Reaction Coordinate); bond lengths of the TS, reactants and products; the energies of different species; and the molecular orbitals.

These data were used to analyse the Transition states and the reactions, including confirmation of the TS by presence of one imaginary frequency in vibration frequencies, the activation barrier and energy change of the reaction from the energies of different species, and the MOs to determine the electron demand of a certain Diels-Alder reaction (inverse or normal electron demand).

In addition, the data confirmed that the reactions followed several existing rules and theories: Woodward-Hoffmann rules in Exercise 1, Frontier Molecular Orbital Theory, etc..

These computational methods could be applied to investigate many other pericyclic reactions, where various aspects of data could be obtained and analysed as like shown in this lab.

Rep:YZ20215TS

2018-02-27T18:11:30Z

Yz20215: /* Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole */

== Introduction ==

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 2(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 2(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 2(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 3. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 4. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 5(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 5(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Therefore, in normal electron demand DA reactions, the orbitals of the electron-rich diene will be higher, therefore, favourable interaction occurs between the HOMO of diene and the LUMO of dienophile; while for inverse electron demand reactions, the LUMO of diene will interact with the HOMO of the dienophile.

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

In this reaction, due to the presence of a heterocyclic reactant, 1,3-dioxole, it is postulated that the reaction could possibly have an inverse electron demand, therefore, energy calculations were done and their single point energies determined in the following section to confirm the postulation.

==== Single point energies ====

{| class="wikitable"
|+ Table 11. Single point energies of reactants
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy of HOMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy of LUMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy difference between this HOMO and the LUMO of the other reactant/ a.u.'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |-0.20554
| style="text-align: center;" |-0.01711
| style="text-align: center;" |0.24349
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-0.19594
| style="text-align: center;" |0.03795
| style="text-align: center;" |0.17883
|}

In this reaction, the energy difference between the HOMO of the dienophile with the LUMO of diene is smaller than that of the other pair, therefore, they will give to a larger overlap of orbitals and more favourable interaciton.

Therefore, we can conclude from the data above that the reaction has an inverse electron demand. This is due to the presence of two oxygen atoms donating their lone pairs, making the dienophile electron rich.

=== Energy analysis ===

{| class="wikitable"
|+ Table 12. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 13. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 14. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
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| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure Secondary orbital interactions in both Endo and Exo TS]]
|}

=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

[[File:Yz20215 E3 scheme.png|x400px|400px|thumb|centre|Scheme 3 Diels-Alder and Cheletropic reaction between Xylylene and Sulfur dioxide]]

The reaction between xylylene and sulfur dioxide was investigated.

The reaction between the reactants could occur either via a Diels-Alder reaction or cheletropic reaction as shown above in Scheme 3. For the Diels-Alder reaction between two, the product could be formed in an Endo or an Exo conformation.

In this exercise, the reactants, Transition States and products were optimised using PM6 Method using GaussView software. Also, the energies of different species were obtained to determine the activation energy and the energy change of reaction with reaction energy profile plotted. Therefore, the most thermodynamically and the most kinetically favoured product was determined.

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 14. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 16; </script>
<uploadedFileContents>Yz20215 E3 DA endo TS.LOG</uploadedFileContents>
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|<jmol>
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<uploadedFileContents>YZ20215 E3 CHE TS.LOG</uploadedFileContents>
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|}

=== IRC calculations ===

{| class="wikitable"
|+ Table 15. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

Looking at IRC of these three reactions, we could see that the activation barrier of the reaction is quite small, this is due to one of the reactants, xylylene, being very unstable and high in energy.

This is because, according to Huckle's Rule, it has only 8 π electrons, which is (4n) instead of (4n+2), therefore, it is antiaromatic. However, due to structure constraint, both of the dienes are cis in xylylene, which is favourable as no energy expense on converting into trans conformation.

During the reaction, the xylyene part will react with the sulfur dioxide molecule to form a bicyclic ring, containing a benzene ring, which is aromatic and stable. Therefore, making it favourable to form the products.

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.021698
| style="text-align: center;" |56.9681033
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.021454
| style="text-align: center;" |56.3274813
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |-0.000002
| style="text-align: center;" |-0.0052510004
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |83.4410224
| style="text-align: center;" |-97.3535473
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |87.4239054
| style="text-align: center;" |-97.9941693
|-
| style="text-align: center;" |Cheletropic
| style="text-align: center;" |105.7656504
| style="text-align: center;" |-154.3269016
|}

The energies of the reactants, Transition States, and different products were obtained from the optimised LOG. files in GaussView, and the reaction profile is plotted showing their relative energies with the proceeding of the three reactions.

All TS and product energies are normalised with respect to reactant energy (reactant energy=0). The reaction profile is shown below.

=== Reaction Profiles ===

[[File:Yz20215 E3 reaction profile.png|x700px|700px|thumb|centre|Figure Reaction profile of three different reaction paths]]

In this profile, we could see that the endo TS is the lowest in energy, therefore will be formed faster compared with other two, and will be the kinetic product of the reaction. The Exo TS has slightly higher but close energy, while the cheletropic TS has the largest activation barrier.

However, if we compare the energies of the products, we could see that the Endo and the Exo products are very close in energy at approximately -98 kJ mol<sup>-1<sup>, while the cheletropic product is the most stable product with energy of around -154 kJ mol<sup>-1<sup>. Therefore, if we provide enough energy for the reaction to overcome its activation barrier, the cheletropic product will be the major product as it is the thermodynamic product of the reaction.

Rep:YZ20215TS

2018-02-27T17:59:02Z

Yz20215: /* IRC calculations */

== Introduction ==

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 2(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 2(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 2(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 3. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 4. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 cyclohexadiene min.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 dioxole min B3LYP.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 product ENDO B3LYP MIN.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents> Yz20215 E2 product EXO B3LYP MIN.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 TS endo TS.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 TS exo TS.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
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|<jmol>
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|<jmol>
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<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
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<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" |HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
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<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
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<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 5(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 5(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

==== Single point energies ====

{| class="wikitable"
|+ Table 11. Single point energies of reactants
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy of HOMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy of LUMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy difference between this HOMO and the LUMO of the other reactant/ a.u.'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |-0.20554
| style="text-align: center;" |-0.01711
| style="text-align: center;" |0.24349
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-0.19594
| style="text-align: center;" |0.03795
| style="text-align: center;" |0.17883
|}

=== Energy analysis ===

{| class="wikitable"
|+ Table 12. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 13. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 14. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
!<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
</jmolApplet>
</jmol>
| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure Secondary orbital interactions in both Endo and Exo TS]]
|}

=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

[[File:Yz20215 E3 scheme.png|x400px|400px|thumb|centre|Scheme 3 Diels-Alder and Cheletropic reaction between Xylylene and Sulfur dioxide]]

The reaction between xylylene and sulfur dioxide was investigated.

The reaction between the reactants could occur either via a Diels-Alder reaction or cheletropic reaction as shown above in Scheme 3. For the Diels-Alder reaction between two, the product could be formed in an Endo or an Exo conformation.

In this exercise, the reactants, Transition States and products were optimised using PM6 Method using GaussView software. Also, the energies of different species were obtained to determine the activation energy and the energy change of reaction with reaction energy profile plotted. Therefore, the most thermodynamically and the most kinetically favoured product was determined.

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 14. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E3 DA endo TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E3 DA TS exo TS PM6.log</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>YZ20215 E3 CHE TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== IRC calculations ===

{| class="wikitable"
|+ Table 15. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

Looking at IRC of these three reactions, we could see that the activation barrier of the reaction is quite small, this is due to one of the reactants, xylylene, being very unstable and high in energy.

This is because, according to Huckle's Rule, it has only 8 π electrons, which is (4n) instead of (4n+2), therefore, it is antiaromatic. However, due to structure constraint, both of the dienes are cis in xylylene, which is favourable as no energy expense on converting into trans conformation.

During the reaction, the xylyene part will react with the sulfur dioxide molecule to form a bicyclic ring, containing a benzene ring, which is aromatic and stable. Therefore, making it favourable to form the products.

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.021698
| style="text-align: center;" |56.9681033
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.021454
| style="text-align: center;" |56.3274813
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |-0.000002
| style="text-align: center;" |-0.0052510004
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |83.4410224
| style="text-align: center;" |-97.3535473
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |87.4239054
| style="text-align: center;" |-97.9941693
|-
| style="text-align: center;" |Cheletropic
| style="text-align: center;" |105.7656504
| style="text-align: center;" |-154.3269016
|}

The energies of the reactants, Transition States, and different products were obtained from the optimised LOG. files in GaussView, and the reaction profile is plotted showing their relative energies with the proceeding of the three reactions.

All TS and product energies are normalised with respect to reactant energy (reactant energy=0). The reaction profile is shown below.

=== Reaction Profiles ===

[[File:Yz20215 E3 reaction profile.png|x700px|700px|thumb|centre|Figure Reaction profile of three different reaction paths]]

In this profile, we could see that the endo TS is the lowest in energy, therefore will be formed faster compared with other two, and will be the kinetic product of the reaction. The Exo TS has slightly higher but close energy, while the cheletropic TS has the largest activation barrier.

However, if we compare the energies of the products, we could see that the Endo and the Exo products are very close in energy at approximately -98 kJ mol<sup>-1<sup>, while the cheletropic product is the most stable product with energy of around -154 kJ mol<sup>-1<sup>. Therefore, if we provide enough energy for the reaction to overcome its activation barrier, the cheletropic product will be the major product as it is the thermodynamic product of the reaction.

Rep:YZ20215TS

2018-02-27T17:40:22Z

Yz20215: /* Energy analysis */

== Introduction ==

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 2(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 2(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 2(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 3. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
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<uploadedFileContents>Yz20215 E1 BUTANDIENE MO.LOG</uploadedFileContents>
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|<jmol>
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<uploadedFileContents>YZ20215 E1 ETHYLENE MO.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
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<uploadedFileContents>YZ20215 E1 TS PM6 MO.LOG</uploadedFileContents>
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|<jmol>
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|<jmol>
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<uploadedFileContents>YZ20215 E1 CYCLOHEXENE MO.LOG</uploadedFileContents>
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|-
| style="text-align: center;" |HOMO
|<jmol>
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==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 4. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 cyclohexadiene min.LOG</uploadedFileContents>
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|<jmol>
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<script>frame 16; </script>
<uploadedFileContents> Yz20215 E2 product EXO B3LYP MIN.LOG</uploadedFileContents>
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 TS endo TS.log</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 TS exo TS.log</uploadedFileContents>
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</jmol>
|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
|<jmol>
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|<jmol>
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<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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|<jmol>
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<color>white</color>
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<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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</jmol>
|}

{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 5(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 5(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

==== Single point energies ====

{| class="wikitable"
|+ Table 11. Single point energies of reactants
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy of HOMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy of LUMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy difference between this HOMO and the LUMO of the other reactant/ a.u.'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |-0.20554
| style="text-align: center;" |-0.01711
| style="text-align: center;" |0.24349
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-0.19594
| style="text-align: center;" |0.03795
| style="text-align: center;" |0.17883
|}

=== Energy analysis ===

{| class="wikitable"
|+ Table 12. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 13. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 14. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
!<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
</jmolApplet>
</jmol>
| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure Secondary orbital interactions in both Endo and Exo TS]]
|}

=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

[[File:Yz20215 E3 scheme.png|x400px|400px|thumb|centre|Scheme 3 Diels-Alder and Cheletropic reaction between Xylylene and Sulfur dioxide]]

The reaction between xylylene and sulfur dioxide was investigated.

The reaction between the reactants could occur either via a Diels-Alder reaction or cheletropic reaction as shown above in Scheme 3. For the Diels-Alder reaction between two, the product could be formed in an Endo or an Exo conformation.

In this exercise, the reactants, Transition States and products were optimised using PM6 Method using GaussView software. Also, the energies of different species were obtained to determine the activation energy and the energy change of reaction with reaction energy profile plotted. Therefore, the most thermodynamically and the most kinetically favoured product was determined.

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 14. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
|<jmol>
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=== IRC calculations ===

{| class="wikitable"
|+ Table 15. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.021698
| style="text-align: center;" |56.9681033
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.021454
| style="text-align: center;" |56.3274813
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |-0.000002
| style="text-align: center;" |-0.0052510004
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |83.4410224
| style="text-align: center;" |-97.3535473
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |87.4239054
| style="text-align: center;" |-97.9941693
|-
| style="text-align: center;" |Cheletropic
| style="text-align: center;" |105.7656504
| style="text-align: center;" |-154.3269016
|}

The energies of the reactants, Transition States, and different products were obtained from the optimised LOG. files in GaussView, and the reaction profile is plotted showing their relative energies with the proceeding of the three reactions.

All TS and product energies are normalised with respect to reactant energy (reactant energy=0). The reaction profile is shown below.

=== Reaction Profiles ===

[[File:Yz20215 E3 reaction profile.png|x700px|700px|thumb|centre|Figure Reaction profile of three different reaction paths]]

In this profile, we could see that the endo TS is the lowest in energy, therefore will be formed faster compared with other two, and will be the kinetic product of the reaction. The Exo TS has slightly higher but close energy, while the cheletropic TS has the largest activation barrier.

However, if we compare the energies of the products, we could see that the Endo and the Exo products are very close in energy at approximately -98 kJ mol<sup>-1<sup>, while the cheletropic product is the most stable product with energy of around -154 kJ mol<sup>-1<sup>. Therefore, if we provide enough energy for the reaction to overcome its activation barrier, the cheletropic product will be the major product as it is the thermodynamic product of the reaction.

Rep:YZ20215TS

2018-02-27T17:32:28Z

Yz20215: /* Excercise 3- Diels-Alder vs Cheletropic */

== Introduction ==

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 2(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 2(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 2(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 3. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 4. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 5(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 5(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

==== Single point energies ====

{| class="wikitable"
|+ Table 11. Single point energies of reactants
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy of HOMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy of LUMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy difference between this HOMO and the LUMO of the other reactant/ a.u.'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |-0.20554
| style="text-align: center;" |-0.01711
| style="text-align: center;" |0.24349
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-0.19594
| style="text-align: center;" |0.03795
| style="text-align: center;" |0.17883
|}

=== Energy analysis ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 13. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
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| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure Secondary orbital interactions in both Endo and Exo TS]]
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=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

[[File:Yz20215 E3 scheme.png|x400px|400px|thumb|centre|Scheme 3 Diels-Alder and Cheletropic reaction between Xylylene and Sulfur dioxide]]

The reaction between xylylene and sulfur dioxide was investigated.

The reaction between the reactants could occur either via a Diels-Alder reaction or cheletropic reaction as shown above in Scheme 3. For the Diels-Alder reaction between two, the product could be formed in an Endo or an Exo conformation.

In this exercise, the reactants, Transition States and products were optimised using PM6 Method using GaussView software. Also, the energies of different species were obtained to determine the activation energy and the energy change of reaction with reaction energy profile plotted. Therefore, the most thermodynamically and the most kinetically favoured product was determined.

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 14. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
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=== IRC calculations ===

{| class="wikitable"
|+ Table 15. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.021698
| style="text-align: center;" |56.9681033
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.021454
| style="text-align: center;" |56.3274813
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |-0.000002
| style="text-align: center;" |-0.0052510004
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |83.4410224
| style="text-align: center;" |-97.3535473
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |87.4239054
| style="text-align: center;" |-97.9941693
|-
| style="text-align: center;" |Cheletropic
| style="text-align: center;" |105.7656504
| style="text-align: center;" |-154.3269016
|}

The energies of the reactants, Transition States, and different products were obtained from the optimised LOG. files in GaussView, and the reaction profile is plotted showing their relative energies with the proceeding of the three reactions.

All TS and product energies are normalised with respect to reactant energy (reactant energy=0). The reaction profile is shown below.

=== Reaction Profiles ===

[[File:Yz20215 E3 reaction profile.png|x700px|700px|thumb|centre|Figure Reaction profile of three different reaction paths]]

In this profile, we could see that the endo TS is the lowest in energy, therefore will be formed faster compared with other two, and will be the kinetic product of the reaction. The Exo TS has slightly higher but close energy, while the cheletropic TS has the largest activation barrier.

However, if we compare the energies of the products, we could see that the Endo and the Exo products are very close in energy at approximately -98 kJ mol<sup>-1<sup>, while the cheletropic product is the most stable product with energy of around -154 kJ mol<sup>-1<sup>. Therefore, if we provide enough energy for the reaction to overcome its activation barrier, the cheletropic product will be the major product as it is the thermodynamic product of the reaction.

File:Yz20215 E3 reaction profile.png

2018-02-27T17:08:59Z

Yz20215:

Rep:YZ20215TS

2018-02-27T17:06:19Z

Yz20215: /* Excercise 3- Diels-Alder vs Cheletropic */

== Introduction ==

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 2(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 2(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 2(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 3. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
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| style="text-align: center;" |HOMO
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==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 4. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 cyclohexadiene min.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 dioxole min B3LYP.log</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 product ENDO B3LYP MIN.LOG</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents> Yz20215 E2 product EXO B3LYP MIN.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 TS endo TS.log</uploadedFileContents>
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|<jmol>
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<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 TS exo TS.log</uploadedFileContents>
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</jmol>
|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
|<jmol>
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|<jmol>
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<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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</jmol>
|-
| style="text-align: center;" |HOMO
|<jmol>
<jmolApplet>
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<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
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|<jmol>
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<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
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|<jmol>
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<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 5(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 5(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

==== Single point energies ====

{| class="wikitable"
|+ Table 11. Single point energies of reactants
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy of HOMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy of LUMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy difference between this HOMO and the LUMO of the other reactant/ a.u.'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |-0.20554
| style="text-align: center;" |-0.01711
| style="text-align: center;" |0.24349
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-0.19594
| style="text-align: center;" |0.03795
| style="text-align: center;" |0.17883
|}

=== Energy analysis ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 13. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
!<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
</jmolApplet>
</jmol>
| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure Secondary orbital interactions in both Endo and Exo TS]]
|}

=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

[[File:Yz20215 E3 scheme.png|x400px|400px|thumb|centre|Scheme 3 Diels-Alder and Cheletropic reaction between Xylylene and Sulfur dioxide]]

The reaction between xylylene and sulfur dioxide was investigated.

The reaction between the reactants could occur either via a Diels-Alder reaction or cheletropic reaction as shown above in Scheme 3. For the Diels-Alder reaction between two, the product could be formed in an Endo or an Exo conformation.

In this exercise, the reactants, Transition States and products were optimised using PM6 Method using GaussView software. Also, the energies of different species were obtained to determine the activation energy and the energy change of reaction with reaction energy profile plotted. Therefore, the most thermodynamically and the most kinetically favoured product was determined.

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 14. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E3 DA endo TS.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
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<script>frame 16; </script>
<uploadedFileContents>Yz20215 E3 DA TS exo TS PM6.log</uploadedFileContents>
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<script>frame 16; </script>
<uploadedFileContents>YZ20215 E3 CHE TS.LOG</uploadedFileContents>
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|}

=== IRC calculations ===

{| class="wikitable"
|+ Table 15. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.021698
| style="text-align: center;" |56.9681033
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.021454
| style="text-align: center;" |56.3274813
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |-0.000002
| style="text-align: center;" |-0.0052510004
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |83.4410224
| style="text-align: center;" |-97.3535473
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |87.4239054
| style="text-align: center;" |-97.9941693
|-
| style="text-align: center;" |Cheletropic
| style="text-align: center;" |105.7656504
| style="text-align: center;" |-154.3269016
|}

=== Reaction Profiles ===

File:Yz20215 E3 scheme.png

2018-02-27T16:53:33Z

Yz20215:

Rep:YZ20215TS

2018-02-27T16:22:42Z

Yz20215: /* Activation and Reaction Energy calculations */

== Introduction ==

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 2(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 2(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 2(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 3. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 4. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
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<uploadedFileContents>Yz20215 E2 cyclohexadiene min.LOG</uploadedFileContents>
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 5(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 5(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

==== Single point energies ====

{| class="wikitable"
|+ Table 11. Single point energies of reactants
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy of HOMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy of LUMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy difference between this HOMO and the LUMO of the other reactant/ a.u.'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |-0.20554
| style="text-align: center;" |-0.01711
| style="text-align: center;" |0.24349
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-0.19594
| style="text-align: center;" |0.03795
| style="text-align: center;" |0.17883
|}

=== Energy analysis ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 13. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
!<jmol>
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| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure Secondary orbital interactions in both Endo and Exo TS]]
|}

=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 14. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
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=== IRC calculations ===

{| class="wikitable"
|+ Table 15. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.021698
| style="text-align: center;" |56.9681033
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.021454
| style="text-align: center;" |56.3274813
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |-0.000002
| style="text-align: center;" |-0.0052510004
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |83.4410224
| style="text-align: center;" |-97.3535473
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |87.4239054
| style="text-align: center;" |-97.9941693
|-
| style="text-align: center;" |Cheletropic
| style="text-align: center;" |105.7656504
| style="text-align: center;" |-154.3269016
|}

=== Reaction Profiles ===

Rep:YZ20215TS

2018-02-27T16:18:56Z

Yz20215: /* Activation and Reaction Energy calculations */

== Introduction ==

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 2(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 2(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 2(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 3. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 4. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 5(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 5(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

==== Single point energies ====

{| class="wikitable"
|+ Table 11. Single point energies of reactants
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy of HOMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy of LUMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy difference between this HOMO and the LUMO of the other reactant/ a.u.'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |-0.20554
| style="text-align: center;" |-0.01711
| style="text-align: center;" |0.24349
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-0.19594
| style="text-align: center;" |0.03795
| style="text-align: center;" |0.17883
|}

=== Energy analysis ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 13. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
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| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure Secondary orbital interactions in both Endo and Exo TS]]
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=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 14. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
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=== IRC calculations ===

{| class="wikitable"
|+ Table 15. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.021698
| style="text-align: center;" |56.9681033
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.021454
| style="text-align: center;" |56.3274813
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |
| style="text-align: center;" |
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |83.4410224
| style="text-align: center;" |-97.3535473
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |87.4239054
| style="text-align: center;" |-97.9941693
|-
| style="text-align: center;" |Cheletropic
| style="text-align: center;" |105.7656504
| style="text-align: center;" |
|}

=== Reaction Profiles ===

Rep:YZ20215TS

2018-02-27T16:11:50Z

Yz20215: /* Activation and Reaction Energy calculations */

== Introduction ==

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 2(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 2(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 2(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 3. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
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| style="text-align: center;" |HOMO
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==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 4. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 cyclohexadiene min.LOG</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 dioxole min B3LYP.log</uploadedFileContents>
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|<jmol>
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|<jmol>
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<script>frame 16; </script>
<uploadedFileContents> Yz20215 E2 product EXO B3LYP MIN.LOG</uploadedFileContents>
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</jmol>
|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
|<jmol>
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
|<jmol>
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|-
| style="text-align: center;" |HOMO
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<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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|}

{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 5(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 5(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

==== Single point energies ====

{| class="wikitable"
|+ Table 11. Single point energies of reactants
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy of HOMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy of LUMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy difference between this HOMO and the LUMO of the other reactant/ a.u.'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |-0.20554
| style="text-align: center;" |-0.01711
| style="text-align: center;" |0.24349
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-0.19594
| style="text-align: center;" |0.03795
| style="text-align: center;" |0.17883
|}

=== Energy analysis ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 13. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
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</jmolApplet>
</jmol>
| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure Secondary orbital interactions in both Endo and Exo TS]]
|}

=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 14. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
|<jmol>
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<script>frame 16; </script>
<uploadedFileContents>Yz20215 E3 DA endo TS.LOG</uploadedFileContents>
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|}

=== IRC calculations ===

{| class="wikitable"
|+ Table 15. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |0.178047
| style="text-align: center;" |467.462434
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.021698
| style="text-align: center;" |56.9681033
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.021454
| style="text-align: center;" |56.3274813
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |
| style="text-align: center;" |
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

=== Reaction Profiles ===

Rep:YZ20215TS

2018-02-27T16:09:16Z

Yz20215: /* Single point energies */

== Introduction ==

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 2(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 2(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 2(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 3. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 4. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 cyclohexadiene min.LOG</uploadedFileContents>
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|<jmol>
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<uploadedFileContents>Yz20215 E2 dioxole min B3LYP.log</uploadedFileContents>
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<script>frame 16; </script>
<uploadedFileContents> Yz20215 E2 product EXO B3LYP MIN.LOG</uploadedFileContents>
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
|<jmol>
<jmolApplet>
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<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 TS endo TS.log</uploadedFileContents>
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|<jmol>
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<uploadedFileContents>Yz20215 E2 TS exo TS.log</uploadedFileContents>
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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|}

{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 5(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 5(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

==== Single point energies ====

{| class="wikitable"
|+ Table 11. Single point energies of reactants
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy of HOMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy of LUMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy difference between this HOMO and the LUMO of the other reactant/ a.u.'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |-0.20554
| style="text-align: center;" |-0.01711
| style="text-align: center;" |0.24349
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-0.19594
| style="text-align: center;" |0.03795
| style="text-align: center;" |0.17883
|}

=== Energy analysis ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 13. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
!<jmol>
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<uploadedFileContents>yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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</jmolApplet>
</jmol>
| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure Secondary orbital interactions in both Endo and Exo TS]]
|}

=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 14. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
|<jmol>
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<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E3 DA endo TS.LOG</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
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<script>frame 16; </script>
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|<jmol>
<jmolApplet>
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<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>YZ20215 E3 CHE TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== IRC calculations ===

{| class="wikitable"
|+ Table 15. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |
| style="text-align: center;" |
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.021698
| style="text-align: center;" |56.9681033
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.021454
| style="text-align: center;" |56.3274813
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |
| style="text-align: center;" |
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

=== Reaction Profiles ===

Rep:YZ20215TS

2018-02-27T16:05:57Z

Yz20215: /* Single point energies */

== Introduction ==

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 2(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 2(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 2(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 3. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 4. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 5(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 5(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

==== Single point energies ====

{| class="wikitable"
|+ Table 11. Single point energies of reactants
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy of HOMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy of LUMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy difference between this HOMO and the LUMO of the other reactant/ a.u.'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |-0.20554
| style="text-align: center;" |-0.01711
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|}

=== Energy analysis ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 13. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
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| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure Secondary orbital interactions in both Endo and Exo TS]]
|}

=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 14. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
|<jmol>
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<script>frame 16; </script>
<uploadedFileContents>Yz20215 E3 DA endo TS.LOG</uploadedFileContents>
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|<jmol>
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<uploadedFileContents>YZ20215 E3 CHE TS.LOG</uploadedFileContents>
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=== IRC calculations ===

{| class="wikitable"
|+ Table 15. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |
| style="text-align: center;" |
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.021698
| style="text-align: center;" |56.9681033
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.021454
| style="text-align: center;" |56.3274813
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |
| style="text-align: center;" |
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

=== Reaction Profiles ===

Rep:YZ20215TS

2018-02-27T16:03:13Z

Yz20215: /* Activation and Reaction Energy calculations */

== Introduction ==

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 2(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 2(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 2(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 3. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 4. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 5(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 5(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

==== Single point energies ====

{| class="wikitable"
|+ Table 11. Single point energies of reactants
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy of HOMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy of LUMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy difference between this HOMO and the LUMO of the other reactant/ a.u.'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|}

=== Energy analysis ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 13. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
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| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure Secondary orbital interactions in both Endo and Exo TS]]
|}

=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 14. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
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=== IRC calculations ===

{| class="wikitable"
|+ Table 15. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |
| style="text-align: center;" |
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.021698
| style="text-align: center;" |56.9681033
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |0.021454
| style="text-align: center;" |56.3274813
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |
| style="text-align: center;" |
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

=== Reaction Profiles ===

Rep:YZ20215TS

2018-02-27T16:02:16Z

Yz20215: /* Single point energies */

== Introduction ==

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 2(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 2(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 2(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 3. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
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| style="text-align: center;" |HOMO
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==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 4. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 cyclohexadiene min.LOG</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 dioxole min B3LYP.log</uploadedFileContents>
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|<jmol>
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<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 product ENDO B3LYP MIN.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
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<script>frame 16; </script>
<uploadedFileContents> Yz20215 E2 product EXO B3LYP MIN.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
|<jmol>
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<uploadedFileContents>Yz20215 E2 TS endo TS.log</uploadedFileContents>
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|<jmol>
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<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 TS exo TS.log</uploadedFileContents>
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</jmol>
|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
|<jmol>
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|<jmol>
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<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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|-
| style="text-align: center;" |HOMO
|<jmol>
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<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
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|<jmol>
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<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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|<jmol>
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<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
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</jmol>
|}

{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 5(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 5(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

==== Single point energies ====

{| class="wikitable"
|+ Table 11. Single point energies of reactants
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy of HOMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy of LUMO/ a.u.'''
| style="text-align: center; background: #2d918b;"|'''Energy difference between this HOMO and the LUMO of the other reactant/ a.u.'''
|-
| style="text-align: center;" |Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|}

=== Energy analysis ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 13. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
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</jmolApplet>
</jmol>
| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure Secondary orbital interactions in both Endo and Exo TS]]
|}

=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 14. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
|<jmol>
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<script>frame 16; </script>
<uploadedFileContents>Yz20215 E3 DA endo TS.LOG</uploadedFileContents>
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|<jmol>
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<uploadedFileContents>YZ20215 E3 CHE TS.LOG</uploadedFileContents>
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</jmol>
|}

=== IRC calculations ===

{| class="wikitable"
|+ Table 15. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |
| style="text-align: center;" |
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.021698
| style="text-align: center;" |56.9681033
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |
| style="text-align: center;" |
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |
| style="text-align: center;" |
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

=== Reaction Profiles ===

Rep:YZ20215TS

2018-02-27T15:21:06Z

Yz20215: /* Activation and Reaction Energy calculations */

== Introduction ==

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 2(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 2(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 2(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 3. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 4. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 5(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 5(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

==== Single point energies ====

=== Energy analysis ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 13. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
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| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure Secondary orbital interactions in both Endo and Exo TS]]
|}

=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 14. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
|<jmol>
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<uploadedFileContents>Yz20215 E3 DA endo TS.LOG</uploadedFileContents>
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<uploadedFileContents>YZ20215 E3 CHE TS.LOG</uploadedFileContents>
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=== IRC calculations ===

{| class="wikitable"
|+ Table 15. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |
| style="text-align: center;" |
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |0.021698
| style="text-align: center;" |56.9681033
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |
| style="text-align: center;" |
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |
| style="text-align: center;" |
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

=== Reaction Profiles ===

Rep:YZ20215TS

2018-02-27T12:59:31Z

Yz20215: /* Activation and Reaction Energy calculations */

== Introduction ==

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 2(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 2(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 2(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 3. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
|<jmol>
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|-
| style="text-align: center;" |HOMO
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==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 4. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
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|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 5(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 5(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

==== Single point energies ====

=== Energy analysis ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 13. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
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| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure Secondary orbital interactions in both Endo and Exo TS]]
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=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 14. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
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=== IRC calculations ===

{| class="wikitable"
|+ Table 15. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

=== Activation and Reaction Energy calculations ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Xylylene
| style="text-align: center;" |
| style="text-align: center;" |
|-
| style="text-align: center;" |Reactant: Sulfur dioxide
| style="text-align: center;" |-0.119269
| style="text-align: center;" |-313.1407834
|-
| style="text-align: center;" |DA: Endo TS
| style="text-align: center;" |0.090559
| style="text-align: center;" |237.762673
|-
| style="text-align: center;" |DA: Exo TS
| style="text-align: center;" |0.092076
| style="text-align: center;" |241.745556
|-
| style="text-align: center;" |Cheletropic: TS
| style="text-align: center;" |0.099062
| style="text-align: center;" |260.087301
|-
| style="text-align: center;" |DA: Endo Product
| style="text-align: center;" |
| style="text-align: center;" |
|-
| style="text-align: center;" |DA: Exo Product
| style="text-align: center;" |
| style="text-align: center;" |
|-
| style="text-align: center;" |Cheletropic Product
| style="text-align: center;" |
| style="text-align: center;" |
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

=== Reaction Profiles ===

Rep:YZ20215TS

2018-02-27T12:34:57Z

Yz20215: /* Excercise 3- Diels-Alder vs Cheletropic */

== Introduction ==

== Excercise 1- Diels-Alder reaction of butadiene with ethylene ==

[[File:Yz20215 E1 scheme.png|centre|thumb|Scheme 1 Diels-Alder reaction of butadiene and ethylene to form cyclohexene]]

This reaction is a classical [4+2] cycloaddition (Diels-Alder) reaction. In this reaction, cis-butadiene reacts with ethylene to form cyclohexene with complete regioselectivity because there are no substituents attached to the reactants.

In Excercise 1, this reaction was investigated and analysed by optimising the reactants, products, and the Transition State to a minimum using PM6 Method in GaussView 5.0.9 software. In addition, their MOs and vibration frequencies, as well as the IRC (Intrinsic Reaction Coordinate) were obtained and analysed.

=== Optimisation ===

==== Optimisation of reactants and products at PM6 level====

{| class="wikitable"
|+ Table 1. Optimisation of reactants and products
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Product'''
|-
| style="text-align: center;" |Reactant: Butadiene
| style="text-align: center;" |Reactant: Ethlyene
| style="text-align: center;" |Product: Cyclohexene
|-
| [[File:Yz20215 E1 butadiene.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E1 ethylene.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E1 cyclohexene.PNG|x400px|400px|Position:centre]]
|}

==== Optimisation of transition state at PM6 level====

{| class="wikitable"
|+ Table 2. Optimisation of TS
| colspan="2" style="text-align: center; background: #2d918b;"| '''Optimisation of Transition State'''
|-
| style="text-align: center;" |Transition state
|-
| [[File:Yz20215 E1 transition state.PNG|x400px|400px|Position:centre]]
|}
=== Confirmation of correst TS using frequency calculation and IRC ===

{| class="wikitable"
|+ Table 3. IRC of the transition state
| colspan="2" style="text-align: center; background: #2d918b;" | '''Frequency calculations and IRC'''
|-
| style="text-align: center;" |Vibration frequencies of the TS
| style="text-align: center;" |IRCs
|-
| [[File:Yz20215 E1 TS vibs.PNG|x400px|400px|centre|thumb|Figure 2(a) Vibration frequencies of the TS]]
| [[File:TS IRC TOTAL E.png|x400px|400px|centre|thumb|Figure 2(b) Total energy along IRC]][[File:TS IRC RMS GRA.png|x400px|400px|centre|thumb|Figure 2(c) RMS gradient along IRC]]
|}

'''Vibration frequencies:'''

'''One imaginary frequency of -948.73 cm <sup>-1</sup>''' confirming the presence of the transition state (a saddle point- the maximum point on the minimum energy path on the PES)

'''IRC:'''

RMS gradient Norm of 0 at reactants, products, as well as the transition state. The middle point with 0 gradient corresponding to the maximum energy point on IRC Total Energy curve, indicating transition state.

=== MO analysis===

[[File:Yz20215 E1 TS Mo diagram.png|centre|thumb|Figure 3. MO of transition state of this reaction]]

{| class="wikitable"
|+ Table 4. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |TS(LUMO and HOMO)
| style="text-align: center;" |TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Cyclohexene
|-
| style="text-align: center;" |LUMO
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|-
| style="text-align: center;" |HOMO
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==== Symmetries and MO interactions ====

In a reaction, only orbitals with the same symmetry are able to overlap and form new MOs.

The orbital symmetry will be determined by its structure and symmetry label:

for a certain orbital to be '''symmetric''', it will have a plane of symmetry ('''σ<sub>v</sub> plane''')

for a certain orbital to be '''asymmetric''', it will have a axis of symmetry ('''C2 axis''')

The orbital overlap integral will be either zero or non-zero with different interactions between symmetric and asymmetric orbitals, zero indicating no interaction between, while non-zero integral indicates existing interaction between two orbitals.The values of orbital overlap integrals are shown as below:

'''symmetric-antisymmetric interaction: zero'''

'''symmetric-symmetric interaction: non-zero'''

'''antisymmetric-antisymmetric interaction: non-zero'''

In this reaction, as we could see from above, the asymmetric orbitals '''(diene HOMO and dienophile LUMO''') will interact with each other to give '''asymmetric HOMO-1 and LUMO+1''' orbitals of the transition state; while the symmetric orbitals ('''diene LUMO and dienophile HOMO''') will interact to give '''symmetric HOMO and LUMO''' of the transition state. The HOMO of diene interacts with the LUMO of dienophile to give a better overlap due to a smaller energy gap between these two orbitals. In addition, the antibonding MOs will be stabilised more than that the bonding MOs are stablised.

Among these two interactions, four new MOs will be formed, indicated by the dotted energy levels. However, the true MOs of the TS, indicated by the solid levels, are higher(HOMO and HOMO-1) /lower (LUMO and LUMO+1) than that predicted. This was possibly due to MO mixing, also, because of this MO is of the transition state of the reaction, which is the maximum point on the minimum energy path, therefore, the energy of the MOs will be higher.

In this [4+2] cycloaddition, two new bonds are formed on the same face of the two set of orbitals, in other words, suprafacially. This is in accordance with the Woodward-Hoffmann Rules, where the reaction is only thermally allowed when an '''odd number''' is obtained from the equation below:

{| width=30%
|<pre>
(4q + 2)s+ (4r)a

=1 + 0

=1

</pre>

s is for suprafacial, a is for antarafacial, and q and r are two constants representing the number of each component. In this reaction, the diene has 4 suprafacial pi electrons, contributing 0 to the equation; while the dienophile has 2 pi suprafacial electrons, contributing 1 to the equation.

Therefore, the reaction has a sum of 1, indicating this reaction is thermally allowed by Woodward-Hoffmann Rule.

=== Bond lengths ===
{| class="wikitable"
|+ Table 5. Bond lengths analysis
| colspan="4" style="text-align: center; background: #2d918b;"| '''Bond length values of reactants, TS, and product'''
|-
| style="text-align: center;" |Butadiene
| style="text-align: center;" |Ethylene
| style="text-align: center;" |Transition state
| style="text-align: center;" |Cyclohexene
|-
| [[File:Yz20215 E1 butadiene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ethylene bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 ts bond len.PNG|x300px|300px|centre]]
| [[File:Yz20215 E1 product bond len.PNG|x300px|300px|centre]]
|-
| style="text-align: center;" |C1=C2 1.335 Å
C2-C3 1.468 Å

C3=C4 1.335 Å
| style="text-align: center;" |C1=C2 1.331 Å
| style="text-align: center;" |C1=C2 1.380 Å
C2=C3 1.411 Å

C3=C4 1.380 Å

C4=C5 2.115 Å

C5=C6 1.382 Å

C6=C1 2.114 Å
| style="text-align: center;" |C1-C2 1.500 Å

C2=C3 1.338 Å

C3-C4 1.500 Å

C4-C5 1.540 Å

C5-C6 1.541 Å

C6-C1 1.540 Å
|}

{| class="wikitable"
|+ Table 6. Standard values of C-C bonds and VdW radius
| colspan="2" style="text-align: center; background: #2d918b;" | '''Typical C-C bond lengths and Ver der Waals' radius'''
|-
| style="text-align: center;" |C-C bond lengths / Å
| style="text-align: center;" |Van der Waals' radius of carbon / Å
|-
| style="text-align: center;" |sp<sup>3</sup>-sp<sup>3</sup> C-C: 1.54

sp<sup>3</sup>-sp<sup>2</sup> C-C: 1.50

sp<sup>2</sup>-sp<sup>2</sup> C-C: 1.47

sp<sup>2</sup>-sp<sup>2</sup> C=C: 1.34
| style="text-align: center;" |1.7
|}

The bond lengths of the reactants, product, and transition state are shown above in Table 2, while the data of typical C-C bond lengths and the Van der Waal's radius of Carbon are shown in Table 3 above.

Comparing the typical values of the carbon-carbon bonds and the experimental results obtained using Gaussview, we could see that for all three molecules of reactants and products (butadiene, ethylene and cyclohexene) have C-C bond lengths same as or very close to that of the standard values.

'''Transition State:'''

Comparison with reactants:

'''Butadiene fragment:'''

1. Lengthening of terminal C=C (C1=C2 AND C3=C4)

2. Shortening of middle C-C (C2-C3)

The terminal C=C bonds of butadiene have longer lengths of around 1.380 Å compared that of the typical value of 1.340 Å of sp<sup>2</sup>-sp<sup>2</sup> C=C bonds, and the original sp<sup>2</sup>-sp<sup>2</sup> C-C bond has a smaller observed value of 1.411 Å (standard value of 1.47 Å).

'''Ethylene fragment:'''

1. Lengthening of C=C (C1=C2, shown as C5=C6 in TS)

'''Between two reactants:'''

The distances between terminal carbon atoms of butadiene and ethylene in the TS are both at around 2.115 Å, which is much smaller than sum of two carbon atoms' Van der Waals' radius of 3.4 Å. It is also larger than the typical value of sp<sup>3</sup>-sp<sup>3</sup> C-C bond, which shows that the bonds are only partially formed.

All of these bond lengths obtained from Gaussview show that the reaction is at its transition state with two '''new sp<sup>3</sup>-sp<sup>3</sup> C-C bonds being formed''' between the terminal carbon atoms, as well as the '''dissociation of two sp<sup>2</sup>-sp<sup>2</sup> C=C bonds into sp<sup>2</sup>-sp<sup>2</sup> C-C bonds'''.

=== Vibrations ===

[[File:Yz20215 E1 TS vib.gif|x300px|300px|centre|thumb|Figure 4. Vibration of the TS]]

The vibration frequency is -948.73 x<sup>-1</sup> , as shown as the first vibration in Figure 2(a).

The formation of the two C-C bonds are synchronous, as we could see in the gif in Figure above that the terminals carbon atoms vibrate towards each other to form the new bonds.

=== Files ===

Optimised LOG File for butadiene: [[File:Yz20215 E1 BUTANDIENE MO.LOG]]

Optimised LOG File for ethylene: [[File:YZ20215 E1 ETHYLENE MO.LOG]]

Optimised LOG File for Transition State: [[File:YZ20215 E1 TS PM6 MO.LOG]]

Optimised LOG File for cyclohexene: [[File:YZ20215 E1 CYCLOHEXENE MO.LOG]]

IRC of the Transition State: [[File:Yz20215 E1 TS PM6 IRC.LOG]]

== Excercise 2- Diels-Alder reaction of cyclohexadiene and 1,3-dioxole ==

[[File:Yz20215 E2 mechanism.png|centre|thumb|Scheme 2 Diels-Alder reaction of Cyclohexadiene and 1,3-dioxole]]

In Exercise 2, the Diels-Alder/[4+2] cycloaddition of cyclohexadiene and 1,3 dioxole was investigated.

Compared with the Diels-Alder reaction in Exercise 1, in E2, both reactants in E2 are consisted of ring structures, rendering them the ability to react both in endo and exo conformations to form two products.

In this excercise, the reactants, products, and Transition states (both endo and exo) were optimised with Method 3 in tutorial using B3LYP/6-31G(d) method in Gaussview software.

In addition, the vibration frequencies, energies and MOs of the molecules were obtained and analysed through optimising the structures.

=== Optimisation of reactants and products ===

{| class="wikitable"
|+ Table 7. Optimisation of reactants and products using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of Reactants and Products'''
|-
|
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |Product: Endo Product
| style="text-align: center;" |Product: Exo Product
|-
| style="text-align: center;" |Structures
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 cyclohexadiene min.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 dioxole min B3LYP.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 product ENDO B3LYP MIN.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents> Yz20215 E2 product EXO B3LYP MIN.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 cyclohexadiene vib.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 dioxole vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 Product endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File: Yz20215 E2 Product exo vib freq.PNG|x400px|400px|Position:centre]]
|}

There are no imaginary frequencies for all the reactants and products, as they are at the local minimum point of energy.

=== Optimisation of Exo and Endo Transition States using B3LYP method===

{| class="wikitable"
|+ Table 8. Optimisation of TS using B3LYP/6-31G(d)
| colspan="5" style="text-align: center; background: #2d918b;" | '''Optimisation of endo and exo TS'''
|-
|
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| style="text-align: center;" |Structures
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 TS endo TS.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E2 TS exo TS.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" |Vibration Frequencies
| [[File:Yz20215 E2 TS endo vib freq.PNG|x400px|400px|Position:centre]]
| [[File:Yz20215 E2 TS exo vib freq.PNG|x400px|400px|Position:centre]]
|}

In either list of vibration frequency, there is one imaginary frequency, representing a saddle point of Transition State (local maximum point on the minimum energy path on PES).

=== MO analysis ===

{| class="wikitable"
|+ Table 9. MOs of reactants, TS and products
|-
| style="text-align: center;" |
| style="text-align: center;" |Endo TS(LUMO and HOMO)
| style="text-align: center;" |Endo TS(LUMO+1 and HOMO-1)
| style="text-align: center;" |Exo TS(LUMO and HOMO)
| style="text-align: center;" |Exo TS(LUMO+1 and HOMO-1)
|-
| style="text-align: center;" |LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| style="text-align: center;" |HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS exo TS MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|+ Table 10. MO diagrams for both TS
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |Exo TS
|-
| [[File:Yz20215 E2 MO Endo.png|x400px|400px|centre|thumb|Figure 5(a). MO diagram for Endo TS]]
| [[File:YZ20215 E2 MO EXO.png|x400px|400px|centre|thumb|Figure 5(b). MO diagram for Exo TS]]
|}

==== Normal VS Inverse electron demand ====

In [4+2] cycloadditions, there are two types of electron demand:

'''Normal''' electron demand: '''Electron-rich diene''' and '''Electron-poor dienophile'''

'''Inverse''' electron demand: '''Electron-poor diene''' and '''Electron-rich dienophile'''

Generally, carbon-based rings formed in Diels-Alder reactions usually have normal electron demand, while heterocycles formed with DA reaction tends to have an inverse electron demand, as the presence of heteroatoms contributing and changing the energies of the orbtials, leading to different interactions between HOMOs and LUMOs.

==== Single point energies ====

=== Energy analysis ===

{| class="wikitable"
|+ Table 11. Energies of reactants, TS, and products
|-
| style="text-align: center; background: #2d918b;"|'''Identity'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ Hartree/Particle'''
| style="text-align: center; background: #2d918b;"|'''Energy obtained using B3LYP/6-31G(d) Method/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Reactant: Cyclohexadiene
| style="text-align: center;" |-233.324375
| style="text-align: center;" |-612593.193227
|-
| style="text-align: center;" |Reactant: 1,3-dioxole
| style="text-align: center;" |-267.068642
| style="text-align: center;" |-701188.772985
|-
| style="text-align: center;" |Endo TS
| style="text-align: center;" |-500.332151
| style="text-align: center;" |-1313622.16252
|-
| style="text-align: center;" |Exo TS
| style="text-align: center;" |-500.329165
| style="text-align: center;" |-1313614.32277
|-
| style="text-align: center;" |Endo Product
| style="text-align: center;" |-500.418702
| style="text-align: center;" |-1313849.40218
|-
| style="text-align: center;" |Exo Product
| style="text-align: center;" |-500.417322
| style="text-align: center;" |-1313845.77899
|}

{| class="wikitable"
|+ Table 12. Activation energies and reaction energies
|-
| style="text-align: center; background: #2d918b;"|'''Product'''
| style="text-align: center; background: #2d918b;"|'''Activation Energy/ kJ mol<sup>-1<sup>'''
| style="text-align: center; background: #2d918b;"|'''ΔG of reaction/ kJ mol<sup>-1<sup>'''
|-
| style="text-align: center;" |Endo
| style="text-align: center;" |159.803692
| style="text-align: center;" |-67.435968
|-
| style="text-align: center;" |Exo
| style="text-align: center;" |167.643442
| style="text-align: center;" |-63.812778
|}

In a certain reaction, the kinetic product has a lower activation energy therefore will be formed faster, while the thermodynamic product is itself lower in energy, therefore, will be the major product if enough energy is provided to overcome the higher activation barrier.

In this reaction, the activation barrier is lower for the Endo product, hence it is the kinetically favoured product. Furthermore, the ΔG of reaction (which is the energy difference between reactants and the product) is also more negative, indicating a more stable product. Therefore, the Endo product is also the thermodynamically favoured product.

Therefore, the '''Endo product is both kinetically and thermodynamically favoured product.'''

==== Secondary Orbital Interaction ====

The Endo product being both the kinetic and thermodynamic product is possibly due to the stablisation from secondary orbital interactions between the p orbitals on the oxygen atoms and the π orbitals of the diene, which only takes place when the TS is in Endo conformation.

For Exo conformation, the 1,3-dioxole molecule points outwards and is unavailable to interact with the cyclohexadiene molecule.

The secondary orbital interactions of both the Endo and Exo TS are shown below in Table 9, as well as graph illustration.

{| class="wikitable"
|+ Table 13. Secondary orbital interactions
| colspan="3" style="text-align: center; background: #2d918b;" | '''MOs and graph of secondary interaction'''
|-
| style="text-align: center;" |HOMO for Endo TS
| style="text-align: center;" |HOMO for Exo TS
| style="text-align: center;" |Graph illustrating secondary orbital interactions
|-
!<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41; mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>yz20215 E2 TS exo TS MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 2; mo 41;mo cutoff 0.01 mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Yz20215 E2 TS endo TS MO 1.log</uploadedFileContents>
</jmolApplet>
</jmol>
| [[File:E2 Secondary orbital interaction.png|x400px|400px|centre|thumb|Figure Secondary orbital interactions in both Endo and Exo TS]]
|}

=== Files ===

Optimised LOG File for cyclohexadiene: [[File:Yz20215 E2 cyclohexadiene min.LOG]]

Optimised LOG File for 1,3-dioxole: [[File:Yz20215 E2 dioxole min B3LYP.log]]

Optimised LOG File for Endo Transition State: [[File:Yz20215 E2 TS endo TS MO 1.log]]

Optimised LOG File for Exo Transition State: [[File:Yz20215 E2 TS exo TS.log]]

Optimised LOG File for Endo product: [[File:Yz20215 E2 product ENDO B3LYP MIN.LOG]]

Optimised LOG File for Exo product: [[File:Yz20215 E2 product EXO B3LYP MIN.LOG]]

== Excercise 3- Diels-Alder vs Cheletropic ==

=== Optimisation of Transitions States using PM6 Method ===

{| class="wikitable"
|+ Table 14. Optimisation of TSs using PM6
| colspan="3" style="text-align: center; background: #2d918b;" | '''Optimisation of Transition states'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Cheletropic
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E3 DA endo TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>Yz20215 E3 DA TS exo TS PM6.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>350</size>
<script>frame 16; </script>
<uploadedFileContents>YZ20215 E3 CHE TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== IRC calculations ===

{| class="wikitable"
|+ Table 15. Animations and IRC for TSs
| colspan="3" style="text-align: center; background: #2d918b;" | '''Gif animations and IRC diagrams for Transition States'''
|-
| style="text-align: center;" |Diels-Alder: Endo TS
| style="text-align: center;" |Diels-Alder: Exo TS
| style="text-align: center;" |Cheletropic TS
|-
| [[File:Yz20215 E3 endo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 exo movie.gif|x450px|450px|centre]]
| [[File:Yz20215 E3 Che movie.gif|x450px|450px|centre]]
|-
| [[File:Yz20215 E3 endo IRC 1.PNG|x600px|600px|centre]]
| [[File:YZ20215 E3 exo IRC.PNG|x600px|600px|centre]]
| [[File: YZ20215 E3 che IRC.PNG|x600px|600px|centre]]
|}

=== Activation and Reaction Energy calculations ===

=== Reaction Profiles ===

File:Yz20215 E3 endo IRC 1.PNG

2018-02-27T12:33:02Z

Yz20215:

File:Yz20215 E3 exo movie.gif

2018-02-27T12:21:40Z

Yz20215:

File:Yz20215 E3 endo movie.gif

2018-02-27T12:21:39Z

Yz20215:

File:Yz20215 E3 Che movie.gif

2018-02-27T12:21:39Z

Yz20215:

File:YZ20215 E3 che IRC.PNG

2018-02-27T11:56:14Z

Yz20215:

File:Yz20215 E3 endo IRC.PNG

2018-02-27T11:56:13Z

Yz20215:

File:YZ20215 E3 exo IRC.PNG

2018-02-27T11:53:22Z

Yz20215:

File:YZ20215 E3 exo IRC RMS gradient 1.png

2018-02-27T11:51:02Z

Yz20215: