ChemWiki - User contributions [en]

Rep:MOD:XZ9215

2018-01-30T14:34:14Z

Xz9215: /* Conclusion */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 3, and IRC of transition state is shown on figure 4.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant. The left stationary point is the product and the right one represents reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 5.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
The C-C bond lengths of the reactants, product and the TS are shown on table 4, the standard C-C bond lengths and the Van der Waals radius of the C atom are presented on table 5.

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on the last picture on table 4, the frequency is -948.50cm<sup>-1</sup> (figure 3). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

====<u>Optimisation at B3LYP/6-31G(d)</u>====

The reactants, product, endo and exo transition state were optimized at B3LYP/6-31G(d) level, and the structures of the optimized geometry are shown on table 6.

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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====<u>Frequency analysis</u>====

{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for both endo and exo TS, and it can be confirmed that all TS were correctly optimised.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
|-
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|-
|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
|-
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity (shown on table 8). Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MO energies calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 12.

{| class="wikitable"
|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at PM6 / kJmol<sup>-1</sup>'''
| '''Substrates'''
| '''Gibbs free energy at PM6 / kJmol<sup>-1</sup>'''
| '''Substrates'''
| '''Gibbs free energy at PM6 / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
| '''Cheletropic-TS'''
| style="text-align: center;" |262.093
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 15.
According to the IRC on table 13 and the data in table 15, the small activation energy might due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure 9 shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-31G(d) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the MO energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be recognised, which has the lowest activation energy and reaction energy. The reaction with lowest activation energy is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, by building molecules or reactive systems in Guassview, we can graphically examine results (single point energy, bond length, dipole moment, geometry optimization, frequency, reaction path following, etc) which enables us to solve the chemical problems more efficiently, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Exercise 1 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 2 files
|-
|Cyclohexadiene
|[[File:XZ9215CYCLOHEXDIENE.LOG]]
|-
|1,3-dioxole
|[[File:XZ921513DIOXOLE.LOG]]
|-
|Exo TS
|[[File:XZ9215E2EXODIOXOLE TS POP.LOG]]
|-
|Endo TS
|[[File:XZ9215E2endoTS POP.LOG]]
|-
|Exo product
|[[File:XZ9215 exo EXODIOXOLE 631GD.LOG]]
|-
|Endo product
|[[File:XZ9215endo1133 TS 631GD.LOG]]
|}

{| class="wikitable"
|+ Exercise 3 files
|-
|Endo TS
|[[File:XZ9215E3 D-A ENDO TS.LOG]]
|-
|Exo TS
|[[File:XZ9215E3 D-A EXO TS.LOG]]
|-
|Cheletropic TS
|[[File:XZ9215 E3 cheletropic PRODUCT TS.LOG]]
|-
|Endo IRC
|[[File:XZ9215 E3ENDO IRC.LOG]]
|-
|Exo IRC
|[[File:XZ9215 E3 EXO IRC.LOG]]
|-
|Cheletropic IRC
|[[File:XZ9215 E3 PRODUCT IRC.LOG]]
|}

Rep:MOD:XZ9215

2018-01-30T14:01:38Z

Xz9215: /* Reaction barrier and reaction energy */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
|<jmol>
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<script>frame 52; </script>
<uploadedFileContents>XZ9215BUTADIENE.LOG</uploadedFileContents>
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|<jmol>
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 3, and IRC of transition state is shown on figure 4.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant. The left stationary point is the product and the right one represents reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 5.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
The C-C bond lengths of the reactants, product and the TS are shown on table 4, the standard C-C bond lengths and the Van der Waals radius of the C atom are presented on table 5.

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on the last picture on table 4, the frequency is -948.50cm<sup>-1</sup> (figure 3). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

====<u>Optimisation at B3LYP/6-31G(d)</u>====

The reactants, product, endo and exo transition state were optimized at B3LYP/6-31G(d) level, and the structures of the optimized geometry are shown on table 6.

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
|<jmol>
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====<u>Frequency analysis</u>====

{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for both endo and exo TS, and it can be confirmed that all TS were correctly optimised.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
|-
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|-
|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
|-
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity (shown on table 8). Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MO energies calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 12.

{| class="wikitable"
|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at PM6 / kJmol<sup>-1</sup>'''
| '''Substrates'''
| '''Gibbs free energy at PM6 / kJmol<sup>-1</sup>'''
| '''Substrates'''
| '''Gibbs free energy at PM6 / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
| '''Cheletropic-TS'''
| style="text-align: center;" |262.093
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 15.
According to the IRC on table 13 and the data in table 15, the small activation energy might due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure 9 shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-31G(d) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Exercise 1 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 2 files
|-
|Cyclohexadiene
|[[File:XZ9215CYCLOHEXDIENE.LOG]]
|-
|1,3-dioxole
|[[File:XZ921513DIOXOLE.LOG]]
|-
|Exo TS
|[[File:XZ9215E2EXODIOXOLE TS POP.LOG]]
|-
|Endo TS
|[[File:XZ9215E2endoTS POP.LOG]]
|-
|Exo product
|[[File:XZ9215 exo EXODIOXOLE 631GD.LOG]]
|-
|Endo product
|[[File:XZ9215endo1133 TS 631GD.LOG]]
|}

{| class="wikitable"
|+ Exercise 3 files
|-
|Endo TS
|[[File:XZ9215E3 D-A ENDO TS.LOG]]
|-
|Exo TS
|[[File:XZ9215E3 D-A EXO TS.LOG]]
|-
|Cheletropic TS
|[[File:XZ9215 E3 cheletropic PRODUCT TS.LOG]]
|-
|Endo IRC
|[[File:XZ9215 E3ENDO IRC.LOG]]
|-
|Exo IRC
|[[File:XZ9215 E3 EXO IRC.LOG]]
|-
|Cheletropic IRC
|[[File:XZ9215 E3 PRODUCT IRC.LOG]]
|}

Rep:MOD:XZ9215

2018-01-30T14:00:19Z

Xz9215: /* Reaction barrier and reaction energy */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 3, and IRC of transition state is shown on figure 4.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant. The left stationary point is the product and the right one represents reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 5.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
The C-C bond lengths of the reactants, product and the TS are shown on table 4, the standard C-C bond lengths and the Van der Waals radius of the C atom are presented on table 5.

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on the last picture on table 4, the frequency is -948.50cm<sup>-1</sup> (figure 3). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

====<u>Optimisation at B3LYP/6-31G(d)</u>====

The reactants, product, endo and exo transition state were optimized at B3LYP/6-31G(d) level, and the structures of the optimized geometry are shown on table 6.

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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====<u>Frequency analysis</u>====

{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for both endo and exo TS, and it can be confirmed that all TS were correctly optimised.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
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|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity (shown on table 8). Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MO energies calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 12.

{| class="wikitable"
|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at PM6 / kJmol<sup>-1</sup>'''
| '''Substrates'''
| '''Gibbs free energy at PM6 / kJmol<sup>-1</sup>'''
| '''Substrates'''
| '''Gibbs free energy at PM6 / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
| '''Cheletropic-TS'''
| style="text-align: center;" |262.093
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 15.
According to the IRC on table 13 and the data in table 15, the small activation energy might due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure 9 shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-31G(d) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Exercise 1 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 2 files
|-
|Cyclohexadiene
|[[File:XZ9215CYCLOHEXDIENE.LOG]]
|-
|1,3-dioxole
|[[File:XZ921513DIOXOLE.LOG]]
|-
|Exo TS
|[[File:XZ9215E2EXODIOXOLE TS POP.LOG]]
|-
|Endo TS
|[[File:XZ9215E2endoTS POP.LOG]]
|-
|Exo product
|[[File:XZ9215 exo EXODIOXOLE 631GD.LOG]]
|-
|Endo product
|[[File:XZ9215endo1133 TS 631GD.LOG]]
|}

{| class="wikitable"
|+ Exercise 3 files
|-
|Endo TS
|[[File:XZ9215E3 D-A ENDO TS.LOG]]
|-
|Exo TS
|[[File:XZ9215E3 D-A EXO TS.LOG]]
|-
|Cheletropic TS
|[[File:XZ9215 E3 cheletropic PRODUCT TS.LOG]]
|-
|Endo IRC
|[[File:XZ9215 E3ENDO IRC.LOG]]
|-
|Exo IRC
|[[File:XZ9215 E3 EXO IRC.LOG]]
|-
|Cheletropic IRC
|[[File:XZ9215 E3 PRODUCT IRC.LOG]]
|}

Rep:MOD:XZ9215

2018-01-30T13:38:51Z

Xz9215: /* Normal or inverse electron demand */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 3, and IRC of transition state is shown on figure 4.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant. The left stationary point is the product and the right one represents reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 5.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
The C-C bond lengths of the reactants, product and the TS are shown on table 4, the standard C-C bond lengths and the Van der Waals radius of the C atom are presented on table 5.

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on the last picture on table 4, the frequency is -948.50cm<sup>-1</sup> (figure 3). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

====<u>Optimisation at B3LYP/6-31G(d)</u>====

The reactants, product, endo and exo transition state were optimized at B3LYP/6-31G(d) level, and the structures of the optimized geometry are shown on table 6.

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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====<u>Frequency analysis</u>====

{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for both endo and exo TS, and it can be confirmed that all TS were correctly optimised.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
|-
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|-
|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
|-
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity (shown on table 8). Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MO energies calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 12.

{| class="wikitable"
|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at PM6 / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 15.
According to the IRC on table 13 and the data in table 15, the small activation energy might due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure 9 shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-31G(d) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Exercise 1 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 2 files
|-
|Cyclohexadiene
|[[File:XZ9215CYCLOHEXDIENE.LOG]]
|-
|1,3-dioxole
|[[File:XZ921513DIOXOLE.LOG]]
|-
|Exo TS
|[[File:XZ9215E2EXODIOXOLE TS POP.LOG]]
|-
|Endo TS
|[[File:XZ9215E2endoTS POP.LOG]]
|-
|Exo product
|[[File:XZ9215 exo EXODIOXOLE 631GD.LOG]]
|-
|Endo product
|[[File:XZ9215endo1133 TS 631GD.LOG]]
|}

{| class="wikitable"
|+ Exercise 3 files
|-
|Endo TS
|[[File:XZ9215E3 D-A ENDO TS.LOG]]
|-
|Exo TS
|[[File:XZ9215E3 D-A EXO TS.LOG]]
|-
|Cheletropic TS
|[[File:XZ9215 E3 cheletropic PRODUCT TS.LOG]]
|-
|Endo IRC
|[[File:XZ9215 E3ENDO IRC.LOG]]
|-
|Exo IRC
|[[File:XZ9215 E3 EXO IRC.LOG]]
|-
|Cheletropic IRC
|[[File:XZ9215 E3 PRODUCT IRC.LOG]]
|}

Rep:MOD:XZ9215

2018-01-30T13:36:08Z

Xz9215: /* Frequency analysis */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 3, and IRC of transition state is shown on figure 4.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant. The left stationary point is the product and the right one represents reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 5.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
The C-C bond lengths of the reactants, product and the TS are shown on table 4, the standard C-C bond lengths and the Van der Waals radius of the C atom are presented on table 5.

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on the last picture on table 4, the frequency is -948.50cm<sup>-1</sup> (figure 3). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

====<u>Optimisation at B3LYP/6-31G(d)</u>====

The reactants, product, endo and exo transition state were optimized at B3LYP/6-31G(d) level, and the structures of the optimized geometry are shown on table 6.

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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====<u>Frequency analysis</u>====

{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for both endo and exo TS, and it can be confirmed that all TS were correctly optimised.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
|-
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|-
|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
|-
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity (shown on table 8). Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 12.

{| class="wikitable"
|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at PM6 / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 15.
According to the IRC on table 13 and the data in table 15, the small activation energy might due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure 9 shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-31G(d) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Exercise 1 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 2 files
|-
|Cyclohexadiene
|[[File:XZ9215CYCLOHEXDIENE.LOG]]
|-
|1,3-dioxole
|[[File:XZ921513DIOXOLE.LOG]]
|-
|Exo TS
|[[File:XZ9215E2EXODIOXOLE TS POP.LOG]]
|-
|Endo TS
|[[File:XZ9215E2endoTS POP.LOG]]
|-
|Exo product
|[[File:XZ9215 exo EXODIOXOLE 631GD.LOG]]
|-
|Endo product
|[[File:XZ9215endo1133 TS 631GD.LOG]]
|}

{| class="wikitable"
|+ Exercise 3 files
|-
|Endo TS
|[[File:XZ9215E3 D-A ENDO TS.LOG]]
|-
|Exo TS
|[[File:XZ9215E3 D-A EXO TS.LOG]]
|-
|Cheletropic TS
|[[File:XZ9215 E3 cheletropic PRODUCT TS.LOG]]
|-
|Endo IRC
|[[File:XZ9215 E3ENDO IRC.LOG]]
|-
|Exo IRC
|[[File:XZ9215 E3 EXO IRC.LOG]]
|-
|Cheletropic IRC
|[[File:XZ9215 E3 PRODUCT IRC.LOG]]
|}

Rep:MOD:XZ9215

2018-01-30T13:34:15Z

Xz9215: /* Frequency analysis */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 3, and IRC of transition state is shown on figure 4.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant. The left stationary point is the product and the right one represents reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 5.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
The C-C bond lengths of the reactants, product and the TS are shown on table 4, the standard C-C bond lengths and the Van der Waals radius of the C atom are presented on table 5.

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on the last picture on table 4, the frequency is -948.50cm<sup>-1</sup> (figure 3). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

====<u>Optimisation at B3LYP/6-31G(d)</u>====

The reactants, product, endo and exo transition state were optimized at B3LYP/6-31G(d) level, and the structures of the optimized geometry are shown on table 6.

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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====<u>Frequency analysis</u>====

{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. Thus, it can be confirmed that TS was correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
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|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity (shown on table 8). Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 12.

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|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at PM6 / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 15.
According to the IRC on table 13 and the data in table 15, the small activation energy might due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure 9 shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-31G(d) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Exercise 1 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 2 files
|-
|Cyclohexadiene
|[[File:XZ9215CYCLOHEXDIENE.LOG]]
|-
|1,3-dioxole
|[[File:XZ921513DIOXOLE.LOG]]
|-
|Exo TS
|[[File:XZ9215E2EXODIOXOLE TS POP.LOG]]
|-
|Endo TS
|[[File:XZ9215E2endoTS POP.LOG]]
|-
|Exo product
|[[File:XZ9215 exo EXODIOXOLE 631GD.LOG]]
|-
|Endo product
|[[File:XZ9215endo1133 TS 631GD.LOG]]
|}

{| class="wikitable"
|+ Exercise 3 files
|-
|Endo TS
|[[File:XZ9215E3 D-A ENDO TS.LOG]]
|-
|Exo TS
|[[File:XZ9215E3 D-A EXO TS.LOG]]
|-
|Cheletropic TS
|[[File:XZ9215 E3 cheletropic PRODUCT TS.LOG]]
|-
|Endo IRC
|[[File:XZ9215 E3ENDO IRC.LOG]]
|-
|Exo IRC
|[[File:XZ9215 E3 EXO IRC.LOG]]
|-
|Cheletropic IRC
|[[File:XZ9215 E3 PRODUCT IRC.LOG]]
|}

Rep:MOD:XZ9215

2018-01-30T13:32:19Z

Xz9215: /* Bond length analysis */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 3, and IRC of transition state is shown on figure 4.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant. The left stationary point is the product and the right one represents reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 5.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}
The C-C bond lengths of the reactants, product and the TS are shown on table 4, the standard C-C bond lengths and the Van der Waals radius of the C atom are presented on table 5.

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on the last picture on table 4, the frequency is -948.50cm<sup>-1</sup> (figure 3). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

====<u>Optimisation at B3LYP/6-31G(d)</u>====

The reactants, product, endo and exo transition state were optimized at B3LYP/6-31G(d) level, and the structures of the optimized geometry are shown on table 6.

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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====<u>Frequency analysis</u>====

{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
|-
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|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity (shown on table 8). Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 12.

{| class="wikitable"
|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at PM6 / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 15.
According to the IRC on table 13 and the data in table 15, the small activation energy might due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure 9 shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-31G(d) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Exercise 1 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 2 files
|-
|Cyclohexadiene
|[[File:XZ9215CYCLOHEXDIENE.LOG]]
|-
|1,3-dioxole
|[[File:XZ921513DIOXOLE.LOG]]
|-
|Exo TS
|[[File:XZ9215E2EXODIOXOLE TS POP.LOG]]
|-
|Endo TS
|[[File:XZ9215E2endoTS POP.LOG]]
|-
|Exo product
|[[File:XZ9215 exo EXODIOXOLE 631GD.LOG]]
|-
|Endo product
|[[File:XZ9215endo1133 TS 631GD.LOG]]
|}

{| class="wikitable"
|+ Exercise 3 files
|-
|Endo TS
|[[File:XZ9215E3 D-A ENDO TS.LOG]]
|-
|Exo TS
|[[File:XZ9215E3 D-A EXO TS.LOG]]
|-
|Cheletropic TS
|[[File:XZ9215 E3 cheletropic PRODUCT TS.LOG]]
|-
|Endo IRC
|[[File:XZ9215 E3ENDO IRC.LOG]]
|-
|Exo IRC
|[[File:XZ9215 E3 EXO IRC.LOG]]
|-
|Cheletropic IRC
|[[File:XZ9215 E3 PRODUCT IRC.LOG]]
|}

Rep:MOD:XZ9215

2018-01-30T13:30:42Z

Xz9215: /* IRC and frequency analysis */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 3, and IRC of transition state is shown on figure 4.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant. The left stationary point is the product and the right one represents reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 5.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table 4, the standard C-C bond lengths and the Van der Waals radius of the C atom are presented on table 5.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on the last picture on table 4, the frequency is -948.50cm<sup>-1</sup> (figure 3). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

====<u>Optimisation at B3LYP/6-31G(d)</u>====

The reactants, product, endo and exo transition state were optimized at B3LYP/6-31G(d) level, and the structures of the optimized geometry are shown on table 6.

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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====<u>Frequency analysis</u>====

{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
|-
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|-
|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
|-
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity (shown on table 8). Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 12.

{| class="wikitable"
|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at PM6 / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 15.
According to the IRC on table 13 and the data in table 15, the small activation energy might due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure 9 shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-31G(d) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Exercise 1 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 2 files
|-
|Cyclohexadiene
|[[File:XZ9215CYCLOHEXDIENE.LOG]]
|-
|1,3-dioxole
|[[File:XZ921513DIOXOLE.LOG]]
|-
|Exo TS
|[[File:XZ9215E2EXODIOXOLE TS POP.LOG]]
|-
|Endo TS
|[[File:XZ9215E2endoTS POP.LOG]]
|-
|Exo product
|[[File:XZ9215 exo EXODIOXOLE 631GD.LOG]]
|-
|Endo product
|[[File:XZ9215endo1133 TS 631GD.LOG]]
|}

{| class="wikitable"
|+ Exercise 3 files
|-
|Endo TS
|[[File:XZ9215E3 D-A ENDO TS.LOG]]
|-
|Exo TS
|[[File:XZ9215E3 D-A EXO TS.LOG]]
|-
|Cheletropic TS
|[[File:XZ9215 E3 cheletropic PRODUCT TS.LOG]]
|-
|Endo IRC
|[[File:XZ9215 E3ENDO IRC.LOG]]
|-
|Exo IRC
|[[File:XZ9215 E3 EXO IRC.LOG]]
|-
|Cheletropic IRC
|[[File:XZ9215 E3 PRODUCT IRC.LOG]]
|}

Rep:MOD:XZ9215

2018-01-26T20:45:52Z

Xz9215: /* Conclusion */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 3, and IRC of transition state is shown on figure 4.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 5.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table 4, the standard C-C bond lengths and the Van der Waals radius of the C atom are presented on table 5.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on the last picture on table 4, the frequency is -948.50cm<sup>-1</sup> (figure 3). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

====<u>Optimisation at B3LYP/6-31G(d)</u>====

The reactants, product, endo and exo transition state were optimized at B3LYP/6-31G(d) level, and the structures of the optimized geometry are shown on table 6.

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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====<u>Frequency analysis</u>====

{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
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|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity (shown on table 8). Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 12.

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|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at PM6 / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 15.
According to the IRC on table 13 and the data in table 15, the small activation energy might due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure 9 shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-31G(d) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Exercise 1 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 2 files
|-
|Cyclohexadiene
|[[File:XZ9215CYCLOHEXDIENE.LOG]]
|-
|1,3-dioxole
|[[File:XZ921513DIOXOLE.LOG]]
|-
|Exo TS
|[[File:XZ9215E2EXODIOXOLE TS POP.LOG]]
|-
|Endo TS
|[[File:XZ9215E2endoTS POP.LOG]]
|-
|Exo product
|[[File:XZ9215 exo EXODIOXOLE 631GD.LOG]]
|-
|Endo product
|[[File:XZ9215endo1133 TS 631GD.LOG]]
|}

{| class="wikitable"
|+ Exercise 3 files
|-
|Endo TS
|[[File:XZ9215E3 D-A ENDO TS.LOG]]
|-
|Exo TS
|[[File:XZ9215E3 D-A EXO TS.LOG]]
|-
|Cheletropic TS
|[[File:XZ9215 E3 cheletropic PRODUCT TS.LOG]]
|-
|Endo IRC
|[[File:XZ9215 E3ENDO IRC.LOG]]
|-
|Exo IRC
|[[File:XZ9215 E3 EXO IRC.LOG]]
|-
|Cheletropic IRC
|[[File:XZ9215 E3 PRODUCT IRC.LOG]]
|}

Rep:MOD:XZ9215

2018-01-26T20:45:27Z

Xz9215: /* Conclusion */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 52; </script>
<uploadedFileContents>XZ9215BUTADIENE.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; </script>
<uploadedFileContents>XZ9215ETHYLENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
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<script>frame 20; </script>
<uploadedFileContents>XZ9215CYCLOHAXENE TS1.LOG</uploadedFileContents>
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 3, and IRC of transition state is shown on figure 4.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 5.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table 4, the standard C-C bond lengths and the Van der Waals radius of the C atom are presented on table 5.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on the last picture on table 4, the frequency is -948.50cm<sup>-1</sup> (figure 3). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

====<u>Optimisation at B3LYP/6-31G(d)</u>====

The reactants, product, endo and exo transition state were optimized at B3LYP/6-31G(d) level, and the structures of the optimized geometry are shown on table 6.

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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====<u>Frequency analysis</u>====

{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
|-
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|-
|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
|-
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity (shown on table 8). Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 12.

{| class="wikitable"
|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at PM6 / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 15.
According to the IRC on table 13 and the data in table 15, the small activation energy might due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure 9 shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-311G(d) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Exercise 1 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 2 files
|-
|Cyclohexadiene
|[[File:XZ9215CYCLOHEXDIENE.LOG]]
|-
|1,3-dioxole
|[[File:XZ921513DIOXOLE.LOG]]
|-
|Exo TS
|[[File:XZ9215E2EXODIOXOLE TS POP.LOG]]
|-
|Endo TS
|[[File:XZ9215E2endoTS POP.LOG]]
|-
|Exo product
|[[File:XZ9215 exo EXODIOXOLE 631GD.LOG]]
|-
|Endo product
|[[File:XZ9215endo1133 TS 631GD.LOG]]
|}

{| class="wikitable"
|+ Exercise 3 files
|-
|Endo TS
|[[File:XZ9215E3 D-A ENDO TS.LOG]]
|-
|Exo TS
|[[File:XZ9215E3 D-A EXO TS.LOG]]
|-
|Cheletropic TS
|[[File:XZ9215 E3 cheletropic PRODUCT TS.LOG]]
|-
|Endo IRC
|[[File:XZ9215 E3ENDO IRC.LOG]]
|-
|Exo IRC
|[[File:XZ9215 E3 EXO IRC.LOG]]
|-
|Cheletropic IRC
|[[File:XZ9215 E3 PRODUCT IRC.LOG]]
|}

Rep:MOD:XZ9215

2018-01-26T20:45:07Z

Xz9215: /* Reaction profile */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 3, and IRC of transition state is shown on figure 4.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 5.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table 4, the standard C-C bond lengths and the Van der Waals radius of the C atom are presented on table 5.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on the last picture on table 4, the frequency is -948.50cm<sup>-1</sup> (figure 3). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

====<u>Optimisation at B3LYP/6-31G(d)</u>====

The reactants, product, endo and exo transition state were optimized at B3LYP/6-31G(d) level, and the structures of the optimized geometry are shown on table 6.

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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====<u>Frequency analysis</u>====

{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
|-
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|-
|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
|-
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity (shown on table 8). Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 12.

{| class="wikitable"
|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at PM6 / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 15.
According to the IRC on table 13 and the data in table 15, the small activation energy might due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure 9 shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-311G(d,p) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Exercise 1 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 2 files
|-
|Cyclohexadiene
|[[File:XZ9215CYCLOHEXDIENE.LOG]]
|-
|1,3-dioxole
|[[File:XZ921513DIOXOLE.LOG]]
|-
|Exo TS
|[[File:XZ9215E2EXODIOXOLE TS POP.LOG]]
|-
|Endo TS
|[[File:XZ9215E2endoTS POP.LOG]]
|-
|Exo product
|[[File:XZ9215 exo EXODIOXOLE 631GD.LOG]]
|-
|Endo product
|[[File:XZ9215endo1133 TS 631GD.LOG]]
|}

{| class="wikitable"
|+ Exercise 3 files
|-
|Endo TS
|[[File:XZ9215E3 D-A ENDO TS.LOG]]
|-
|Exo TS
|[[File:XZ9215E3 D-A EXO TS.LOG]]
|-
|Cheletropic TS
|[[File:XZ9215 E3 cheletropic PRODUCT TS.LOG]]
|-
|Endo IRC
|[[File:XZ9215 E3ENDO IRC.LOG]]
|-
|Exo IRC
|[[File:XZ9215 E3 EXO IRC.LOG]]
|-
|Cheletropic IRC
|[[File:XZ9215 E3 PRODUCT IRC.LOG]]
|}

Rep:MOD:XZ9215

2018-01-26T20:44:37Z

Xz9215: /* Reaction barrier and reaction energy */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 3, and IRC of transition state is shown on figure 4.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 5.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table 4, the standard C-C bond lengths and the Van der Waals radius of the C atom are presented on table 5.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on the last picture on table 4, the frequency is -948.50cm<sup>-1</sup> (figure 3). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

====<u>Optimisation at B3LYP/6-31G(d)</u>====

The reactants, product, endo and exo transition state were optimized at B3LYP/6-31G(d) level, and the structures of the optimized geometry are shown on table 6.

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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====<u>Frequency analysis</u>====

{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
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|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity (shown on table 8). Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 12.

{| class="wikitable"
|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at PM6 / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 15.
According to the IRC on table 13 and the data in table 15, the small activation energy might due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-311G(d,p) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Exercise 1 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 2 files
|-
|Cyclohexadiene
|[[File:XZ9215CYCLOHEXDIENE.LOG]]
|-
|1,3-dioxole
|[[File:XZ921513DIOXOLE.LOG]]
|-
|Exo TS
|[[File:XZ9215E2EXODIOXOLE TS POP.LOG]]
|-
|Endo TS
|[[File:XZ9215E2endoTS POP.LOG]]
|-
|Exo product
|[[File:XZ9215 exo EXODIOXOLE 631GD.LOG]]
|-
|Endo product
|[[File:XZ9215endo1133 TS 631GD.LOG]]
|}

{| class="wikitable"
|+ Exercise 3 files
|-
|Endo TS
|[[File:XZ9215E3 D-A ENDO TS.LOG]]
|-
|Exo TS
|[[File:XZ9215E3 D-A EXO TS.LOG]]
|-
|Cheletropic TS
|[[File:XZ9215 E3 cheletropic PRODUCT TS.LOG]]
|-
|Endo IRC
|[[File:XZ9215 E3ENDO IRC.LOG]]
|-
|Exo IRC
|[[File:XZ9215 E3 EXO IRC.LOG]]
|-
|Cheletropic IRC
|[[File:XZ9215 E3 PRODUCT IRC.LOG]]
|}

Rep:MOD:XZ9215

2018-01-26T20:43:24Z

Xz9215: /* Reaction barrier and reaction energy */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
|<jmol>
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<color>white</color>
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<script>frame 52; </script>
<uploadedFileContents>XZ9215BUTADIENE.LOG</uploadedFileContents>
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|<jmol>
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<script>frame 14; </script>
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 3, and IRC of transition state is shown on figure 4.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 5.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table 4, the standard C-C bond lengths and the Van der Waals radius of the C atom are presented on table 5.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on the last picture on table 4, the frequency is -948.50cm<sup>-1</sup> (figure 3). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

====<u>Optimisation at B3LYP/6-31G(d)</u>====

The reactants, product, endo and exo transition state were optimized at B3LYP/6-31G(d) level, and the structures of the optimized geometry are shown on table 6.

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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====<u>Frequency analysis</u>====

{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
|-
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|-
|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity (shown on table 8). Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 12.

{| class="wikitable"
|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at PM6 / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 15.
According to the IRC on table 13 and the activation energy data in table 15, the small activation energy is due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-311G(d,p) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Exercise 1 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 2 files
|-
|Cyclohexadiene
|[[File:XZ9215CYCLOHEXDIENE.LOG]]
|-
|1,3-dioxole
|[[File:XZ921513DIOXOLE.LOG]]
|-
|Exo TS
|[[File:XZ9215E2EXODIOXOLE TS POP.LOG]]
|-
|Endo TS
|[[File:XZ9215E2endoTS POP.LOG]]
|-
|Exo product
|[[File:XZ9215 exo EXODIOXOLE 631GD.LOG]]
|-
|Endo product
|[[File:XZ9215endo1133 TS 631GD.LOG]]
|}

{| class="wikitable"
|+ Exercise 3 files
|-
|Endo TS
|[[File:XZ9215E3 D-A ENDO TS.LOG]]
|-
|Exo TS
|[[File:XZ9215E3 D-A EXO TS.LOG]]
|-
|Cheletropic TS
|[[File:XZ9215 E3 cheletropic PRODUCT TS.LOG]]
|-
|Endo IRC
|[[File:XZ9215 E3ENDO IRC.LOG]]
|-
|Exo IRC
|[[File:XZ9215 E3 EXO IRC.LOG]]
|-
|Cheletropic IRC
|[[File:XZ9215 E3 PRODUCT IRC.LOG]]
|}

Rep:MOD:XZ9215

2018-01-26T20:40:35Z

Xz9215: /* Reaction barrier and reaction energy */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 3, and IRC of transition state is shown on figure 4.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 5.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table 4, the standard C-C bond lengths and the Van der Waals radius of the C atom are presented on table 5.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on the last picture on table 4, the frequency is -948.50cm<sup>-1</sup> (figure 3). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

====<u>Optimisation at B3LYP/6-31G(d)</u>====

The reactants, product, endo and exo transition state were optimized at B3LYP/6-31G(d) level, and the structures of the optimized geometry are shown on table 6.

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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====<u>Frequency analysis</u>====

{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
|-
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|-
|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
|-
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity (shown on table 8). Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 12.

{| class="wikitable"
|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at PM6 / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 4.
According to figure 11 and table 4, the small activation energy is due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-311G(d,p) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Exercise 1 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 2 files
|-
|Cyclohexadiene
|[[File:XZ9215CYCLOHEXDIENE.LOG]]
|-
|1,3-dioxole
|[[File:XZ921513DIOXOLE.LOG]]
|-
|Exo TS
|[[File:XZ9215E2EXODIOXOLE TS POP.LOG]]
|-
|Endo TS
|[[File:XZ9215E2endoTS POP.LOG]]
|-
|Exo product
|[[File:XZ9215 exo EXODIOXOLE 631GD.LOG]]
|-
|Endo product
|[[File:XZ9215endo1133 TS 631GD.LOG]]
|}

{| class="wikitable"
|+ Exercise 3 files
|-
|Endo TS
|[[File:XZ9215E3 D-A ENDO TS.LOG]]
|-
|Exo TS
|[[File:XZ9215E3 D-A EXO TS.LOG]]
|-
|Cheletropic TS
|[[File:XZ9215 E3 cheletropic PRODUCT TS.LOG]]
|-
|Endo IRC
|[[File:XZ9215 E3ENDO IRC.LOG]]
|-
|Exo IRC
|[[File:XZ9215 E3 EXO IRC.LOG]]
|-
|Cheletropic IRC
|[[File:XZ9215 E3 PRODUCT IRC.LOG]]
|}

Rep:MOD:XZ9215

2018-01-26T20:39:07Z

Xz9215: /* Optimisation at B3LYP/6-31G(d) */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 3, and IRC of transition state is shown on figure 4.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 5.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table 4, the standard C-C bond lengths and the Van der Waals radius of the C atom are presented on table 5.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on the last picture on table 4, the frequency is -948.50cm<sup>-1</sup> (figure 3). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

====<u>Optimisation at B3LYP/6-31G(d)</u>====

The reactants, product, endo and exo transition state were optimized at B3LYP/6-31G(d) level, and the structures of the optimized geometry are shown on table 6.

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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====<u>Frequency analysis</u>====

{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
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|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity (shown on table 8). Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 12.

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|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at B3LYP (6-31G(d)) / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 4.
According to figure 11 and table 4, the small activation energy is due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-311G(d,p) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Exercise 1 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 2 files
|-
|Cyclohexadiene
|[[File:XZ9215CYCLOHEXDIENE.LOG]]
|-
|1,3-dioxole
|[[File:XZ921513DIOXOLE.LOG]]
|-
|Exo TS
|[[File:XZ9215E2EXODIOXOLE TS POP.LOG]]
|-
|Endo TS
|[[File:XZ9215E2endoTS POP.LOG]]
|-
|Exo product
|[[File:XZ9215 exo EXODIOXOLE 631GD.LOG]]
|-
|Endo product
|[[File:XZ9215endo1133 TS 631GD.LOG]]
|}

{| class="wikitable"
|+ Exercise 3 files
|-
|Endo TS
|[[File:XZ9215E3 D-A ENDO TS.LOG]]
|-
|Exo TS
|[[File:XZ9215E3 D-A EXO TS.LOG]]
|-
|Cheletropic TS
|[[File:XZ9215 E3 cheletropic PRODUCT TS.LOG]]
|-
|Endo IRC
|[[File:XZ9215 E3ENDO IRC.LOG]]
|-
|Exo IRC
|[[File:XZ9215 E3 EXO IRC.LOG]]
|-
|Cheletropic IRC
|[[File:XZ9215 E3 PRODUCT IRC.LOG]]
|}

Rep:MOD:XZ9215

2018-01-26T20:38:35Z

Xz9215: /* Optimisation of TS at PM6 level */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 3, and IRC of transition state is shown on figure 4.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 5.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table 4, the standard C-C bond lengths and the Van der Waals radius of the C atom are presented on table 5.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on the last picture on table 4, the frequency is -948.50cm<sup>-1</sup> (figure 3). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

====<u>Optimisation at B3LYP/6-31G(d)</u>====

The reactants, product and transition state were optimized at B3LYP/6-31G(d) level, and the structures of the optimized geometry are shown on table 6.

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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====<u>Frequency analysis</u>====

{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
|-
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|-
|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity (shown on table 8). Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 12.

{| class="wikitable"
|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at B3LYP (6-31G(d)) / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 4.
According to figure 11 and table 4, the small activation energy is due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-311G(d,p) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Exercise 1 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 2 files
|-
|Cyclohexadiene
|[[File:XZ9215CYCLOHEXDIENE.LOG]]
|-
|1,3-dioxole
|[[File:XZ921513DIOXOLE.LOG]]
|-
|Exo TS
|[[File:XZ9215E2EXODIOXOLE TS POP.LOG]]
|-
|Endo TS
|[[File:XZ9215E2endoTS POP.LOG]]
|-
|Exo product
|[[File:XZ9215 exo EXODIOXOLE 631GD.LOG]]
|-
|Endo product
|[[File:XZ9215endo1133 TS 631GD.LOG]]
|}

{| class="wikitable"
|+ Exercise 3 files
|-
|Endo TS
|[[File:XZ9215E3 D-A ENDO TS.LOG]]
|-
|Exo TS
|[[File:XZ9215E3 D-A EXO TS.LOG]]
|-
|Cheletropic TS
|[[File:XZ9215 E3 cheletropic PRODUCT TS.LOG]]
|-
|Endo IRC
|[[File:XZ9215 E3ENDO IRC.LOG]]
|-
|Exo IRC
|[[File:XZ9215 E3 EXO IRC.LOG]]
|-
|Cheletropic IRC
|[[File:XZ9215 E3 PRODUCT IRC.LOG]]
|}

Rep:MOD:XZ9215

2018-01-26T20:38:10Z

Xz9215: /* Normal or inverse electron demand */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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<script>frame 52; </script>
<uploadedFileContents>XZ9215BUTADIENE.LOG</uploadedFileContents>
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|<jmol>
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 3, and IRC of transition state is shown on figure 4.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 5.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table 4, the standard C-C bond lengths and the Van der Waals radius of the C atom are presented on table 5.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on the last picture on table 4, the frequency is -948.50cm<sup>-1</sup> (figure 3). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

====<u>Optimisation at B3LYP/6-31G(d)</u>====

The reactants, product and transition state were optimized at B3LYP/6-31G(d) level, and the structures of the optimized geometry are shown on table 6.

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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====<u>Frequency analysis</u>====

{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
|-
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|-
|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
|-
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity (shown on table 8). Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at B3LYP (6-31G(d)) / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 4.
According to figure 11 and table 4, the small activation energy is due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-311G(d,p) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Exercise 1 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 2 files
|-
|Cyclohexadiene
|[[File:XZ9215CYCLOHEXDIENE.LOG]]
|-
|1,3-dioxole
|[[File:XZ921513DIOXOLE.LOG]]
|-
|Exo TS
|[[File:XZ9215E2EXODIOXOLE TS POP.LOG]]
|-
|Endo TS
|[[File:XZ9215E2endoTS POP.LOG]]
|-
|Exo product
|[[File:XZ9215 exo EXODIOXOLE 631GD.LOG]]
|-
|Endo product
|[[File:XZ9215endo1133 TS 631GD.LOG]]
|}

{| class="wikitable"
|+ Exercise 3 files
|-
|Endo TS
|[[File:XZ9215E3 D-A ENDO TS.LOG]]
|-
|Exo TS
|[[File:XZ9215E3 D-A EXO TS.LOG]]
|-
|Cheletropic TS
|[[File:XZ9215 E3 cheletropic PRODUCT TS.LOG]]
|-
|Endo IRC
|[[File:XZ9215 E3ENDO IRC.LOG]]
|-
|Exo IRC
|[[File:XZ9215 E3 EXO IRC.LOG]]
|-
|Cheletropic IRC
|[[File:XZ9215 E3 PRODUCT IRC.LOG]]
|}

Rep:MOD:XZ9215

2018-01-26T20:37:10Z

Xz9215: /* Optimisation at B3LYP/6-31G(d) */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 3, and IRC of transition state is shown on figure 4.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 5.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table 4, the standard C-C bond lengths and the Van der Waals radius of the C atom are presented on table 5.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on the last picture on table 4, the frequency is -948.50cm<sup>-1</sup> (figure 3). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

====<u>Optimisation at B3LYP/6-31G(d)</u>====

The reactants, product and transition state were optimized at B3LYP/6-31G(d) level, and the structures of the optimized geometry are shown on table 6.

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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====<u>Frequency analysis</u>====

{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
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|-
|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity. Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

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|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at B3LYP (6-31G(d)) / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 4.
According to figure 11 and table 4, the small activation energy is due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-311G(d,p) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Exercise 1 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 2 files
|-
|Cyclohexadiene
|[[File:XZ9215CYCLOHEXDIENE.LOG]]
|-
|1,3-dioxole
|[[File:XZ921513DIOXOLE.LOG]]
|-
|Exo TS
|[[File:XZ9215E2EXODIOXOLE TS POP.LOG]]
|-
|Endo TS
|[[File:XZ9215E2endoTS POP.LOG]]
|-
|Exo product
|[[File:XZ9215 exo EXODIOXOLE 631GD.LOG]]
|-
|Endo product
|[[File:XZ9215endo1133 TS 631GD.LOG]]
|}

{| class="wikitable"
|+ Exercise 3 files
|-
|Endo TS
|[[File:XZ9215E3 D-A ENDO TS.LOG]]
|-
|Exo TS
|[[File:XZ9215E3 D-A EXO TS.LOG]]
|-
|Cheletropic TS
|[[File:XZ9215 E3 cheletropic PRODUCT TS.LOG]]
|-
|Endo IRC
|[[File:XZ9215 E3ENDO IRC.LOG]]
|-
|Exo IRC
|[[File:XZ9215 E3 EXO IRC.LOG]]
|-
|Cheletropic IRC
|[[File:XZ9215 E3 PRODUCT IRC.LOG]]
|}

Rep:MOD:XZ9215

2018-01-26T20:36:20Z

Xz9215: /* Exercise 2 */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 3, and IRC of transition state is shown on figure 4.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 5.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table 4, the standard C-C bond lengths and the Van der Waals radius of the C atom are presented on table 5.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on the last picture on table 4, the frequency is -948.50cm<sup>-1</sup> (figure 3). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

====<u>Optimisation at B3LYP/6-31G(d)</u>====

The reactants, product and transition state were optimized at B3LYP/6-31G(d) level, and the structures of the optimized geometry are shown on table 6.

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
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|-
|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity. Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at B3LYP (6-31G(d)) / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 4.
According to figure 11 and table 4, the small activation energy is due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-311G(d,p) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Exercise 1 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 2 files
|-
|Cyclohexadiene
|[[File:XZ9215CYCLOHEXDIENE.LOG]]
|-
|1,3-dioxole
|[[File:XZ921513DIOXOLE.LOG]]
|-
|Exo TS
|[[File:XZ9215E2EXODIOXOLE TS POP.LOG]]
|-
|Endo TS
|[[File:XZ9215E2endoTS POP.LOG]]
|-
|Exo product
|[[File:XZ9215 exo EXODIOXOLE 631GD.LOG]]
|-
|Endo product
|[[File:XZ9215endo1133 TS 631GD.LOG]]
|}

{| class="wikitable"
|+ Exercise 3 files
|-
|Endo TS
|[[File:XZ9215E3 D-A ENDO TS.LOG]]
|-
|Exo TS
|[[File:XZ9215E3 D-A EXO TS.LOG]]
|-
|Cheletropic TS
|[[File:XZ9215 E3 cheletropic PRODUCT TS.LOG]]
|-
|Endo IRC
|[[File:XZ9215 E3ENDO IRC.LOG]]
|-
|Exo IRC
|[[File:XZ9215 E3 EXO IRC.LOG]]
|-
|Cheletropic IRC
|[[File:XZ9215 E3 PRODUCT IRC.LOG]]
|}

Rep:MOD:XZ9215

2018-01-26T20:32:26Z

Xz9215: /* Bond length analysis */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 3, and IRC of transition state is shown on figure 4.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 5.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table 4, the standard C-C bond lengths and the Van der Waals radius of the C atom are presented on table 5.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on the last picture on table 4, the frequency is -948.50cm<sup>-1</sup> (figure 3). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
|-
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|-
|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
|-
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity. Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at B3LYP (6-31G(d)) / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 4.
According to figure 11 and table 4, the small activation energy is due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-311G(d,p) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Exercise 1 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 2 files
|-
|Cyclohexadiene
|[[File:XZ9215CYCLOHEXDIENE.LOG]]
|-
|1,3-dioxole
|[[File:XZ921513DIOXOLE.LOG]]
|-
|Exo TS
|[[File:XZ9215E2EXODIOXOLE TS POP.LOG]]
|-
|Endo TS
|[[File:XZ9215E2endoTS POP.LOG]]
|-
|Exo product
|[[File:XZ9215 exo EXODIOXOLE 631GD.LOG]]
|-
|Endo product
|[[File:XZ9215endo1133 TS 631GD.LOG]]
|}

{| class="wikitable"
|+ Exercise 3 files
|-
|Endo TS
|[[File:XZ9215E3 D-A ENDO TS.LOG]]
|-
|Exo TS
|[[File:XZ9215E3 D-A EXO TS.LOG]]
|-
|Cheletropic TS
|[[File:XZ9215 E3 cheletropic PRODUCT TS.LOG]]
|-
|Endo IRC
|[[File:XZ9215 E3ENDO IRC.LOG]]
|-
|Exo IRC
|[[File:XZ9215 E3 EXO IRC.LOG]]
|-
|Cheletropic IRC
|[[File:XZ9215 E3 PRODUCT IRC.LOG]]
|}

Rep:MOD:XZ9215

2018-01-26T20:32:03Z

Xz9215: /* Bond length analysis */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 3, and IRC of transition state is shown on figure 4.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 5.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table 4, the standard C-C bond lengths and the Van der Waals radius of the C atom are presented on table 5.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on the last picture on table 5, the frequency is -948.50cm<sup>-1</sup> (figure 3). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
|-
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|-
|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity. Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

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|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at B3LYP (6-31G(d)) / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 4.
According to figure 11 and table 4, the small activation energy is due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-311G(d,p) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Exercise 1 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 2 files
|-
|Cyclohexadiene
|[[File:XZ9215CYCLOHEXDIENE.LOG]]
|-
|1,3-dioxole
|[[File:XZ921513DIOXOLE.LOG]]
|-
|Exo TS
|[[File:XZ9215E2EXODIOXOLE TS POP.LOG]]
|-
|Endo TS
|[[File:XZ9215E2endoTS POP.LOG]]
|-
|Exo product
|[[File:XZ9215 exo EXODIOXOLE 631GD.LOG]]
|-
|Endo product
|[[File:XZ9215endo1133 TS 631GD.LOG]]
|}

{| class="wikitable"
|+ Exercise 3 files
|-
|Endo TS
|[[File:XZ9215E3 D-A ENDO TS.LOG]]
|-
|Exo TS
|[[File:XZ9215E3 D-A EXO TS.LOG]]
|-
|Cheletropic TS
|[[File:XZ9215 E3 cheletropic PRODUCT TS.LOG]]
|-
|Endo IRC
|[[File:XZ9215 E3ENDO IRC.LOG]]
|-
|Exo IRC
|[[File:XZ9215 E3 EXO IRC.LOG]]
|-
|Cheletropic IRC
|[[File:XZ9215 E3 PRODUCT IRC.LOG]]
|}

Rep:MOD:XZ9215

2018-01-26T20:30:25Z

Xz9215: /* Bond length analysis */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
|<jmol>
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<color>white</color>
<size>200</size>
<script>frame 52; </script>
<uploadedFileContents>XZ9215BUTADIENE.LOG</uploadedFileContents>
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|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; </script>
<uploadedFileContents>XZ9215ETHYLENE.LOG</uploadedFileContents>
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 3, and IRC of transition state is shown on figure 4.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 5.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table 4, the standard C-C bond lengths and the Van der Waals radius of the C atom are presented on table 5.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on above figure 6, the frequency is -950cm<sup>-1</sup> (figure 5). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
|-
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|-
|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity. Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at B3LYP (6-31G(d)) / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 4.
According to figure 11 and table 4, the small activation energy is due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-311G(d,p) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Exercise 1 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 2 files
|-
|Cyclohexadiene
|[[File:XZ9215CYCLOHEXDIENE.LOG]]
|-
|1,3-dioxole
|[[File:XZ921513DIOXOLE.LOG]]
|-
|Exo TS
|[[File:XZ9215E2EXODIOXOLE TS POP.LOG]]
|-
|Endo TS
|[[File:XZ9215E2endoTS POP.LOG]]
|-
|Exo product
|[[File:XZ9215 exo EXODIOXOLE 631GD.LOG]]
|-
|Endo product
|[[File:XZ9215endo1133 TS 631GD.LOG]]
|}

{| class="wikitable"
|+ Exercise 3 files
|-
|Endo TS
|[[File:XZ9215E3 D-A ENDO TS.LOG]]
|-
|Exo TS
|[[File:XZ9215E3 D-A EXO TS.LOG]]
|-
|Cheletropic TS
|[[File:XZ9215 E3 cheletropic PRODUCT TS.LOG]]
|-
|Endo IRC
|[[File:XZ9215 E3ENDO IRC.LOG]]
|-
|Exo IRC
|[[File:XZ9215 E3 EXO IRC.LOG]]
|-
|Cheletropic IRC
|[[File:XZ9215 E3 PRODUCT IRC.LOG]]
|}

Rep:MOD:XZ9215

2018-01-26T20:29:27Z

Xz9215: /* Molecular orbitals analysis */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 3, and IRC of transition state is shown on figure 4.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 5.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table above. The standard C-C bond lengths and the Van der Waals radius of the C atom are presented below.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on above figure 6, the frequency is -950cm<sup>-1</sup> (figure 5). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
|-
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|-
|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
|-
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity. Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at B3LYP (6-31G(d)) / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 4.
According to figure 11 and table 4, the small activation energy is due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-311G(d,p) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Exercise 1 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 2 files
|-
|Cyclohexadiene
|[[File:XZ9215CYCLOHEXDIENE.LOG]]
|-
|1,3-dioxole
|[[File:XZ921513DIOXOLE.LOG]]
|-
|Exo TS
|[[File:XZ9215E2EXODIOXOLE TS POP.LOG]]
|-
|Endo TS
|[[File:XZ9215E2endoTS POP.LOG]]
|-
|Exo product
|[[File:XZ9215 exo EXODIOXOLE 631GD.LOG]]
|-
|Endo product
|[[File:XZ9215endo1133 TS 631GD.LOG]]
|}

{| class="wikitable"
|+ Exercise 3 files
|-
|Endo TS
|[[File:XZ9215E3 D-A ENDO TS.LOG]]
|-
|Exo TS
|[[File:XZ9215E3 D-A EXO TS.LOG]]
|-
|Cheletropic TS
|[[File:XZ9215 E3 cheletropic PRODUCT TS.LOG]]
|-
|Endo IRC
|[[File:XZ9215 E3ENDO IRC.LOG]]
|-
|Exo IRC
|[[File:XZ9215 E3 EXO IRC.LOG]]
|-
|Cheletropic IRC
|[[File:XZ9215 E3 PRODUCT IRC.LOG]]
|}

Rep:MOD:XZ9215

2018-01-26T20:28:40Z

Xz9215: /* Molecular orbitals analysis */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 3, and IRC of transition state is shown on figure 4.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 6.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table above. The standard C-C bond lengths and the Van der Waals radius of the C atom are presented below.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on above figure 6, the frequency is -950cm<sup>-1</sup> (figure 5). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
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|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity. Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at B3LYP (6-31G(d)) / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 4.
According to figure 11 and table 4, the small activation energy is due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-311G(d,p) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Exercise 1 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 2 files
|-
|Cyclohexadiene
|[[File:XZ9215CYCLOHEXDIENE.LOG]]
|-
|1,3-dioxole
|[[File:XZ921513DIOXOLE.LOG]]
|-
|Exo TS
|[[File:XZ9215E2EXODIOXOLE TS POP.LOG]]
|-
|Endo TS
|[[File:XZ9215E2endoTS POP.LOG]]
|-
|Exo product
|[[File:XZ9215 exo EXODIOXOLE 631GD.LOG]]
|-
|Endo product
|[[File:XZ9215endo1133 TS 631GD.LOG]]
|}

{| class="wikitable"
|+ Exercise 3 files
|-
|Endo TS
|[[File:XZ9215E3 D-A ENDO TS.LOG]]
|-
|Exo TS
|[[File:XZ9215E3 D-A EXO TS.LOG]]
|-
|Cheletropic TS
|[[File:XZ9215 E3 cheletropic PRODUCT TS.LOG]]
|-
|Endo IRC
|[[File:XZ9215 E3ENDO IRC.LOG]]
|-
|Exo IRC
|[[File:XZ9215 E3 EXO IRC.LOG]]
|-
|Cheletropic IRC
|[[File:XZ9215 E3 PRODUCT IRC.LOG]]
|}

Rep:MOD:XZ9215

2018-01-26T20:27:11Z

Xz9215: /* IRC and frequency analysis */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 52; </script>
<uploadedFileContents>XZ9215BUTADIENE.LOG</uploadedFileContents>
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</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; </script>
<uploadedFileContents>XZ9215ETHYLENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; </script>
<uploadedFileContents>XZ9215CYCLOHAXENE TS1.LOG</uploadedFileContents>
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|}

====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 3, and IRC of transition state is shown on figure 4.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 6.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table above. The standard C-C bond lengths and the Van der Waals radius of the C atom are presented below.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on above figure 6, the frequency is -950cm<sup>-1</sup> (figure 5). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
|-
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|-
|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
|-
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity. Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at B3LYP (6-31G(d)) / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 4.
According to figure 11 and table 4, the small activation energy is due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-311G(d,p) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Exercise 1 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 2 files
|-
|Cyclohexadiene
|[[File:XZ9215CYCLOHEXDIENE.LOG]]
|-
|1,3-dioxole
|[[File:XZ921513DIOXOLE.LOG]]
|-
|Exo TS
|[[File:XZ9215E2EXODIOXOLE TS POP.LOG]]
|-
|Endo TS
|[[File:XZ9215E2endoTS POP.LOG]]
|-
|Exo product
|[[File:XZ9215 exo EXODIOXOLE 631GD.LOG]]
|-
|Endo product
|[[File:XZ9215endo1133 TS 631GD.LOG]]
|}

{| class="wikitable"
|+ Exercise 3 files
|-
|Endo TS
|[[File:XZ9215E3 D-A ENDO TS.LOG]]
|-
|Exo TS
|[[File:XZ9215E3 D-A EXO TS.LOG]]
|-
|Cheletropic TS
|[[File:XZ9215 E3 cheletropic PRODUCT TS.LOG]]
|-
|Endo IRC
|[[File:XZ9215 E3ENDO IRC.LOG]]
|-
|Exo IRC
|[[File:XZ9215 E3 EXO IRC.LOG]]
|-
|Cheletropic IRC
|[[File:XZ9215 E3 PRODUCT IRC.LOG]]
|}

Rep:MOD:XZ9215

2018-01-26T20:25:51Z

Xz9215: /* Files */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 4, and IRC of transition state is shown on figure 5.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 6.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table above. The standard C-C bond lengths and the Van der Waals radius of the C atom are presented below.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on above figure 6, the frequency is -950cm<sup>-1</sup> (figure 5). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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<uploadedFileContents>XZ9215EXODIOXOLE.LOG</uploadedFileContents>
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</jmol>
|}

{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
|-
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|-
|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
|-
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity. Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at B3LYP (6-31G(d)) / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 4.
According to figure 11 and table 4, the small activation energy is due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-311G(d,p) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Exercise 1 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 2 files
|-
|Cyclohexadiene
|[[File:XZ9215CYCLOHEXDIENE.LOG]]
|-
|1,3-dioxole
|[[File:XZ921513DIOXOLE.LOG]]
|-
|Exo TS
|[[File:XZ9215E2EXODIOXOLE TS POP.LOG]]
|-
|Endo TS
|[[File:XZ9215E2endoTS POP.LOG]]
|-
|Exo product
|[[File:XZ9215 exo EXODIOXOLE 631GD.LOG]]
|-
|Endo product
|[[File:XZ9215endo1133 TS 631GD.LOG]]
|}

{| class="wikitable"
|+ Exercise 3 files
|-
|Endo TS
|[[File:XZ9215E3 D-A ENDO TS.LOG]]
|-
|Exo TS
|[[File:XZ9215E3 D-A EXO TS.LOG]]
|-
|Cheletropic TS
|[[File:XZ9215 E3 cheletropic PRODUCT TS.LOG]]
|-
|Endo IRC
|[[File:XZ9215 E3ENDO IRC.LOG]]
|-
|Exo IRC
|[[File:XZ9215 E3 EXO IRC.LOG]]
|-
|Cheletropic IRC
|[[File:XZ9215 E3 PRODUCT IRC.LOG]]
|}

Rep:MOD:XZ9215

2018-01-26T20:25:18Z

Xz9215: /* Files */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 4, and IRC of transition state is shown on figure 5.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 6.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table above. The standard C-C bond lengths and the Van der Waals radius of the C atom are presented below.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on above figure 6, the frequency is -950cm<sup>-1</sup> (figure 5). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
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|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity. Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

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|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at B3LYP (6-31G(d)) / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 4.
According to figure 11 and table 4, the small activation energy is due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-311G(d,p) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Exercise 1 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 2 files
|-
|Cyclohexadiene
|[[File:XZ9215CYCLOHEXDIENE.LOG]]
|-
|1,3-dioxole
|[[File:XZ921513DIOXOLE.LOG]]
|-
|Exo TS
|[[File:XZ9215E2EXODIOXOLE TS POP.LOG]]
|-
|Endo TS
|[[File:XZ9215E2endoTS POP.LOG]]
|-
|Exo product
|[[File:XZ9215 exo EXODIOXOLE 631GD.LOG]]
|-
|Endo product
|[[File:XZ9215endo1133 TS 631GD.LOG]]
|}

{| class="wikitable"
|+ Exercise 3 files
|-
|Endo TS
|[[File:XZ9215E3 D-A ENDO TS.LOG]]
|-
|Exo TS
|[[File:XZ9215E3 D-A EXO TS.LOG]]
|-
|Cheletropic TS
|[[File:XZ9215 E3 cheletropic PRODUCT TS.LOG]]
|-
|Endo IRC
|[[File:File:XZ9215 E3ENDO IRC.LOG]]
|-
|Exo IRC
|[[File:File:XZ9215 E3 EXO IRC.LOG]]
|-
|Cheletropic IRC
|[[File:File:XZ9215 E3 PRODUCT IRC.LOG]]
|}

File:XZ9215 E3 PRODUCT IRC.LOG

2018-01-26T20:24:02Z

Xz9215:

File:XZ9215 E3ENDO IRC.LOG

2018-01-26T20:23:28Z

Xz9215:

File:XZ9215 E3 EXO IRC.LOG

2018-01-26T20:22:42Z

Xz9215:

Rep:MOD:XZ9215

2018-01-26T20:21:45Z

Xz9215: /* Transition states and reactivity */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 4, and IRC of transition state is shown on figure 5.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 6.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table above. The standard C-C bond lengths and the Van der Waals radius of the C atom are presented below.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on above figure 6, the frequency is -950cm<sup>-1</sup> (figure 5). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
|-
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|-
|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
|-
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity. Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at B3LYP (6-31G(d)) / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 4.
According to figure 11 and table 4, the small activation energy is due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-311G(d,p) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Exercise 1 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 2 files
|-
|Cyclohexadiene
|[[File:XZ9215CYCLOHEXDIENE.LOG]]
|-
|1,3-dioxole
|[[File:XZ921513DIOXOLE.LOG]]
|-
|Exo TS
|[[File:XZ9215E2EXODIOXOLE TS POP.LOG.LOG]]
|-
|Endo TS
|[[File:XZ9215E2endoTS POP.LOG]]
|-
|Exo product
|[[File:XZ9215 exo EXODIOXOLE 631GD.LOG]]
|-
|Endo product
|[[File:XZ9215endo1133 TS 631GD.LOG]]
|}

{| class="wikitable"
|+ Exercise 3 files
|-
|Endo TS
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Exo TS
|[[File:XZ9215ETHYLENE.LOG]]
|-
|Cheletropic TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Endo IRC
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|Exo IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|-
|Cheletropic IRC
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|}

Rep:MOD:XZ9215

2018-01-26T20:14:20Z

Xz9215: /* Files */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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<script>frame 52; </script>
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|<jmol>
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<uploadedFileContents>XZ9215ETHYLENE.LOG</uploadedFileContents>
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 4, and IRC of transition state is shown on figure 5.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 6.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table above. The standard C-C bond lengths and the Van der Waals radius of the C atom are presented below.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on above figure 6, the frequency is -950cm<sup>-1</sup> (figure 5). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
|-
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|-
|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
|-
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity. Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at B3LYP (6-31G(d)) / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 4.
According to figure 11 and table 4, the small activation energy is due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-311G(d,p) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Exercise 1 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 2 files
|-
|Cyclohexadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|1,3-dioxole
|[[File:XZ9215ETHYLENE.LOG]]
|-
|Exo TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Endo TS
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|Exo product
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|-
|Endo product
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 3 files
|-
|Endo TS
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Exo TS
|[[File:XZ9215ETHYLENE.LOG]]
|-
|Cheletropic TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Endo IRC
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|Exo IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|-
|Cheletropic IRC
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|}

Rep:MOD:XZ9215

2018-01-26T20:12:42Z

Xz9215: /* Files */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 4, and IRC of transition state is shown on figure 5.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 6.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table above. The standard C-C bond lengths and the Van der Waals radius of the C atom are presented below.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on above figure 6, the frequency is -950cm<sup>-1</sup> (figure 5). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
|-
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|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity. Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at B3LYP (6-31G(d)) / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 4.
According to figure 11 and table 4, the small activation energy is due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-311G(d,p) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Exercise 1 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 2 files
|-
|Cyclohexadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|1,3-dioxole
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS of EXO
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|TS of Endo
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|Exo product
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|-
|Endo product
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 3 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|}

Rep:MOD:XZ9215

2018-01-26T20:12:11Z

Xz9215: /* Files */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 4, and IRC of transition state is shown on figure 5.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 6.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table above. The standard C-C bond lengths and the Van der Waals radius of the C atom are presented below.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on above figure 6, the frequency is -950cm<sup>-1</sup> (figure 5). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
|-
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|-
|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
|-
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity. Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at B3LYP (6-31G(d)) / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 4.
According to figure 11 and table 4, the small activation energy is due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-311G(d,p) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Exercise 1 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 2 files
|-
|Cyclohexadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|1,3-dioxole
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS of EXO
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|TS of Endo
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|Exo product
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|-
|Endo product
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 3 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

Rep:MOD:XZ9215

2018-01-26T20:10:13Z

Xz9215: /* Files */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 4, and IRC of transition state is shown on figure 5.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 6.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table above. The standard C-C bond lengths and the Van der Waals radius of the C atom are presented below.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on above figure 6, the frequency is -950cm<sup>-1</sup> (figure 5). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
|-
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|-
|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
|-
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity. Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at B3LYP (6-31G(d)) / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 4.
According to figure 11 and table 4, the small activation energy is due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-311G(d,p) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Exercise 1 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 2 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

{| class="wikitable"
|+ Exercise 3 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

Rep:MOD:XZ9215

2018-01-26T20:09:23Z

Xz9215: /* Files */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 4, and IRC of transition state is shown on figure 5.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 6.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table above. The standard C-C bond lengths and the Van der Waals radius of the C atom are presented below.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on above figure 6, the frequency is -950cm<sup>-1</sup> (figure 5). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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|}

{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
|-
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|-
|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
|-
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity. Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at B3LYP (6-31G(d)) / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 4.
According to figure 11 and table 4, the small activation energy is due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-311G(d,p) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Table 1. Exercise 1 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215 E1 CYCLOHAXENE TS.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

File:XZ9215 E1 CYCLOHAXENE TS.LOG

2018-01-26T20:09:03Z

Xz9215:

Rep:MOD:XZ9215

2018-01-26T20:07:16Z

Xz9215: /* Files */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 4, and IRC of transition state is shown on figure 5.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 6.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table above. The standard C-C bond lengths and the Van der Waals radius of the C atom are presented below.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on above figure 6, the frequency is -950cm<sup>-1</sup> (figure 5). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
|-
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|-
|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity. Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at B3LYP (6-31G(d)) / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 4.
According to figure 11 and table 4, the small activation energy is due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-311G(d,p) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Table 1. Exercise 1 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:XZ9215E1CYCLOHAXENE IRC.LOG]]
|}

File:XZ9215E1CYCLOHAXENE IRC.LOG

2018-01-26T20:06:32Z

Xz9215:

Rep:MOD:XZ9215

2018-01-26T20:04:09Z

Xz9215: /* Files */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 4, and IRC of transition state is shown on figure 5.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
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The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 6.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table above. The standard C-C bond lengths and the Van der Waals radius of the C atom are presented below.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on above figure 6, the frequency is -950cm<sup>-1</sup> (figure 5). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
|-
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|-
|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity. Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at B3LYP (6-31G(d)) / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 4.
According to figure 11 and table 4, the small activation energy is due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-311G(d,p) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Table 1. Exercise 1 files
|-
|Butadiene
|[[File:XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[File:XZ9215ETHYLENE.LOG]]
|-
|TS
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|Cyclohexene
|[[File:XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:Ywu ex1 IRC.LOG]]
|}

Rep:MOD:XZ9215

2018-01-26T20:03:01Z

Xz9215: /* Transition states and reactivity */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 4, and IRC of transition state is shown on figure 5.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
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The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 6.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table above. The standard C-C bond lengths and the Van der Waals radius of the C atom are presented below.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on above figure 6, the frequency is -950cm<sup>-1</sup> (figure 5). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
|-
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|-
|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity. Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at B3LYP (6-31G(d)) / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 4.
According to figure 11 and table 4, the small activation energy is due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-311G(d,p) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Table 1. Exercise 1 files
|-
|Butadiene
|[[XZ9215BUTADIENE.LOG]]
|-
|Ethene
|[[XZ9215ETHYLENE.LOG]]
|-
|TS
|[[XZ9215CYCLOHAXENE TS1.LOG]]
|-
|Cyclohexene
|[[XZ9215CYCLOHAXENE TS1.LOG]]
|-
|IRC
|[[File:Ywu ex1 IRC.LOG]]
|}

Rep:MOD:XZ9215

2018-01-26T19:53:47Z

Xz9215: /* Transition states and reactivity */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 4, and IRC of transition state is shown on figure 5.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 6.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table above. The standard C-C bond lengths and the Van der Waals radius of the C atom are presented below.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on above figure 6, the frequency is -950cm-1 (figure 5). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
|-
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|-
|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
|-
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity. Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

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|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at B3LYP (6-31G(d)) / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 4.
According to figure 11 and table 4, the small activation energy is due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-311G(d,p) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

====<u>Files</u>====

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
|-
|Butadiene
|[[File:YWU EX1 BUTADIENE.LOG]]
|-
|Ethene
|[[File:YWU EX1 ETHYLENE.LOG]]
|-
|TS
|[[File:YWU EX1 TS.LOG]]
|-
|Cyclohexene
|[[File:YWU EX1 PRODUCT.LOG]]
|-
|IRC
|[[File:Ywu ex1 IRC.LOG]]
|}

Rep:MOD:XZ9215

2018-01-26T19:50:57Z

Xz9215: /* Conclusion */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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|<jmol>
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<script>frame 14; </script>
<uploadedFileContents>XZ9215ETHYLENE.LOG</uploadedFileContents>
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 4, and IRC of transition state is shown on figure 5.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 6.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table above. The standard C-C bond lengths and the Van der Waals radius of the C atom are presented below.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on above figure 6, the frequency is -950cm-1 (figure 5). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
|-
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|-
|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
|-
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity. Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at B3LYP (6-31G(d)) / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 4.
According to figure 11 and table 4, the small activation energy is due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
A basis set of PM6 was first used to optimise the structures of TS which is not very accurate. Thus, in order to obtain a better optimisation, basis set 6-311G(d,p) could be used.

Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO constructed by Gaussview, a diagram of the TS MO could be drawn which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

By calculating the activation barrier and reaction energy of a particular reaction, the most favoured reaction pathway could be told, which has the lowest activation energy and reaction energy, and the lowest activation energy reaction is often under kinetic control while the reaction require highest energy of activation is under thermodynamic control. In conclusion, Gaussview did computer simulation which enables us to solve the chemical problems more efficiently and effectively, and it also help us to understand the reaction better.

Rep:MOD:XZ9215

2018-01-26T19:27:41Z

Xz9215: /* Conclusion */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 4, and IRC of transition state is shown on figure 5.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 6.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table above. The standard C-C bond lengths and the Van der Waals radius of the C atom are presented below.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on above figure 6, the frequency is -950cm-1 (figure 5). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
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|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity. Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

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|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at B3LYP (6-31G(d)) / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 4.
According to figure 11 and table 4, the small activation energy is due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO analysis, a diagram of the TS MO could be constructed which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

Rep:MOD:XZ9215

2018-01-26T19:27:26Z

Xz9215: /* Conclusion */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 4, and IRC of transition state is shown on figure 5.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 6.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table above. The standard C-C bond lengths and the Van der Waals radius of the C atom are presented below.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on above figure 6, the frequency is -950cm-1 (figure 5). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
|-
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|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity. Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at B3LYP (6-31G(d)) / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 4.
According to figure 11 and table 4, the small activation energy is due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===
Frequency and IRC analysis allow us to determine the correct TS geometry by checking if the first mode of vibration has a negative imaginary frequency and if all reactants, products and TS geometry have gradient of 0, respectively. From MO analysis, a diagram of the TS MO could be constructed which follow the rule that only MO with same symmetry label could overlap. Also, single point energy calculation of MO enables us to find whether this cycloaddition reaction is inverse electron demand or normal electron demand according to the energy levels of reactants.

Rep:MOD:XZ9215

2018-01-26T19:13:32Z

Xz9215: /* Transition states and reactivity */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 4, and IRC of transition state is shown on figure 5.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 6.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table above. The standard C-C bond lengths and the Van der Waals radius of the C atom are presented below.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on above figure 6, the frequency is -950cm-1 (figure 5). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
|-
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|-
|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
|-
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity. Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

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|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at B3LYP (6-31G(d)) / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 4.
According to figure 11 and table 4, the small activation energy is due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

===<u>Conclusion</u>===

Rep:MOD:XZ9215

2018-01-26T19:11:24Z

Xz9215: /* Reaction profile */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 4, and IRC of transition state is shown on figure 5.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 6.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table above. The standard C-C bond lengths and the Van der Waals radius of the C atom are presented below.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on above figure 6, the frequency is -950cm-1 (figure 5). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
|-
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|-
|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
|-
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity. Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at B3LYP (6-31G(d)) / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 4.
According to figure 11 and table 4, the small activation energy is due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 9. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

Rep:MOD:XZ9215

2018-01-26T19:10:52Z

Xz9215: /* Reaction barrier and reaction energy */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 4, and IRC of transition state is shown on figure 5.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 6.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table above. The standard C-C bond lengths and the Van der Waals radius of the C atom are presented below.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on above figure 6, the frequency is -950cm-1 (figure 5). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
|-
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|-
|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity. Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
|+ Table 14. Transition state MO
| '''Substrates'''
| '''Gibbs free energy at B3LYP (6-31G(d)) / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
|+ Table 15. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 4.
According to figure 11 and table 4, the small activation energy is due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 12. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

Rep:MOD:XZ9215

2018-01-26T19:09:50Z

Xz9215: /* IRC analysis */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 4, and IRC of transition state is shown on figure 5.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
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The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 6.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table above. The standard C-C bond lengths and the Van der Waals radius of the C atom are presented below.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on above figure 6, the frequency is -950cm-1 (figure 5). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
|-
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|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity. Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table13. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
| '''Substrates'''
| '''Gibbs free energy at B3LYP (6-31G(d)) / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 4.
According to figure 11 and table 4, the small activation energy is due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 12. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.

Rep:MOD:XZ9215

2018-01-26T19:09:21Z

Xz9215: /* Optimisation of TS at PM6 level */

==Transition states and reactivity==
===<u>Introduction</u>===

The number of normal modes of vibration = 3N–5 for linear and 3N–6 for nonlinear molecules which is also the number of degree of freedom. Hence, the potential energy surface (PES) is plotted with potential energy against every degree of freedom. Potential energy surface could be to analyse the molecular geometry and reaction dynamics. The necessary points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. A stationary point on a PES is a nuclear configuration where all the forces vanish, <math>\frac{\partial V}{\partial q}=0 </math> (q is the order parameter), which could be mixima or minima. Energy minima correspond to stable chemical species which refers to products and reactants and saddle point represents transition states which is the highest point of energy on the reaction coordinate. This reaction pathway is also the lowest energy pathway.

At reactants and products, the curvature is positive,<math>\frac{\partial^2V}{\partial q^2}</math>>0, because they are at local minima, and in transition state, the second derivative at this point is negative, because it is a maximum point, and along the order parameter, energy will always decrease to form either products or reactants.

In the TS, because the bonds between atoms are being stretched or compressed, a simple harmonic oscillator model could be used to relate frequencies of TS and the second derivative of TS energy. The equations are shown below.

The second derivative of potential energy is equal to force constant: <math>k = \frac{\partial^2E}{\partial q^2} </math>

Thus frequency could be calculated: <math>\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}} </math> where <math> \mu = \frac{m_1m_2}{m_1+m_2}</math>

This explains why the first mode of TS vibrational frequency is always negative and imaginary.

[[File:XZ9215PES.PNG|600px|thumb|center|Figure1. PES and the position of reactants, products, TS on it ]]

===<u>Exercise 1</u>===
The Diels-Alder reaction of butadiene with ethylene is shown below, and the product, cyclohexene is formed from cis butadiene exclusively, which is due to trans butadiene is unable to form orbital overlap with ethylene.

[[File:XZ9215-E1-Reaction.PNG|600px|thumb|center|Figure2.Reaction of Butadiene with Ethylene]]

====<u>Optimization</u>====
The reactants, product and transition state were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

{| class="wikitable"
|+ Table 1. Optimized structures by PM6 calculation
! colspan="4" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | 1,3-butadiene
| style="text-align: center;" | Ethylene
| style="text-align: center;" | Transition State
| style="text-align: center;" | Cyclohexene
|-
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====<u>IRC and frequency analysis</u>====

The transition state could be confirmed by doing frequency analysis and IRC in Gaussview. The diagram of the vibration is shown on figure 4, and IRC of transition state is shown on figure 5.

The negative frequency are imaginary since frequencies are computed from the square roots of negative force constants which is due to the bond formation or breaking. Frequencies indicate the curvature of the potential energy, the negative frequency means a saddle point (transition state), which is a potential energy maximum. Thus, for the transition state, a negtive frequency is expected for the first vibrational mode (one and only one).

[[File:XZ9215Vibration.PNG|800px|thumb|center|Figure3. Frequencies of TS]]

[[File:XZ9215IRC Exercise 1.PNG|800px|thumb|center|Figure4. Upper graph: total energy along IRC; Lower graph: RMS gradient norm along IRC]]

The minimum energy pathway is shown on the upper graph while the lower graph is the gradient norm along IRC where products, transition states and reactants (maxima/minima) all have a gradient of 0. Comparing the 3 stationary points on the upper graph with the 3 minima on the lower graph, they all match with each other which further confirmed the transition state geometry is correct.
However, the Gaussview calculate the IRC from the transition state which has the highest energy, both reactants and products have lower energy than the transition state, so the intrinsic reaction coordinate could start from reactant to product or from product to reactant.

====<u>Molecular orbitals analysis</u>====

{| class="wikitable"
|+ Table 2. MO calculated of TS and reactants
|-
| style="text-align: center;" |HOMO of diene, Symmetric
| style="text-align: center;" |LUMO of diene, Antisymmetric
| style="text-align: center;" |HOMO of alkene, Symmetric
| style="text-align: center;" |LUMO of alkene, Antisymmetric
|-
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|-
| style="text-align: center;" |HOMO-1 of TS, Antisymmetric
| style="text-align: center;" |HOMO of TS, Symmetric
| style="text-align: center;" |LUMO of TS, Symmetric
| style="text-align: center;" |LUMO+1 of TS, Antisymmetric
|-
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The molecular orbital diagram could be constructed by observing the MOs illustrated in the Gaussview. Due to butadiene is more electron rich, the energy gap between butadiene HOMO and LUMO is smaller than that of ethylene. According to the experimental data, the energy of TS HOMO and HOMO-1 are higher than expected while LUMO, LUMO+1 have lower energy than expected. This phenomenon is due to mixing which tends to be large when the MOs are in HOMO-LUMO region. Also at TS the electrons are delocalized on the molecular orbitals thus stabilized the antibonding orbitals and destabilized the bonding orbitals.

[[File:XZ9215MO exercise 1.PNG|700px|thumb|center|Figure5. MO diagram of TS]]

According to woodward-hoffmann rule, only orbitals with the same symmetry could interact and form overlap with each other. For this Diels-Alder reaction, the symmetric LUMO of butadiene interact with symmetric HOMO of ethylene and form transition state MOs with the same symmetry label. Antisymmetric LUMO and HOMO of the reactants form antisymmetric LUMO+1 and HOMO-1 of transition state as illustrated on figure 6.

{| class="wikitable" border="1"
|+ Table 3. Woodward Hoffmann rule
|-
! colspan="3" style="text-align: left;"|Illustration of asymmetric and symmetric MOs
! colspan="3" style="text-align: left;"|Requirement of MO overlap
|-
| colspan="3" align="center"|[[File:XZ9215Symmetric asymmertric.PNG|400px]]
| colspan="3" align="center"|[[File:XZ9215Symmetric table.PNG|400px]]
|}

====<u>Bond length analysis</u>====
{| class="wikitable"
|+ Table 4. bond length comparison
! colspan="5" style="text-align: center;" style="background: #0D4F8B; color: white;" | The C-C bond lengths in the reaction coordinate
|-
| [[File:XZ9215Alkene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Butadiene picture.PNG|thumb|center|250px]]
| [[File:XZ9215Cyclo picture.PNG|thumb|center|250px]]
| [[File:XZ9215Product picture.PNG|thumb|center|250px]]
| [[File:XZ9215Animation TS.gif]]
|-
|C1-C2 double bond= 1.35Å

|C3-C4 double bond= 1.33Å
C4-C5 single bond= 1.47Å<br>
C5-C6 double bond= 1.33Å<br>

|C1-C2 double bond breaking= 1.38Å
C2-C3 single bond forming= 2.11Å<br>
C3-C4 double bond breaking= 1.38Å<br>
C4-C5 double bond forming= 1.41Å<br>
C5-C6 double bond breaking= 1.38Å<br>
C6-C1 single bond forming= 2.11Å<br>

|C1-C2 single bond = 1.54Å
C2-C3 single bond = 1.54Å<br>
C3-C4 single bond = 1.50Å<br>
C4-C5 double bond = 1.34Å<br>
C5-C6 single bond = 1.50Å<br>
C6-C1 single bond = 1.54Å<br>

|Amination of butadiene and ethylene approaches with each other

|}

The C-C bond lengths of the reactants, product and the TS are presented in the table above. The standard C-C bond lengths and the Van der Waals radius of the C atom are presented below.

{| class="wikitable"
|+ Table 5
! colspan="7" style="text-align: center;" style="background: #0D4F8B; color: white;" | The standard carbon-carbon bond lengths
|-
|C-C bond
|sp<sup>3</sup>carbon - sp<sup>3</sup>carbon single bond
|sp<sup>3</sup>carbon - sp<sup>2</sup>carbon single bond
|sp<sup>2</sup>carbon - sp<sup>2</sup>carbon single bond
|carbon=carbon double bond
|van der Waals radius of carbon atom
|van der Waals distance of 2 carbon atoms
|-
|Bond length
| style="text-align:center;"| 1.54Å
| style="text-align:center;"| 1.50Å
| style="text-align:center;"| 1.47Å
| style="text-align:center;"| 1.34Å
| style="text-align:center;"| 1.70Å
| style="text-align:center;"| 3.40Å
|}

At transition state, the C=C double bond of butadiene and ethylene become longer, because the double bonds are only partially breaking, the electrons are delocalized and on the way to form a single bond.

Also, the distance between terminal carbon atoms in the TS is 2.11 Å, which is much smaller than the standard Van der Waals radius between 2 carbon atoms which is 3.4 Å and longer than standard sp3-sp3 C-C single bond 1.54 Å. This indicates the single bonds in the transition state are only partially formed, but the distance between carbon atoms need to be remained within the Van der Waals radius to provide enough affinity for the bond formation. C2-C3 and C1-C6 distances are reduced from 2.11 Å at transition state to 1.54 Å in the product, this is an indication of new single bond formation in the product.

The animation of the vibration mode is shown on above figure 6, the frequency is -950cm-1 (figure 5). The 2 terminal carbons on butadiene and 2 carbons on ethylene vibrates and approaches to each other simultaneously.

===<u>Exercise 2</u>===

This Diels-Alder reaction between cyclohexadiene and 1,3-dioxole will lead to exo or endo product which is under thermodynamic control and kinetic control respectively. The reaction activation barrier of forming both products are investigated in this exercise.

[[File:XZ9215 E2 Reaction scheme.PNG|600px|thumb|center|Figure 6.Reaction of Cyclohexadiene and 1,3-Dioxole]]

{| class="wikitable"
|+ Table 6. Optimized structures by B3LYP/6-31G(d) calculation
! colspan="6" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
| style="text-align: center;" | Endo TS
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo product
| style="text-align: center;" | Exo product
|-
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{| class="wikitable"
|+ Table 7. Vibrational frequencies
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | The frequencies of endo TS and exo TS
|-
| [[File:XZ9215Endo vibration.PNG|thumb|center|500px]]
| [[File:XZ9215E2EXOVibrations.PNG|thumb|center|500px]]
|-
|style="text-align:center;"| Endo TS vibrations

|style="text-align:center;"| Exo TS vibrations

|}

From the frequency analysis, there is only one negative imaginary frequency for each TS. For products and reactants, all the frequencies are positive. They are all confirmed to be correctly optimized.

====<u>MO analysis</u>====
{| class="wikitable"
|+ Table 8. Transition state MO
|[[File:XZ9215E2Endo MO diagram.PNG|600px|thumb|center|Endo transition state MO]]
|[[File:XZ9215 E2 Exo MO diagram.PNG|600px|thumb|center|Exo transition state MO]]
|}

{| class="wikitable"
|+ Table 9. MO calculated of TS, products and reactants
|-
|HOMO of cyclohexadiene, Antiymmetric
|LUMO of cyclohexadiene, Symmetric
|HOMO of 1,3-dioxole, Symmetric
|LUMO of 1,3-dioxole, Antisymmetric
|-
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|-
|HOMO-1 of endo TS, Antisymmetric
|HOMO of endo TS, Symmetric
|LUMO of endo TS, Symmetric
|LUMO+1 of endo TS, Antisymmetric
|-
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|HOMO-1 of exo TS, Antisymmetric
|HOMO of exo TS, Symmetric
|LUMO of exo TS, Symmetric
|LUMO+1 of exo TS, Antisymmetric
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====Normal or inverse electron demand====

The relative energies of the frontier MOs (including HOMO and LUMO) could be used to explain the reactivity. Because the key interaction in cycloaddition TS is between the HOMO of one reactant and LUMO of another reactant which could be either dienophile or diene, as a result, 2 types of interaction could be identified.
For normal electron demand, HOMO of diene will overlap with LUMO of dienophile, this happens when the diene is electron rich and the dienophile is electron deficient. Inverse electron demand is achieved by reverse the substitution pattern, the electron withdrawing group on the diene makes it electron poor thus decrease the LUMO energy, and electron donating group on dienophile raised the energy of HOMO up. The energy gap between LUMO of diene and HOMO of dienophile is reduced, hence interact with each other.

A single point energy calculation at the combined reactant geometries was done, The MOs calculated confirmed both reactions are inverse electron demand. Both LUMO and HOMO of Cyclohexadiene have lower energies than 1,3-Dioxole. But the energy gap between 1,3-Dioxole HOMO-LUMO is larger than that of cyclohexadiene. Because the 2 oxygen atoms on the dienophile (1,3-dioxole) will donate electron to the C=C double bond and makes it electron rich thus raise up the energy levels of 1,3-Dioxole. The resultant energy gap between LUMO of cyclohexadiene and HOMO of 1,3 dioxole is 540.66 KJ/mol which is smaller than the energy gap between HOMO of cyclohexadiene and LUMO of 1,3-dioxole 612.88 KJ/mol. Hence, both exo and endo have inverse electron demand.

====Reaction barriers and reaction energies at room temperature====

{| class="wikitable"
|+ Table 10. Transition state MO
| '''Substrates'''
| '''Gibbs free energy optimised at PM6 / KJmol<sup>-1</sup>'''
| '''Gibbs free energy optimised at B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| '''Cyclohexadiene'''
| style="text-align: center;" |-395.4563
| style="text-align: center;" |-612382.638
|-
| '''1,3-Dioxole'''
| style="text-align: center;" |-55.29825
| style="text-align: center;" |-700975.023
|-
| '''Sum of reactant energy'''
| style="text-align: center;" |-450.7545
| style="text-align: center;" |-1313357.588
|-
| '''Exo-TS'''
| style="text-align: center;" |-479.59275
| style="text-align: center;" |-1313249.199
|-
| '''Exo-Product'''
| style="text-align: center;" |-208.02075
| style="text-align: center;" |-1313460.488
|-
| '''Endo-TS'''
| style="text-align: center;" |-477.763125
| style="text-align: center;" |-1313255.094
|-
| '''Endo-Product'''
| style="text-align: center;" |-207.225375
| style="text-align: center;" |-1313464.163
|}

{| class="wikitable"
|+ Table 11. Transition state MO
! rowspan="2" style="text-align: center;" |
! colspan="2" style="text-align: center;" | '''PM6 / KJmol<sup>-1</sup>'''
! colspan="3" style="text-align: center;" | '''B3LYP (6-31G(d)) / KJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
| style="text-align: center;" | '''Endo'''
| style="text-align: center;" | '''Exo'''
|-
| '''Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 28.838
| style="text-align: center;" | + 27.009
| style="text-align: center;" | + 102.503
| style="text-align: center;" | + 108.392
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 243.531
| style="text-align: center;" | - 242.732
| style="text-align: center;" | - 106.575
| style="text-align: center;" | -102.900
|}
The activation energy and total energy of reaction were calculated and summarized in table 3. (Activation barrier could be calculated by the difference in energy between TS and reactants. The total energy of the reaction is the energy difference between reactants and products.) From the table, we can see endo reaction possess with a lower activation energy and reaction energy, which makes it a more favorable reaction kinetically under normal conditions.

[[File:XZ9215Secondary orbital interaction.PNG|500px|thumb|center|Figure7. Endo transition state MO]]

Endo approach is often preferred because of secondary orbital interactions(SOI) between the C-O non-bonding p-orbital lobes and the back lobes of the cyclohexadiene HOMO. No bonds are formed from these interactions, but the transition state energy is lowered by such interaction, and this endo product will be formed faster, this is an indication of lower activation barrier. However, the lower total reaction energy cannot be explained by SOI because this type of interaction is not shown on the product.The higher reaction energy and activation barrier of exo reaction comes from the exo product is more sterically hindered due to the presence of sp3 hybridized bridge carbon (energy need to be put in to force the geometry to be formed). As a conclusion, exo product is thermodynamically favored while endo product is kinetically favored.

===<u>Exercise 3</u>===

Xylylene and sulfur dioxide could undergo 3 different mechanisms which refers to endo Diels Alder reaction, exo Diels Alder reaction and cheletropic reaction to form corresponding products.
Which reaction route is most preferred is investigated in this exercise.

[[File:XZ9215E3Reaction scheme 3.PNG|600px|thumb|center|Figure 8. o-Xylylene and SO<sub>2</sub> Cycloaddition ]]

====<u>Optimisation of TS at PM6 level</u>====

The transition state of exo D-A, endo D-A and cheletropic reaction were optimized at PM6 level, and the structures of the optimized geometry are shown on table 1.

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|+ Table 12. Optimized structures by PM6 calculation
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Optimized Structure
|-
| style="text-align: center;" | Diels-Alder endo
| style="text-align: center;" | Diels-Alder exo
| style="text-align: center;" | Cheletropic
|-
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====<u>IRC analysis</u>====

{| class="wikitable"
|+ Table9. Approach trajectory of 3 reactions and their IRC
| style="text-align: centre;" | Approach trajectory of endo product formation
| style="text-align: centre;" | Endo product formation IRC
|-
|[[File:XZ9215 E3 Endo approch.gif]]
|[[File:XZ9215 E3 IRC endo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of exo product formation
| style="text-align: centre;" | Exo product formation IRC
|-
|[[File:XZ9215 E3 Exo approch.gif]]
|[[File:XZ9215 E3 IRC exo.PNG|600px]]
|-
| style="text-align: centre;" | Approach trajectory of cheletropic product formation
| style="text-align: centre;" | Cheletropic product IRC
|-
|[[File:XZ9215 E3 Cheletropic approch.gif]]
|[[File:XZ9215 E3 Cheletropic IRC product.PNG|600px]]
|}

====<u>Reaction barrier and reaction energy</u>====

{| class="wikitable"
| '''Substrates'''
| '''Gibbs free energy at B3LYP (6-31G(d)) / kJmol<sup>-1</sup>'''
|-
| '''SO<sub>2</sub>'''
| style="text-align: center;" |-313.534
|-
| '''Xylylene'''
| style="text-align: center;" |469.783
|-
| '''Sum of reactants energy'''
| style="text-align: center;" |156.249
|-
| '''Exo-DA-TS'''
| style="text-align: center;" |243.983
|-
| '''Endo-DA-TS'''
| style="text-align: center;" |239.880
|-
| '''Exo-Cheletropic-TS'''
| style="text-align: center;" |262.093
|-
| '''Exo-DA-product'''
| style="text-align: center;" |58.548
|-
| '''Endo-DA-product'''
| style="text-align: center;" |59.152
|-
| '''Cheletropic product'''
| style="text-align: center;" |-0.0148
|}

{| class="wikitable"
! rowspan="2" style="text-align: center;" |
! colspan="3" style="text-align: center;" | '''PM6 / kJmol<sup>-1</sup>'''
|-
| style="text-align: center;" | '''Exo DA'''
| style="text-align: center;" | '''Endo DA'''
| style="text-align: center;" | '''Cheletropic'''
|-
| '''Activation energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | + 87.734
| style="text-align: center;" | + 83.631
| style="text-align: center;" | + 105.844
|-
| '''Reaction energy /kJmol<sup>-1</sup>'''
| style="text-align: center;" | - 97.701
| style="text-align: center;" | - 97.097
| style="text-align: center;" | - 156.234
|}

The IRC provide information of the activation barrier and total reaction energy. The calculation of the energies was done and summarized on table 4.
According to figure 11 and table 4, the small activation energy is due to the highly unstable reactant xylylene.

The driving force of the reaction is the formation of more stable 6-membered aromatic ring in the product. Also, the rigid structure of the exocyclic cis diene (constrained to cis position) makes this reaction favorable.
The bond length between carbon atoms in 6-membered ring of xylylene in TS and product are analyzed. The C=C double bond within the xylylene ring become longer and C-C single bond become slightly shorter during the formation of transition state. In the product, all carbon-carbon bonds length become equal due to the delocalization of electrons. This could be observed by the transition state approach trajectories of 3 reaction routes which are shown above.

====<u>Reaction profile</u>====
[[File:XZ9215 Reaction profile new.PNG|600px|thumb|center|Figure 12. Reaction profile of endo, exo Diels-Alder reaction and cheletropic reaction ]]

The reaction profile is shown above. As figure shown, endo Diels-Alder reaction needs least amount of activation energy, the product forms most quickly and is under kinetic control. The cheletropic reaction requires the largest amount of activation energy thus forms the most stable thermodynamic product which is favored under high temperatures. Also, unlike the 2 reactants in exercise 2 which forms exo product with higher activation barrier because of the steric reasons, the contribution of steric effect is quite small in cycloaddition of xylylene and sulfur dioxide, thus the difference between exo and endo activation barrier is small in exercise 3. The cheletropic product is favoured thermodynamically because it gives a more stable 5-membered ring.