Rep:Llt15 TS

2017-10-24T15:02:04Z

==Transition States and Reactivity==

===Introduction===

A transition state is the saddle point which is a local maxima on the minimum energy path linking reactants and the products whereas the reactants and products correspond to the minimum in the potential energy surface (PES). Therefore, at both minimum point and transition structure, the total gradient of the potential energy surface will have a value of zero. This is defined by the first derivative of potential energy vs bond distances graph: ∂V(r<sub>i</sub>)/∂r<sub>i</sub> = 0

For non-linear molecules, there are 3N - 6 normal vibrational modes or so-called degree of freedom. Using a harmonic oscillator model, each vibrational modes has the restoring force defined by Hookes law:<br>
F = -'''k'''x <br>where ''''k'''' is the force/spring constant<br> 'x' is the displacement of spring which resemble bonds from its equilibrium position.<br>
The reactants and products sit in a well at the minimum and vibrate 'forever' unless sufficient energy is provided for them to react. The transition state has a different mode of vibration along the reaction coordinate which take the TS downhill towards the reactant or product, without a restoring force. This lead to a negative '''k'''. Thus, the calculation of second derivative of the curvature ('''k''') in the PES (∂<sup>2</sup>V(r<sub>i</sub>)/∂r<sub>i</sub><sup>2</sup>) helps to distinguish the minimum and TS. As the frequency calculation involves taking square root of a force constant '''k''' and the square root of negative value leads to an imaginary number, at every transition state there must be only one imaginary frequency as all other coordinates are minimised. Hence, it is concluded that a negative value of second derivative of gradient indicated a transition structure whereas positive value represented the minimum point (reactant and product) of the reaction path and the same thing applies in frequency calculation.

[[File:Usetis_IR_equation_llt15.PNG|thumb|center|400px| Figure 1. Equation to calculate the vibrational frequency (\nu) for diatomic molecules <ref>Donald L. Pavia, Gary M. Lampman, George S. Kriz, James A. Vyvyan, 2009. ''Introduction to Spectroscopy'' 4th ed., ''Chap. 2'', pp.21.</ref>]]

For a thermodynamically controlled reaction, the reaction is reversible and the energetically more stable product is favoured. Therefore, the relative energy of transition state is not important as the product with the lowest energy (most stabilized) will eventually predominate under equilibrating condition. For a kinetic controlled reaction, the energy of the transition state determines the predominant product as the product forms irreversibly once the TS is reached. Hence, the pathway that requires lower activation energy to reach the transition state will be chosen. As a result, the most rapidly formed product predominates under kinetic control reaction.

[[File:Thermo_vs_kinetic_llt15_intro.PNG|thumb|center|400px| Figure 2. Schematic diagram for kinetic versus thermodynamic control<ref>King-Chuen Lin, 1988. ''Understanding Product Optimization:
Kinetic versus Thermodynamic Control'', 65(10), pp.857.</ref>]]

===Exercise 1: Cycloaddition of Butadiene and Ethylene===

<br>
[[File:cycloadd_q1_llt15.png|thumb|center|550px|Figure 3. Reaction scheme for cycloaddition of 1,3-butadiene and ethylene.]]

'''Method used for optimization and analysis:'''

The geometry of the reactants are optimized at PM6 level and the optimized reactants are used to construct the transition state of the reaction. The distance 2.20 Å is used in the guess of TS for the approximate separation between the terminal carbon atoms in both reactants as this is the intermediate value between a normal C-C single bond and the Van der Waals distance of 2 carbon atoms. The guess TS structure is optimized at PM6 level and the optimized TS is used to run a IRC to obtained the product. The product is again optimized to a minimum at PM6 level. The optimized structure of reactants, transition state and product are shown in 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>250</size>
<script>frame 16</script>
<uploadedFileContents>BUTADIENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 4</script>
<uploadedFileContents>ETHENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6</script>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>PRODUCT_Q1_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Correlate these MOs with the ones in your MO diagram to show which orbitals interact. What can you conclude about the requirements for symmetry for a reaction (when is a reaction 'allowed' and when is it 'forbidden')? ====

{| class="wikitable"
|+ Table 2. HOMO and LUMO of reactants and transition state (TS)
! style="background: #0D4F8B; color: white;" | Chemical Structure
! style="background: #0D4F8B; color: white;" | HOMO
! style="background: #0D4F8B; color: white;" | LUMO
! style="background: #0D4F8B; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|<jmol>
<jmolApplet>
<title>MO11 (Aysmmetric)</title>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>MO12 (Symmetric)</title>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="3"|[[File:Q1_MO_corrected_llt15_new.png|thumb|center|550px|Figure 4. Idealized MO diagram of [4+2] cycloaddition with with labelled symmetry (Antisymmetric= A, Symmetric= S).]]
|-
|<nowiki>Ethylene</nowiki>
| <jmol>
<jmolApplet>
<title>MO6 (Symmetric)</title>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_Q1_LLT15_REDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>MO7 (Asymmetric)</title>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_Q1_LLT15_REDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| <nowiki>Transition State</nowiki>
| <jmol>
<jmolApplet>
<title>MO16 (HOMO -1)</title>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
<jmol>
<jmolApplet>
<title>MO17 (HOMO)</title>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>MO19 (LUMO + 1)</title>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
<jmol>
<jmolApplet>
<title>MO18 (LUMO)</title>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The HOMO-LUMO interactions shown in the MO diagram of the cycloaddition between butadiene and ethylene are listed below:
Butadiene HOMO (MO 11, A) + Ethylene LUMO (MO 7, A) = Transition State HOMO (MO 16)
Butadiene HOMO (MO 11, A) - Ethylene LUMO (MO 7, A) = Transition State LUMO (MO 19)<br>
Butadiene LUMO (MO 12, S) + Ethylene HOMO (MO 6, S) = Transition State HOMO (MO 17)
Butadiene LUMO (MO 12, S) - Ethylene HOMO (MO 6, S) = Transition State LUMO (MO 18)

The symmetry label 'A' and 'S' corresponds to whether the molecular orbital (MO) is antisymmetric or symmetrical with respect to the mirror plane orthogonal to the sigma bond which lies in the middle of MO.

According to the Woodward Hoffmann rules, the total number of (4q + 2)<sub>s</sub> + (4r)<sub>a</sub> must be odd for the pericyclic reaction to be thermally allowed. The letters 'q' and 'r' stand for integer starting from zero whereas the suffix 's' stands for suprafacial and 'a' for antarafacial. A suprafacial component forms new bonds on the same face whereas an antarafacial components formes new bonds on opposite faces at both ends. However, the reaction is considered to be thermally forbidden but photochemically allowed if the total number of (4q + 2)<sub>s</sub> + (4r)<sub>a</sub> equals to zero or an even number.<br><br>The [<sub>π</sub>4<sub>s</sub> +
<sub>π</sub>2<sub>s</sub>] cycloaddition between butadiene and ethylene is allowed as shown:
(4q + 2)<sub>s</sub> + (4r)<sub>a</sub>
= 1 + 0
= 1
= thermally allowed reaction when q and r equal to 0

<br><br>
'''Write whether the orbital overlap integral is zero or non-zero for the case of a symmetric-antisymmetric interaction, a symmetric-symmetric interaction and an antisymmetric-antisymmetric interaction:'''
{| class="wikitable"
|+ Table 3. Effect of the symmetry of interactions on the orbital overlap integral
! style="background: #0D4F8B; color: white;" | Type of interactions
! style="background: #0D4F8B; color: white;" | Orbital overlap integral
|-
| Symmetric-symmetric
| Non-zero
|-
| Symmetric-antisymmetric
| Zero
|-
| Antisymmetric-antisymmetric
| Non-zero
|}

<br>
'''Include measurements of the 4 C-C bond lengths of the reactants and the 6 C-C bond lengths of the TS and products. How do the bond lengths change as the reaction progresses?'''

{| class="wikitable"
|+ Table 4. The changes in bond length of the reactants, TS and product molecules as reaction progress
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | C-C Bond lenghths
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | C-C Bond lenghths
|-
| <jmol>
<jmolApplet>
<title> Reactant: Ethylene</title>
<color>white</color>
<size>150</size>
<script>frame 4</script>
<script>select atomno=1, atomno=4; label display</script>
<uploadedFileContents>ETHENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| C1-C4 (double bond)= 1.33 Å
| <jmol>
<jmolApplet>
<title>Reactant: 1,3-Butadiene</title>
<color>white</color>
<size>150</size>
<script>frame 16</script>
<script>select atomno=7, atomno=6, atomno=4, atomno=1; label display</script>
<uploadedFileContents>BUTADIENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| C1-C4 (double bond)= 1.34 Å<br>C4-C6 (single bond) = 1.47 Å<br>C6-C7 (double bond)= 1.34 Å
|-
| <jmol>
<jmolApplet>
<title>Transition State</title>
<color>white</color>
<size>150</size>
<script>frame 4</script>
<script>select atomno=1, atomno=4, atomno=6, atomno=7, atomno=11, atomno=14; label display</script>
<uploadedFileContents>TRIAL_TS_2_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| C1-C4 (double bond-breaking)= 1.38 Å<br> C4-C6 (double bond-forming) = 1.41 Å<br> C6-C7 (double bond-breaking)= 1.38 Å<br> C7-C11 (single bond-forming) = 2.11 Å<br> C11-C14 (double bond-breaking)= 1.38 Å<br> C14-C1 (single bond-forming) = 2.11 Å
| <jmol>
<jmolApplet>
<title> Product: Cyclohexene</title>
<color>white</color>
<size>150</size>
<script>frame 10</script>
<script>select atomno=6, atomno=4, atomno=1, atomno=14, atomno=11, atomno=7; label display</script>
<uploadedFileContents>PRODUCT_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| C6-C4 = 1.34 Å, C=C sp<sup>2</sup>-sp<sup>2</sup> bond<br> C4-C1 = 1.50 Å, C-C sp<sup>3</sup>-sp<sup>2</sup> bond<br> C1-C14 = 1.54 Å, C-C sp<sup>3</sup>-sp<sup>3</sup> bond<br> C14-C11 = 1.54 Å, C-C sp<sup>3</sup>-sp<sup>3</sup> bond<br> C11-C7 = 1.54 Å, C-C sp<sup>3</sup>-sp<sup>3</sup> bond<br> C7-C6 = 1.50 Å, C-C sp<sup>3</sup>-sp<sup>2</sup> bond
|}

==== What are typical sp3 and sp2 C-C bond lengths? What is the Van der Waals radius of the C atom? How does this compare with the length of the partly formed C-C bonds in the TS.====

Typical C-C bond length<ref>Popov, E.M., Kogan, G.A. & Zheltova, V.N., 1972. Theor Exp Chem ''6''(1), pp.11-19. https://doi.org/10.1007/BF00525890</ref>:
:sp<sup>3</sup>-sp<sup>3</sup>: 1.54 Å
:sp<sup>3</sup>-sp<sup>2</sup>: 1.50 Å
:sp<sup>2</sup>-sp<sup>2</sup>: 1.47 Å
Van der Waals radius of a carbon atom: 1.70 Å<br>Van der Waals distance of 2 carbon atoms: 3.40 Å

In the transition state of cycloaddition process between butadiene and ethylene, the partly formed C-C single bond lengths are about 2.12 Å which is an intermediate value between typical sp<sup>3</sup> C-C bond length and Van der Waals distance of 2 carbon atoms. For the breaking double bond, the bond lengths are increased upon the change in the carbon hybridisation from sp<sup>2</sup> to sp<sup>3</sup>. In other words, the reduced in s orbital character from sp<sup>2</sup>(33%) to sp<sup>3</sup>(25%) makes the C-C bond longer and weaker as the electrons are less strongly held to the nucleus. On the other hand, the single bond on butadiene is shorter in the transition state as the carbon is hybridised from sp<sup>3</sup> to sp<sup>2</sup> upon double bond formation.

For cyclohexene, there is only a double bond between the sp<sup>2</sup> hybridised C6 and C7, and the remaining carbons are sp<sup>3</sup> hybridised. Thus, there is no delocalisation of electron cloud in the cyclohexene and the electrons are localised along the C-C bond. This explains the existence of the three different bond lengths (1.34 Å, 1.50 Å and 1.54 Å) as the C-C bond lengths vary based on different carbon hybridisation.

{| class="wikitable"
|+ Table 5. The changes in bond length along the reaction path
! style="background: #0D4F8B; color: white;" | Type of Bond
! style="background: #0D4F8B; color: white;" | Bond Length vs reaction coordinate
! style="background: #0D4F8B; color: white;" | Discussion
|-
|C1-C4 and C6-C7 and C11-C14
|[[File:C1C4_dbbreak_q1_llt15.PNG|250px]][[File:C6C7_dbbreak_q1_llt15.PNG|250px]][[File:C11C14_dbbreak_q1_ethene_llt15.PNG|250px]]
|Change in bond order: double bond to single bond<br><br>The graphs show that the bond length increase gradually from 1.34 Å to 1.50 Å upon product formation. The increase in bond length indicates the breaking of the C1-C4 and C6-C7 double bonds due to the change in carbon hybridisation (C1, C7, C11 and C14) from sp<sup>2</sup> to sp<sup>3</sup>. This causes a decrease in electron density between two carbons thus the single bonds are weaken and lengthen.
|-
|C4-C6
|[[File:C4C6_dbform_q1_llt15.PNG|250px]]
|Change in bond order: single bond to double bond<br><br>The graph shows that the bond length decreases gradually from 1.47 Å to 1.34 Å upon product formation. The decrease in bond length indicates the double bond formation between C4 and C6. The additional pi overlap between C4-C6 strengthen the bond and hold the 2 carbon nucleus stronger together resulting in a shorter bond length.
|-
|C7-C11 and C14-C1
|[[File:C7C11_sbform_q1_llt15.PNG|250px]][[File:C14C1_sbform_q1_llt15.PNG|250px]]
|The graphs show a steep decrease in bond length (or distance between 2 carbons) along the reaction coordinate. In this case, the two non-bonding carbon atoms from 1,3-butadiene and ethylene approach each other from Van der Waals distance (3.40 Å) and their orbitals start to overlap across the space in the transition state in order to form the new single bonds in the product stage. All of the 4 carbons change their hybridisation (sp<sup>2</sup> to sp<sup>3</sup>) to form 2 new sigma bonds with typical carbon sp<sup>3</sup>-sp<sup>3</sup> bond length at 1.54 Å.
|-
|}

====Illustrate the vibration that corresponds to the reaction path at the transition state (TS). Is the formation of the two bonds synchronous or asynchronous?====

'''Figure 5. Imaginary vibration of the TS of 1,3-butadiene and ethylene'''
<jmol>
<jmolApplet>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 7; rotate x -20; frank off</script>
<name>TRIAL_TS_2_LLT15_FREQ</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>TRIAL_TS_2_LLT15_FREQ</target>
</jmolbutton>
<jmolbutton>
<script>measure 8 25; measure 7 26</script>
<text>C-C Distances</text>
<target>TRIAL_TS_2_LLT15_FREQ</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>TRIAL_TS_2_LLT15_FREQ</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 7; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i949/cm<sup>-1</sup></text>
<target>TRIAL_TS_2_LLT15_FREQ</target>
</item>
</jmolmenu>
</jmol>

The vibration mode that resembles to the reaction coordinate at TS is shown in figure 4.<br>This mode has a negative force constant which results in an imaginary frequency of value -949 cm<sup>-1</sup>.<br>From the animation, it shows that the concerted formation of the two new C-C bonds is synchronous in terms of the movement of the 2 terminal carbons of 1,3-butadiene and the 2 carbons of ethylene towards each other at the same rate to form the product cyclohexene.

====Additional information====
For exercise 2, go to https://wiki.ch.ic.ac.uk/wiki/index.php?title=Llt15_TS_2<br>
For exercise 3, go to https://wiki.ch.ic.ac.uk/wiki/index.php?title=Llt15_TS_3

log file for IRC calculation is for exercise 1 available at [[File:TRIAL_TS_2_IRC_CORRECTED_LLT15.LOG]]

==References==
<references />

File:Q1 MO corrected llt15 new.png

2017-10-24T15:00:47Z

Llt15:

File:MO endo q2 energy 631G llt15.png

2017-10-24T14:58:25Z

Llt15: Llt15 uploaded a new version of File:MO endo q2 energy 631G llt15.png

Rep:Llt15 TS

2017-10-24T14:46:21Z

Llt15: /* Transition States and Reactivity */

==Transition States and Reactivity==

===Introduction===

A transition state is the saddle point which is a local maxima on the minimum energy path linking reactants and the products whereas the reactants and products correspond to the minimum in the potential energy surface (PES). Therefore, at both minimum point and transition structure, the total gradient of the potential energy surface will have a value of zero. This is defined by the first derivative of potential energy vs bond distances graph: ∂V(r<sub>i</sub>)/∂r<sub>i</sub> = 0

For non-linear molecules, there are 3N - 6 normal vibrational modes or so-called degree of freedom. Using a harmonic oscillator model, each vibrational modes has the restoring force defined by Hookes law:<br>
F = -'''k'''x <br>where ''''k'''' is the force/spring constant<br> 'x' is the displacement of spring which resemble bonds from its equilibrium position.<br>
The reactants and products sit in a well at the minimum and vibrate 'forever' unless sufficient energy is provided for them to react. The transition state has a different mode of vibration along the reaction coordinate which take the TS downhill towards the reactant or product, without a restoring force. This lead to a negative '''k'''. Thus, the calculation of second derivative of the curvature ('''k''') in the PES (∂<sup>2</sup>V(r<sub>i</sub>)/∂r<sub>i</sub><sup>2</sup>) helps to distinguish the minimum and TS. As the frequency calculation involves taking square root of a force constant '''k''' and the square root of negative value leads to an imaginary number, at every transition state there must be only one imaginary frequency as all other coordinates are minimised. Hence, it is concluded that a negative value of second derivative of gradient indicated a transition structure whereas positive value represented the minimum point (reactant and product) of the reaction path and the same thing applies in frequency calculation.

[[File:Usetis_IR_equation_llt15.PNG|thumb|center|400px| Figure 1. Equation to calculate the vibrational frequency (\nu) for diatomic molecules <ref>Donald L. Pavia, Gary M. Lampman, George S. Kriz, James A. Vyvyan, 2009. ''Introduction to Spectroscopy'' 4th ed., ''Chap. 2'', pp.21.</ref>]]

For a thermodynamically controlled reaction, the reaction is reversible and the energetically more stable product is favoured. Therefore, the relative energy of transition state is not important as the product with the lowest energy (most stabilized) will eventually predominate under equilibrating condition. For a kinetic controlled reaction, the energy of the transition state determines the predominant product as the product forms irreversibly once the TS is reached. Hence, the pathway that requires lower activation energy to reach the transition state will be chosen. As a result, the most rapidly formed product predominates under kinetic control reaction.

[[File:Thermo_vs_kinetic_llt15_intro.PNG|thumb|center|400px| Figure 2. Schematic diagram for kinetic versus thermodynamic control<ref>King-Chuen Lin, 1988. ''Understanding Product Optimization:
Kinetic versus Thermodynamic Control'', 65(10), pp.857.</ref>]]

===Exercise 1: Cycloaddition of Butadiene and Ethylene===

<br>
[[File:cycloadd_q1_llt15.png|thumb|center|550px|Figure 3. Reaction scheme for cycloaddition of 1,3-butadiene and ethylene.]]

'''Method used for optimization and analysis:'''

The geometry of the reactants are optimized at PM6 level and the optimized reactants are used to construct the transition state of the reaction. The distance 2.20 Å is used in the guess of TS for the approximate separation between the terminal carbon atoms in both reactants as this is the intermediate value between a normal C-C single bond and the Van der Waals distance of 2 carbon atoms. The guess TS structure is optimized at PM6 level and the optimized TS is used to run a IRC to obtained the product. The product is again optimized to a minimum at PM6 level. The optimized structure of reactants, transition state and product are shown in 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>250</size>
<script>frame 16</script>
<uploadedFileContents>BUTADIENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 4</script>
<uploadedFileContents>ETHENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6</script>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>PRODUCT_Q1_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Correlate these MOs with the ones in your MO diagram to show which orbitals interact. What can you conclude about the requirements for symmetry for a reaction (when is a reaction 'allowed' and when is it 'forbidden')? ====

{| class="wikitable"
|+ Table 2. HOMO and LUMO of reactants and transition state (TS)
! style="background: #0D4F8B; color: white;" | Chemical Structure
! style="background: #0D4F8B; color: white;" | HOMO
! style="background: #0D4F8B; color: white;" | LUMO
! style="background: #0D4F8B; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|<jmol>
<jmolApplet>
<title>MO11 (Aysmmetric)</title>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>MO12 (Symmetric)</title>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="3"|[[File:Q1_MO_corrected_llt15.png|thumb|center|550px|Figure 4. Idealized MO diagram of [4+2] cycloaddition with with labelled symmetry (Antisymmetric= A, Symmetric= S).]]
|-
|<nowiki>Ethylene</nowiki>
| <jmol>
<jmolApplet>
<title>MO6 (Symmetric)</title>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_Q1_LLT15_REDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>MO7 (Asymmetric)</title>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_Q1_LLT15_REDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| <nowiki>Transition State</nowiki>
| <jmol>
<jmolApplet>
<title>MO16 (HOMO -1)</title>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
<jmol>
<jmolApplet>
<title>MO17 (HOMO)</title>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>MO19 (LUMO + 1)</title>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
<jmol>
<jmolApplet>
<title>MO18 (LUMO)</title>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The HOMO-LUMO interactions shown in the MO diagram of the cycloaddition between butadiene and ethylene are listed below:
Butadiene HOMO (MO 11, A) + Ethylene LUMO (MO 7, A) = Transition State HOMO (MO 16)
Butadiene HOMO (MO 11, A) - Ethylene LUMO (MO 7, A) = Transition State LUMO (MO 19)<br>
Butadiene LUMO (MO 12, S) + Ethylene HOMO (MO 6, S) = Transition State HOMO (MO 17)
Butadiene LUMO (MO 12, S) - Ethylene HOMO (MO 6, S) = Transition State LUMO (MO 18)

The symmetry label 'A' and 'S' corresponds to whether the molecular orbital (MO) is antisymmetric or symmetrical with respect to the mirror plane orthogonal to the sigma bond which lies in the middle of MO.

According to the Woodward Hoffmann rules, the total number of (4q + 2)<sub>s</sub> + (4r)<sub>a</sub> must be odd for the pericyclic reaction to be thermally allowed. The letters 'q' and 'r' stand for integer starting from zero whereas the suffix 's' stands for suprafacial and 'a' for antarafacial. A suprafacial component forms new bonds on the same face whereas an antarafacial components formes new bonds on opposite faces at both ends. However, the reaction is considered to be thermally forbidden but photochemically allowed if the total number of (4q + 2)<sub>s</sub> + (4r)<sub>a</sub> equals to zero or an even number.<br><br>The [<sub>π</sub>4<sub>s</sub> +
<sub>π</sub>2<sub>s</sub>] cycloaddition between butadiene and ethylene is allowed as shown:
(4q + 2)<sub>s</sub> + (4r)<sub>a</sub>
= 1 + 0
= 1
= thermally allowed reaction when q and r equal to 0

<br><br>
'''Write whether the orbital overlap integral is zero or non-zero for the case of a symmetric-antisymmetric interaction, a symmetric-symmetric interaction and an antisymmetric-antisymmetric interaction:'''
{| class="wikitable"
|+ Table 3. Effect of the symmetry of interactions on the orbital overlap integral
! style="background: #0D4F8B; color: white;" | Type of interactions
! style="background: #0D4F8B; color: white;" | Orbital overlap integral
|-
| Symmetric-symmetric
| Non-zero
|-
| Symmetric-antisymmetric
| Zero
|-
| Antisymmetric-antisymmetric
| Non-zero
|}

<br>
'''Include measurements of the 4 C-C bond lengths of the reactants and the 6 C-C bond lengths of the TS and products. How do the bond lengths change as the reaction progresses?'''

{| class="wikitable"
|+ Table 4. The changes in bond length of the reactants, TS and product molecules as reaction progress
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | C-C Bond lenghths
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | C-C Bond lenghths
|-
| <jmol>
<jmolApplet>
<title> Reactant: Ethylene</title>
<color>white</color>
<size>150</size>
<script>frame 4</script>
<script>select atomno=1, atomno=4; label display</script>
<uploadedFileContents>ETHENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| C1-C4 (double bond)= 1.33 Å
| <jmol>
<jmolApplet>
<title>Reactant: 1,3-Butadiene</title>
<color>white</color>
<size>150</size>
<script>frame 16</script>
<script>select atomno=7, atomno=6, atomno=4, atomno=1; label display</script>
<uploadedFileContents>BUTADIENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| C1-C4 (double bond)= 1.34 Å<br>C4-C6 (single bond) = 1.47 Å<br>C6-C7 (double bond)= 1.34 Å
|-
| <jmol>
<jmolApplet>
<title>Transition State</title>
<color>white</color>
<size>150</size>
<script>frame 4</script>
<script>select atomno=1, atomno=4, atomno=6, atomno=7, atomno=11, atomno=14; label display</script>
<uploadedFileContents>TRIAL_TS_2_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| C1-C4 (double bond-breaking)= 1.38 Å<br> C4-C6 (double bond-forming) = 1.41 Å<br> C6-C7 (double bond-breaking)= 1.38 Å<br> C7-C11 (single bond-forming) = 2.11 Å<br> C11-C14 (double bond-breaking)= 1.38 Å<br> C14-C1 (single bond-forming) = 2.11 Å
| <jmol>
<jmolApplet>
<title> Product: Cyclohexene</title>
<color>white</color>
<size>150</size>
<script>frame 10</script>
<script>select atomno=6, atomno=4, atomno=1, atomno=14, atomno=11, atomno=7; label display</script>
<uploadedFileContents>PRODUCT_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| C6-C4 = 1.34 Å, C=C sp<sup>2</sup>-sp<sup>2</sup> bond<br> C4-C1 = 1.50 Å, C-C sp<sup>3</sup>-sp<sup>2</sup> bond<br> C1-C14 = 1.54 Å, C-C sp<sup>3</sup>-sp<sup>3</sup> bond<br> C14-C11 = 1.54 Å, C-C sp<sup>3</sup>-sp<sup>3</sup> bond<br> C11-C7 = 1.54 Å, C-C sp<sup>3</sup>-sp<sup>3</sup> bond<br> C7-C6 = 1.50 Å, C-C sp<sup>3</sup>-sp<sup>2</sup> bond
|}

==== What are typical sp3 and sp2 C-C bond lengths? What is the Van der Waals radius of the C atom? How does this compare with the length of the partly formed C-C bonds in the TS.====

Typical C-C bond length<ref>Popov, E.M., Kogan, G.A. & Zheltova, V.N., 1972. Theor Exp Chem ''6''(1), pp.11-19. https://doi.org/10.1007/BF00525890</ref>:
:sp<sup>3</sup>-sp<sup>3</sup>: 1.54 Å
:sp<sup>3</sup>-sp<sup>2</sup>: 1.50 Å
:sp<sup>2</sup>-sp<sup>2</sup>: 1.47 Å
Van der Waals radius of a carbon atom: 1.70 Å<br>Van der Waals distance of 2 carbon atoms: 3.40 Å

In the transition state of cycloaddition process between butadiene and ethylene, the partly formed C-C single bond lengths are about 2.12 Å which is an intermediate value between typical sp<sup>3</sup> C-C bond length and Van der Waals distance of 2 carbon atoms. For the breaking double bond, the bond lengths are increased upon the change in the carbon hybridisation from sp<sup>2</sup> to sp<sup>3</sup>. In other words, the reduced in s orbital character from sp<sup>2</sup>(33%) to sp<sup>3</sup>(25%) makes the C-C bond longer and weaker as the electrons are less strongly held to the nucleus. On the other hand, the single bond on butadiene is shorter in the transition state as the carbon is hybridised from sp<sup>3</sup> to sp<sup>2</sup> upon double bond formation.

For cyclohexene, there is only a double bond between the sp<sup>2</sup> hybridised C6 and C7, and the remaining carbons are sp<sup>3</sup> hybridised. Thus, there is no delocalisation of electron cloud in the cyclohexene and the electrons are localised along the C-C bond. This explains the existence of the three different bond lengths (1.34 Å, 1.50 Å and 1.54 Å) as the C-C bond lengths vary based on different carbon hybridisation.

{| class="wikitable"
|+ Table 5. The changes in bond length along the reaction path
! style="background: #0D4F8B; color: white;" | Type of Bond
! style="background: #0D4F8B; color: white;" | Bond Length vs reaction coordinate
! style="background: #0D4F8B; color: white;" | Discussion
|-
|C1-C4 and C6-C7 and C11-C14
|[[File:C1C4_dbbreak_q1_llt15.PNG|250px]][[File:C6C7_dbbreak_q1_llt15.PNG|250px]][[File:C11C14_dbbreak_q1_ethene_llt15.PNG|250px]]
|Change in bond order: double bond to single bond<br><br>The graphs show that the bond length increase gradually from 1.34 Å to 1.50 Å upon product formation. The increase in bond length indicates the breaking of the C1-C4 and C6-C7 double bonds due to the change in carbon hybridisation (C1, C7, C11 and C14) from sp<sup>2</sup> to sp<sup>3</sup>. This causes a decrease in electron density between two carbons thus the single bonds are weaken and lengthen.
|-
|C4-C6
|[[File:C4C6_dbform_q1_llt15.PNG|250px]]
|Change in bond order: single bond to double bond<br><br>The graph shows that the bond length decreases gradually from 1.47 Å to 1.34 Å upon product formation. The decrease in bond length indicates the double bond formation between C4 and C6. The additional pi overlap between C4-C6 strengthen the bond and hold the 2 carbon nucleus stronger together resulting in a shorter bond length.
|-
|C7-C11 and C14-C1
|[[File:C7C11_sbform_q1_llt15.PNG|250px]][[File:C14C1_sbform_q1_llt15.PNG|250px]]
|The graphs show a steep decrease in bond length (or distance between 2 carbons) along the reaction coordinate. In this case, the two non-bonding carbon atoms from 1,3-butadiene and ethylene approach each other from Van der Waals distance (3.40 Å) and their orbitals start to overlap across the space in the transition state in order to form the new single bonds in the product stage. All of the 4 carbons change their hybridisation (sp<sup>2</sup> to sp<sup>3</sup>) to form 2 new sigma bonds with typical carbon sp<sup>3</sup>-sp<sup>3</sup> bond length at 1.54 Å.
|-
|}

====Illustrate the vibration that corresponds to the reaction path at the transition state (TS). Is the formation of the two bonds synchronous or asynchronous?====

'''Figure 5. Imaginary vibration of the TS of 1,3-butadiene and ethylene'''
<jmol>
<jmolApplet>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 7; rotate x -20; frank off</script>
<name>TRIAL_TS_2_LLT15_FREQ</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>TRIAL_TS_2_LLT15_FREQ</target>
</jmolbutton>
<jmolbutton>
<script>measure 8 25; measure 7 26</script>
<text>C-C Distances</text>
<target>TRIAL_TS_2_LLT15_FREQ</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>TRIAL_TS_2_LLT15_FREQ</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 7; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i949/cm<sup>-1</sup></text>
<target>TRIAL_TS_2_LLT15_FREQ</target>
</item>
</jmolmenu>
</jmol>

The vibration mode that resembles to the reaction coordinate at TS is shown in figure 4.<br>This mode has a negative force constant which results in an imaginary frequency of value -949 cm<sup>-1</sup>.<br>From the animation, it shows that the concerted formation of the two new C-C bonds is synchronous in terms of the movement of the 2 terminal carbons of 1,3-butadiene and the 2 carbons of ethylene towards each other at the same rate to form the product cyclohexene.

====Additional information====
For exercise 2, go to https://wiki.ch.ic.ac.uk/wiki/index.php?title=Llt15_TS_2<br>
For exercise 3, go to https://wiki.ch.ic.ac.uk/wiki/index.php?title=Llt15_TS_3

log file for IRC calculation is for exercise 1 available at [[File:TRIAL_TS_2_IRC_CORRECTED_LLT15.LOG]]

==References==
<references />

File:Q1 MO corrected llt15.png

2017-10-24T14:41:47Z

Llt15: Llt15 uploaded a new version of File:Q1 MO corrected llt15.png

Rep:Llt15 TS

2017-10-23T15:28:00Z

Llt15: /* Transition States and Reactivity */

==Transition States and Reactivity==

===Introduction===

A transition state is the saddle point which is a local maxima on the minimum energy path linking reactants and the products where the reactant and products correspond to the minimum in the potential energy surface (PES). Therefore, at both minimum point and transition structure, the total gradient of the potential energy surface will have a value of zero. This is defined by the first derivative of potential energy vs bond distances graph: ∂V(r<sub>i</sub>)/∂r<sub>i</sub> = 0

[[File:Usetis_IR_equation_llt15.PNG|thumb|center|400px| Figure 1. Equation to calculate the vibrational frequency (\nu) for diatomic molecules <ref>Donald L. Pavia, Gary M. Lampman, George S. Kriz, James A. Vyvyan, 2009. ''Introduction to Spectroscopy'' 4th ed., ''Chap. 2'', pp.21.</ref>]]

For a thermodynamically controlled reaction, the reaction is reversible and the energetically more stable product is favoured. Therefore, the relative energy of transition state is not important as the product with the lowest energy (most stabilized) will eventually predominate under equilibrating condition. For a kinetic controlled reaction, the energy of the transition state determines the predominant product as the product forms irreversibly once the TS is reached. Hence, the pathway that requires lower activation energy to reach the transition state will be chosen. As a result, the most rapidly formed product predominates under kinetic control reaction.

[[File:Thermo_vs_kinetic_llt15_intro.PNG|thumb|center|400px| Figure 2. Schematic diagram for kinetic versus thermodynamic control<ref>King-Chuen Lin, 1988. ''Understanding Product Optimization:
Kinetic versus Thermodynamic Control'', 65(10), pp.857.</ref>]]

For non-linear molecules, there are 3N - 6 normal vibrational modes or so-called degree of freedom. Using a harmonic oscillator model, each vibrational modes has the restoring force defined by Hookes law:<br>
F = -'''k'''x <br>where ''''k'''' is the force/spring constant<br> 'x' is the displacement of spring which resemble bonds from its equilibrium position.<br>
The reactants and products sit in a well at the minimum and vibrate 'forever' unless sufficient energy is provided for them to react. The transition state has a different mode of vibration along the reaction coordinate which take the TS downhill towards the reactant or product, without a restoring force. This lead to a negative '''k'''. Thus, the calculation of second derivative of the curvature ('''k''') in the PES (∂<sup>2</sup>V(r<sub>i</sub>)/∂r<sub>i</sub><sup>2</sup>) helps to distinguish the minimum and TS. As the frequency calculation involves taking square root of a force constant '''k''' and the square root of negative value leads to an imaginary number, at every transition state there must be only one imaginary frequency as all other coordinates are minimised. Hence, it is concluded that a negative value of second derivative of gradient indicated a transition structure whereas positive value represented the minimum point (reactant and product) of the reaction path and the same thing applies in frequency calculation.

===Exercise 1: Cycloaddition of Butadiene and Ethylene===

<br>
[[File:cycloadd_q1_llt15.png|thumb|center|550px|Figure 3. Reaction scheme for cycloaddition of 1,3-butadiene and ethylene.]]

'''Method used for optimization and analysis:'''

The geometry of the reactants are optimized at PM6 level and the optimized reactants are used to construct the transition state of the reaction. The distance 2.20 Å is used in the guess of TS for the approximate separation between the terminal carbon atoms in both reactants as this is the intermediate value between a normal C-C single bond and the Van der Waals distance of 2 carbon atoms. The guess TS structure is optimized at PM6 level and the optimized TS is used to run a IRC to obtained the product. The product is again optimized to a minimum at PM6 level. The optimized structure of reactants, transition state and product are shown in 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>250</size>
<script>frame 16</script>
<uploadedFileContents>BUTADIENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 4</script>
<uploadedFileContents>ETHENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6</script>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>PRODUCT_Q1_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Correlate these MOs with the ones in your MO diagram to show which orbitals interact. What can you conclude about the requirements for symmetry for a reaction (when is a reaction 'allowed' and when is it 'forbidden')? ====

{| class="wikitable"
|+ Table 2. HOMO and LUMO of reactants and transition state (TS)
! style="background: #0D4F8B; color: white;" | Chemical Structure
! style="background: #0D4F8B; color: white;" | HOMO
! style="background: #0D4F8B; color: white;" | LUMO
! style="background: #0D4F8B; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|<jmol>
<jmolApplet>
<title>MO11 (Aysmmetric)</title>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>MO12 (Symmetric)</title>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="3"|[[File:Q1_MO_corrected_llt15.png|thumb|center|550px|Figure 4. Idealized MO diagram of [4+2] cycloaddition with with labelled symmetry (Antisymmetric= A, Symmetric= S).]]
|-
|<nowiki>Ethylene</nowiki>
| <jmol>
<jmolApplet>
<title>MO6 (Symmetric)</title>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_Q1_LLT15_REDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>MO7 (Asymmetric)</title>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_Q1_LLT15_REDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| <nowiki>Transition State</nowiki>
| <jmol>
<jmolApplet>
<title>MO16 (HOMO -1)</title>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
<jmol>
<jmolApplet>
<title>MO17 (HOMO)</title>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>MO19 (LUMO + 1)</title>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
<jmol>
<jmolApplet>
<title>MO18 (LUMO)</title>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The HOMO-LUMO interactions shown in the MO diagram of the cycloaddition between butadiene and ethylene are listed below:
Butadiene HOMO (MO 11, A) + Ethylene LUMO (MO 7, A) = Transition State HOMO (MO 16)
Butadiene HOMO (MO 11, A) - Ethylene LUMO (MO 7, A) = Transition State LUMO (MO 19)<br>
Butadiene LUMO (MO 12, S) + Ethylene HOMO (MO 6, S) = Transition State HOMO (MO 17)
Butadiene LUMO (MO 12, S) - Ethylene HOMO (MO 6, S) = Transition State LUMO (MO 18)

The symmetry label 'A' and 'S' corresponds to whether the molecular orbital (MO) is antisymmetric or symmetrical with respect to the mirror plane orthogonal to the sigma bond which lies in the middle of MO.

According to the Woodward Hoffmann rules, the total number of (4q + 2)<sub>s</sub> + (4r)<sub>a</sub> must be odd for the pericyclic reaction to be thermally allowed. The letters 'q' and 'r' stand for integer starting from zero whereas the suffix 's' stands for suprafacial and 'a' for antarafacial. A suprafacial component forms new bonds on the same face whereas an antarafacial components formes new bonds on opposite faces at both ends. However, the reaction is considered to be thermally forbidden but photochemically allowed if the total number of (4q + 2)<sub>s</sub> + (4r)<sub>a</sub> equals to zero or an even number.<br><br>The [<sub>π</sub>4<sub>s</sub> +
<sub>π</sub>2<sub>s</sub>] cycloaddition between butadiene and ethylene is allowed as shown:
(4q + 2)<sub>s</sub> + (4r)<sub>a</sub>
= 1 + 0
= 1
= thermally allowed reaction when q and r equal to 0

<br><br>
'''Write whether the orbital overlap integral is zero or non-zero for the case of a symmetric-antisymmetric interaction, a symmetric-symmetric interaction and an antisymmetric-antisymmetric interaction:'''
{| class="wikitable"
|+ Table 3. Effect of the symmetry of interactions on the orbital overlap integral
! style="background: #0D4F8B; color: white;" | Type of interactions
! style="background: #0D4F8B; color: white;" | Orbital overlap integral
|-
| Symmetric-symmetric
| Non-zero
|-
| Symmetric-antisymmetric
| Zero
|-
| Antisymmetric-antisymmetric
| Non-zero
|}

<br>
'''Include measurements of the 4 C-C bond lengths of the reactants and the 6 C-C bond lengths of the TS and products. How do the bond lengths change as the reaction progresses?'''

{| class="wikitable"
|+ Table 4. The changes in bond length of the reactants, TS and product molecules as reaction progress
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | C-C Bond lenghths
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | C-C Bond lenghths
|-
| <jmol>
<jmolApplet>
<title> Reactant: Ethylene</title>
<color>white</color>
<size>150</size>
<script>frame 4</script>
<script>select atomno=1, atomno=4; label display</script>
<uploadedFileContents>ETHENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| C1-C4 (double bond)= 1.33 Å
| <jmol>
<jmolApplet>
<title>Reactant: 1,3-Butadiene</title>
<color>white</color>
<size>150</size>
<script>frame 16</script>
<script>select atomno=7, atomno=6, atomno=4, atomno=1; label display</script>
<uploadedFileContents>BUTADIENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| C1-C4 (double bond)= 1.34 Å<br>C4-C6 (single bond) = 1.47 Å<br>C6-C7 (double bond)= 1.34 Å
|-
| <jmol>
<jmolApplet>
<title>Transition State</title>
<color>white</color>
<size>150</size>
<script>frame 4</script>
<script>select atomno=1, atomno=4, atomno=6, atomno=7, atomno=11, atomno=14; label display</script>
<uploadedFileContents>TRIAL_TS_2_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| C1-C4 (double bond-breaking)= 1.38 Å<br> C4-C6 (double bond-forming) = 1.41 Å<br> C6-C7 (double bond-breaking)= 1.38 Å<br> C7-C11 (single bond-forming) = 2.11 Å<br> C11-C14 (double bond-breaking)= 1.38 Å<br> C14-C1 (single bond-forming) = 2.11 Å
| <jmol>
<jmolApplet>
<title> Product: Cyclohexene</title>
<color>white</color>
<size>150</size>
<script>frame 10</script>
<script>select atomno=6, atomno=4, atomno=1, atomno=14, atomno=11, atomno=7; label display</script>
<uploadedFileContents>PRODUCT_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| C6-C4 = 1.34 Å, C=C sp<sup>2</sup>-sp<sup>2</sup> bond<br> C4-C1 = 1.50 Å, C-C sp<sup>3</sup>-sp<sup>2</sup> bond<br> C1-C14 = 1.54 Å, C-C sp<sup>3</sup>-sp<sup>3</sup> bond<br> C14-C11 = 1.54 Å, C-C sp<sup>3</sup>-sp<sup>3</sup> bond<br> C11-C7 = 1.54 Å, C-C sp<sup>3</sup>-sp<sup>3</sup> bond<br> C7-C6 = 1.50 Å, C-C sp<sup>3</sup>-sp<sup>2</sup> bond
|}

==== What are typical sp3 and sp2 C-C bond lengths? What is the Van der Waals radius of the C atom? How does this compare with the length of the partly formed C-C bonds in the TS.====

Typical C-C bond length<ref>Popov, E.M., Kogan, G.A. & Zheltova, V.N., 1972. Theor Exp Chem ''6''(1), pp.11-19. https://doi.org/10.1007/BF00525890</ref>:
:sp<sup>3</sup>-sp<sup>3</sup>: 1.54 Å
:sp<sup>3</sup>-sp<sup>2</sup>: 1.50 Å
:sp<sup>2</sup>-sp<sup>2</sup>: 1.47 Å
Van der Waals radius of a carbon atom: 1.70 Å<br>Van der Waals distance of 2 carbon atoms: 3.40 Å

In the transition state of cycloaddition process between butadiene and ethylene, the partly formed C-C single bond lengths are about 2.12 Å which is an intermediate value between typical sp<sup>3</sup> C-C bond length and Van der Waals distance of 2 carbon atoms. For the breaking double bond, the bond lengths are increased upon the change in the carbon hybridisation from sp<sup>2</sup> to sp<sup>3</sup>. In other words, the reduced in s orbital character from sp<sup>2</sup>(33%) to sp<sup>3</sup>(25%) makes the C-C bond longer and weaker as the electrons are less strongly held to the nucleus. On the other hand, the single bond on butadiene is shorter in the transition state as the carbon is hybridised from sp<sup>3</sup> to sp<sup>2</sup> upon double bond formation.

For cyclohexene, there is only a double bond between the sp<sup>2</sup> hybridised C6 and C7, and the remaining carbons are sp<sup>3</sup> hybridised. Thus, there is no delocalisation of electron cloud in the cyclohexene and the electrons are localised along the C-C bond. This explains the existence of the three different bond lengths (1.34 Å, 1.50 Å and 1.54 Å) as the C-C bond lengths vary based on different carbon hybridisation.

{| class="wikitable"
|+ Table 5. The changes in bond length along the reaction path
! style="background: #0D4F8B; color: white;" | Type of Bond
! style="background: #0D4F8B; color: white;" | Bond Length vs reaction coordinate
! style="background: #0D4F8B; color: white;" | Discussion
|-
|C1-C4 and C6-C7 and C11-C14
|[[File:C1C4_dbbreak_q1_llt15.PNG|250px]][[File:C6C7_dbbreak_q1_llt15.PNG|250px]][[File:C11C14_dbbreak_q1_ethene_llt15.PNG|250px]]
|Change in bond order: double bond to single bond<br><br>The graphs show that the bond length increase gradually from 1.34 Å to 1.50 Å upon product formation. The increase in bond length indicates the breaking of the C1-C4 and C6-C7 double bonds due to the change in carbon hybridisation (C1, C7, C11 and C14) from sp<sup>2</sup> to sp<sup>3</sup>. This causes a decrease in electron density between two carbons thus the single bonds are weaken and lengthen.
|-
|C4-C6
|[[File:C4C6_dbform_q1_llt15.PNG|250px]]
|Change in bond order: single bond to double bond<br><br>The graph shows that the bond length decreases gradually from 1.47 Å to 1.34 Å upon product formation. The decrease in bond length indicates the double bond formation between C4 and C6. The additional pi overlap between C4-C6 strengthen the bond and hold the 2 carbon nucleus stronger together resulting in a shorter bond length.
|-
|C7-C11 and C14-C1
|[[File:C7C11_sbform_q1_llt15.PNG|250px]][[File:C14C1_sbform_q1_llt15.PNG|250px]]
|The graphs show a steep decrease in bond length (or distance between 2 carbons) along the reaction coordinate. In this case, the two non-bonding carbon atoms from 1,3-butadiene and ethylene approach each other from Van der Waals distance (3.40 Å) and their orbitals start to overlap across the space in the transition state in order to form the new single bonds in the product stage. All of the 4 carbons change their hybridisation (sp<sup>2</sup> to sp<sup>3</sup>) to form 2 new sigma bonds with typical carbon sp<sup>3</sup>-sp<sup>3</sup> bond length at 1.54 Å.
|-
|}

====Illustrate the vibration that corresponds to the reaction path at the transition state (TS). Is the formation of the two bonds synchronous or asynchronous?====

'''Figure 5. Imaginary vibration of the TS of 1,3-butadiene and ethylene'''
<jmol>
<jmolApplet>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 7; rotate x -20; frank off</script>
<name>TRIAL_TS_2_LLT15_FREQ</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>TRIAL_TS_2_LLT15_FREQ</target>
</jmolbutton>
<jmolbutton>
<script>measure 8 25; measure 7 26</script>
<text>C-C Distances</text>
<target>TRIAL_TS_2_LLT15_FREQ</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>TRIAL_TS_2_LLT15_FREQ</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 7; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i949/cm<sup>-1</sup></text>
<target>TRIAL_TS_2_LLT15_FREQ</target>
</item>
</jmolmenu>
</jmol>

The vibration mode that resembles to the reaction coordinate at TS is shown in figure 4.<br>This mode has a negative force constant which results in an imaginary frequency of value -949 cm<sup>-1</sup>.<br>From the animation, it shows that the concerted formation of the two new C-C bonds is synchronous in terms of the movement of the 2 terminal carbons of 1,3-butadiene and the 2 carbons of ethylene towards each other at the same rate to form the product cyclohexene.

====Additional information====
For exercise 2, go to https://wiki.ch.ic.ac.uk/wiki/index.php?title=Llt15_TS_2<br>
For exercise 3, go to https://wiki.ch.ic.ac.uk/wiki/index.php?title=Llt15_TS_3

log file for IRC calculation is for exercise 1 available at [[File:TRIAL_TS_2_IRC_CORRECTED_LLT15.LOG]]

==References==
<references />

Rep:Llt15 TS

2017-10-23T15:23:08Z

Llt15: /* Transition States and Reactivity */

==Transition States and Reactivity==

===Introduction===

A transition state is the saddle point which is a local maxima on the minimum energy path linking reactants and the products where the reactant and products correspond to the minimum in the potential energy surface (PES). Therefore, at both minimum point and transition structure, the total gradient of the potential energy surface will have a value of zero. This is defined by the first derivative of potential energy vs bond distances graph: ∂V(r<sub>i</sub>)/∂r<sub>i</sub> = 0

[[File:Usetis_IR_equation_llt15.PNG|thumb|center|400px| Figure 1. Equation to calculate the vibrational frequency (\nu) for diatomic molecules <ref>Donald L. Pavia, Gary M. Lampman, George S. Kriz, James A. Vyvyan, 2009. ''Introduction to Spectroscopy'' 4th ed., ''Chap. 2'', pp.21.</ref>]]

For a thermodynamically controlled reaction, the reaction is reversible and the energetically more stable product is favoured. Therefore, the relative energy of transition state is not important as the product with the lowest energy (most stabilized) will eventually predominate under equilibrating condition. For a kinetic controlled reaction, the transition state energy determines the predominant product as the reaction is irreversible. Hence, the pathway that requires lower activation energy to reach the transition state will be chosen. As a result, the most rapidly formed product predominates under kinetic control reaction.

[[File:Thermo_vs_kinetic_llt15_intro.PNG|thumb|center|400px| Figure 2. Schematic diagram for kinetic versus thermodynamic control<ref>King-Chuen Lin, 1988. ''Understanding Product Optimization:
Kinetic versus Thermodynamic Control'', 65(10), pp.857.</ref>]]

For non-linear molecules, there are 3N - 6 normal vibrational modes or so-called degree of freedom. Using a harmonic oscillator model, each vibrational modes has the restoring force defined by Hookes law:<br>
F = -'''k'''x <br>where ''''k'''' is the force/spring constant<br> 'x' is the displacement of spring which resemble bonds from its equilibrium position.<br>
The reactants and products sit in a well at the minimum and vibrate 'forever' unless sufficient energy is provided for them to react. The transition state has a different mode of vibration along the reaction coordinate which take the TS downhill towards the reactant or product, without a restoring force. This lead to a negative '''k'''. Thus, the calculation of second derivative of the curvature ('''k''') in the PES (∂<sup>2</sup>V(r<sub>i</sub>)/∂r<sub>i</sub><sup>2</sup>) helps to distinguish the minimum and TS. As the frequency calculation involves taking square root of a force constant '''k''' and the square root of negative value leads to an imaginary number, at every transition state there must be only one imaginary frequency as all other coordinates are minimised. Hence, it is concluded that a negative value of second derivative of gradient indicated a transition structure whereas positive value represented the minimum point (reactant and product) of the reaction path and the same thing applies in frequency calculation.

===Exercise 1: Cycloaddition of Butadiene and Ethylene===

<br>
[[File:cycloadd_q1_llt15.png|thumb|center|550px|Figure 3. Reaction scheme for cycloaddition of 1,3-butadiene and ethylene.]]

'''Method used for optimization and analysis:'''

The geometry of the reactants are optimized at PM6 level and the optimized reactants are used to construct the transition state of the reaction. The distance 2.20 Å is used in the guess of TS for the approximate separation between the terminal carbon atoms in both reactants as this is the intermediate value between a normal C-C single bond and the Van der Waals distance of 2 carbon atoms. The guess TS structure is optimized at PM6 level and the optimized TS is used to run a IRC to obtained the product. The product is again optimized to a minimum at PM6 level. The optimized structure of reactants, transition state and product are shown in 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>250</size>
<script>frame 16</script>
<uploadedFileContents>BUTADIENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 4</script>
<uploadedFileContents>ETHENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6</script>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>PRODUCT_Q1_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Correlate these MOs with the ones in your MO diagram to show which orbitals interact. What can you conclude about the requirements for symmetry for a reaction (when is a reaction 'allowed' and when is it 'forbidden')? ====

{| class="wikitable"
|+ Table 2. HOMO and LUMO of reactants and transition state (TS)
! style="background: #0D4F8B; color: white;" | Chemical Structure
! style="background: #0D4F8B; color: white;" | HOMO
! style="background: #0D4F8B; color: white;" | LUMO
! style="background: #0D4F8B; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|<jmol>
<jmolApplet>
<title>MO11 (Aysmmetric)</title>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>MO12 (Symmetric)</title>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="3"|[[File:Q1_MO_corrected_llt15.png|thumb|center|550px|Figure 4. Idealized MO diagram of [4+2] cycloaddition with with labelled symmetry (Antisymmetric= A, Symmetric= S).]]
|-
|<nowiki>Ethylene</nowiki>
| <jmol>
<jmolApplet>
<title>MO6 (Symmetric)</title>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_Q1_LLT15_REDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>MO7 (Asymmetric)</title>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_Q1_LLT15_REDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| <nowiki>Transition State</nowiki>
| <jmol>
<jmolApplet>
<title>MO16 (HOMO -1)</title>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
<jmol>
<jmolApplet>
<title>MO17 (HOMO)</title>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>MO19 (LUMO + 1)</title>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
<jmol>
<jmolApplet>
<title>MO18 (LUMO)</title>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The HOMO-LUMO interactions shown in the MO diagram of the cycloaddition between butadiene and ethylene are listed below:
Butadiene HOMO (MO 11, A) + Ethylene LUMO (MO 7, A) = Transition State HOMO (MO 16)
Butadiene HOMO (MO 11, A) - Ethylene LUMO (MO 7, A) = Transition State LUMO (MO 19)<br>
Butadiene LUMO (MO 12, S) + Ethylene HOMO (MO 6, S) = Transition State HOMO (MO 17)
Butadiene LUMO (MO 12, S) - Ethylene HOMO (MO 6, S) = Transition State LUMO (MO 18)

The symmetry label 'A' and 'S' corresponds to whether the molecular orbital (MO) is antisymmetric or symmetrical with respect to the mirror plane orthogonal to the sigma bond which lies in the middle of MO.

According to the Woodward Hoffmann rules, the total number of (4q + 2)<sub>s</sub> + (4r)<sub>a</sub> must be odd for the pericyclic reaction to be thermally allowed. The letters 'q' and 'r' stand for integer starting from zero whereas the suffix 's' stands for suprafacial and 'a' for antarafacial. A suprafacial component forms new bonds on the same face whereas an antarafacial components formes new bonds on opposite faces at both ends. However, the reaction is considered to be thermally forbidden but photochemically allowed if the total number of (4q + 2)<sub>s</sub> + (4r)<sub>a</sub> equals to zero or an even number.<br><br>The [<sub>π</sub>4<sub>s</sub> +
<sub>π</sub>2<sub>s</sub>] cycloaddition between butadiene and ethylene is allowed as shown:
(4q + 2)<sub>s</sub> + (4r)<sub>a</sub>
= 1 + 0
= 1
= thermally allowed reaction when q and r equal to 0

<br><br>
'''Write whether the orbital overlap integral is zero or non-zero for the case of a symmetric-antisymmetric interaction, a symmetric-symmetric interaction and an antisymmetric-antisymmetric interaction:'''
{| class="wikitable"
|+ Table 3. Effect of the symmetry of interactions on the orbital overlap integral
! style="background: #0D4F8B; color: white;" | Type of interactions
! style="background: #0D4F8B; color: white;" | Orbital overlap integral
|-
| Symmetric-symmetric
| Non-zero
|-
| Symmetric-antisymmetric
| Zero
|-
| Antisymmetric-antisymmetric
| Non-zero
|}

<br>
'''Include measurements of the 4 C-C bond lengths of the reactants and the 6 C-C bond lengths of the TS and products. How do the bond lengths change as the reaction progresses?'''

{| class="wikitable"
|+ Table 4. The changes in bond length of the reactants, TS and product molecules as reaction progress
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | C-C Bond lenghths
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | C-C Bond lenghths
|-
| <jmol>
<jmolApplet>
<title> Reactant: Ethylene</title>
<color>white</color>
<size>150</size>
<script>frame 4</script>
<script>select atomno=1, atomno=4; label display</script>
<uploadedFileContents>ETHENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| C1-C4 (double bond)= 1.33 Å
| <jmol>
<jmolApplet>
<title>Reactant: 1,3-Butadiene</title>
<color>white</color>
<size>150</size>
<script>frame 16</script>
<script>select atomno=7, atomno=6, atomno=4, atomno=1; label display</script>
<uploadedFileContents>BUTADIENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| C1-C4 (double bond)= 1.34 Å<br>C4-C6 (single bond) = 1.47 Å<br>C6-C7 (double bond)= 1.34 Å
|-
| <jmol>
<jmolApplet>
<title>Transition State</title>
<color>white</color>
<size>150</size>
<script>frame 4</script>
<script>select atomno=1, atomno=4, atomno=6, atomno=7, atomno=11, atomno=14; label display</script>
<uploadedFileContents>TRIAL_TS_2_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| C1-C4 (double bond-breaking)= 1.38 Å<br> C4-C6 (double bond-forming) = 1.41 Å<br> C6-C7 (double bond-breaking)= 1.38 Å<br> C7-C11 (single bond-forming) = 2.11 Å<br> C11-C14 (double bond-breaking)= 1.38 Å<br> C14-C1 (single bond-forming) = 2.11 Å
| <jmol>
<jmolApplet>
<title> Product: Cyclohexene</title>
<color>white</color>
<size>150</size>
<script>frame 10</script>
<script>select atomno=6, atomno=4, atomno=1, atomno=14, atomno=11, atomno=7; label display</script>
<uploadedFileContents>PRODUCT_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| C6-C4 = 1.34 Å, C=C sp<sup>2</sup>-sp<sup>2</sup> bond<br> C4-C1 = 1.50 Å, C-C sp<sup>3</sup>-sp<sup>2</sup> bond<br> C1-C14 = 1.54 Å, C-C sp<sup>3</sup>-sp<sup>3</sup> bond<br> C14-C11 = 1.54 Å, C-C sp<sup>3</sup>-sp<sup>3</sup> bond<br> C11-C7 = 1.54 Å, C-C sp<sup>3</sup>-sp<sup>3</sup> bond<br> C7-C6 = 1.50 Å, C-C sp<sup>3</sup>-sp<sup>2</sup> bond
|}

==== What are typical sp3 and sp2 C-C bond lengths? What is the Van der Waals radius of the C atom? How does this compare with the length of the partly formed C-C bonds in the TS.====

Typical C-C bond length<ref>Popov, E.M., Kogan, G.A. & Zheltova, V.N., 1972. Theor Exp Chem ''6''(1), pp.11-19. https://doi.org/10.1007/BF00525890</ref>:
:sp<sup>3</sup>-sp<sup>3</sup>: 1.54 Å
:sp<sup>3</sup>-sp<sup>2</sup>: 1.50 Å
:sp<sup>2</sup>-sp<sup>2</sup>: 1.47 Å
Van der Waals radius of a carbon atom: 1.70 Å<br>Van der Waals distance of 2 carbon atoms: 3.40 Å

In the transition state of cycloaddition process between butadiene and ethylene, the partly formed C-C single bond lengths are about 2.12 Å which is an intermediate value between typical sp<sup>3</sup> C-C bond length and Van der Waals distance of 2 carbon atoms. For the breaking double bond, the bond lengths are increased upon the change in the carbon hybridisation from sp<sup>2</sup> to sp<sup>3</sup>. In other words, the reduced in s orbital character from sp<sup>2</sup>(33%) to sp<sup>3</sup>(25%) makes the C-C bond longer and weaker as the electrons are less strongly held to the nucleus. On the other hand, the single bond on butadiene is shorter in the transition state as the carbon is hybridised from sp<sup>3</sup> to sp<sup>2</sup> upon double bond formation.

For cyclohexene, there is only a double bond between the sp<sup>2</sup> hybridised C6 and C7, and the remaining carbons are sp<sup>3</sup> hybridised. Thus, there is no delocalisation of electron cloud in the cyclohexene and the electrons are localised along the C-C bond. This explains the existence of the three different bond lengths (1.34 Å, 1.50 Å and 1.54 Å) as the C-C bond lengths vary based on different carbon hybridisation.

{| class="wikitable"
|+ Table 5. The changes in bond length along the reaction path
! style="background: #0D4F8B; color: white;" | Type of Bond
! style="background: #0D4F8B; color: white;" | Bond Length vs reaction coordinate
! style="background: #0D4F8B; color: white;" | Discussion
|-
|C1-C4 and C6-C7 and C11-C14
|[[File:C1C4_dbbreak_q1_llt15.PNG|250px]][[File:C6C7_dbbreak_q1_llt15.PNG|250px]][[File:C11C14_dbbreak_q1_ethene_llt15.PNG|250px]]
|Change in bond order: double bond to single bond<br><br>The graphs show that the bond length increase gradually from 1.34 Å to 1.50 Å upon product formation. The increase in bond length indicates the breaking of the C1-C4 and C6-C7 double bonds due to the change in carbon hybridisation (C1, C7, C11 and C14) from sp<sup>2</sup> to sp<sup>3</sup>. This causes a decrease in electron density between two carbons thus the single bonds are weaken and lengthen.
|-
|C4-C6
|[[File:C4C6_dbform_q1_llt15.PNG|250px]]
|Change in bond order: single bond to double bond<br><br>The graph shows that the bond length decreases gradually from 1.47 Å to 1.34 Å upon product formation. The decrease in bond length indicates the double bond formation between C4 and C6. The additional pi overlap between C4-C6 strengthen the bond and hold the 2 carbon nucleus stronger together resulting in a shorter bond length.
|-
|C7-C11 and C14-C1
|[[File:C7C11_sbform_q1_llt15.PNG|250px]][[File:C14C1_sbform_q1_llt15.PNG|250px]]
|The graphs show a steep decrease in bond length (or distance between 2 carbons) along the reaction coordinate. In this case, the two non-bonding carbon atoms from 1,3-butadiene and ethylene approach each other from Van der Waals distance (3.40 Å) and their orbitals start to overlap across the space in the transition state in order to form the new single bonds in the product stage. All of the 4 carbons change their hybridisation (sp<sup>2</sup> to sp<sup>3</sup>) to form 2 new sigma bonds with typical carbon sp<sup>3</sup>-sp<sup>3</sup> bond length at 1.54 Å.
|-
|}

====Illustrate the vibration that corresponds to the reaction path at the transition state (TS). Is the formation of the two bonds synchronous or asynchronous?====

'''Figure 5. Imaginary vibration of the TS of 1,3-butadiene and ethylene'''
<jmol>
<jmolApplet>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 7; rotate x -20; frank off</script>
<name>TRIAL_TS_2_LLT15_FREQ</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>TRIAL_TS_2_LLT15_FREQ</target>
</jmolbutton>
<jmolbutton>
<script>measure 8 25; measure 7 26</script>
<text>C-C Distances</text>
<target>TRIAL_TS_2_LLT15_FREQ</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>TRIAL_TS_2_LLT15_FREQ</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 7; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i949/cm<sup>-1</sup></text>
<target>TRIAL_TS_2_LLT15_FREQ</target>
</item>
</jmolmenu>
</jmol>

The vibration mode that resembles to the reaction coordinate at TS is shown in figure 4.<br>This mode has a negative force constant which results in an imaginary frequency of value -949 cm<sup>-1</sup>.<br>From the animation, it shows that the concerted formation of the two new C-C bonds is synchronous in terms of the movement of the 2 terminal carbons of 1,3-butadiene and the 2 carbons of ethylene towards each other at the same rate to form the product cyclohexene.

====Additional information====
For exercise 2, go to https://wiki.ch.ic.ac.uk/wiki/index.php?title=Llt15_TS_2<br>
For exercise 3, go to https://wiki.ch.ic.ac.uk/wiki/index.php?title=Llt15_TS_3

log file for IRC calculation is for exercise 1 available at [[File:TRIAL_TS_2_IRC_CORRECTED_LLT15.LOG]]

==References==
<references />

File:Thermo vs kinetic llt15 intro.PNG

2017-10-23T15:16:08Z

Llt15:

2017-10-21T21:57:56Z

Llt15: /* What are typical sp3 and sp2 C-C bond lengths? What is the Van der Waals radius of the C atom? How does this compare with the length of the partly formed C-C bonds in the TS. */

==Transition States and Reactivity==

===Introduction===

A transition state is the saddle point which is a local maxima on the minimum energy path linking reactants and the products where the reactant and products correspond to the minimum in the PES. Therefore, at both minimum point and transition structure, the total gradient of the potential energy surface will have a value of zero. This is defined by the first derivative of potential energy vs bond distances graph: ∂V(r<sub>i</sub>)/∂r<sub>i</sub> = 0

[[File:Usetis_IR_equation_llt15.PNG|thumb|center|400px| Figure 1. Equation to calculate the vibrational frequency (\nu) for diatomic molecules <ref>Donald L. Pavia, Gary M. Lampman, George S. Kriz, James A. Vyvyan, 2009. ''Introduction to Spectroscopy'' 4th ed., ''Chap. 2'', pp.21.</ref>]]

For non-linear molecules, there are 3N - 6 normal vibrational modes or so-called degree of freedom. Using a harmonic oscillator model, each vibrational modes has the restoring force defined by Hookes law:<br>
F = -'''k'''x <br>where ''''k'''' is the force/spring constant<br> 'x' is the displacement of spring which resemble bonds from its equilibrium position.<br>
The reactants and products sit in a well at the minimum and vibrate 'forever' unless sufficient energy is provided for them to react. The transition state has a different mode of vibration along the reaction coordinate which take the TS downhill towards the reactant or product, without a restoring force. This lead to a negative '''k'''. Thus, the calculation of second derivative of the curvature ('''k''') in the PES (∂<sup>2</sup>V(r<sub>i</sub>)/∂r<sub>i</sub><sup>2</sup>) helps to distinguish the minimum and TS. As the frequency calculation involves taking square root of a force constant '''k''' and the square root of negative value leads to an imaginary number, at every transition state there must be only one imaginary frequency as all other coordinates are minimised. Hence, it is concluded that a negative value of second derivative of gradient indicated a transition structure whereas positive value represented the minimum point (reactant and product) of the reaction path and the same thing applies in frequency calculation.

===Exercise 1: Cycloaddition of Butadiene and Ethylene===

<br>
[[File:cycloadd_q1_llt15.png|thumb|center|550px|Figure 2. Reaction scheme for cycloaddition of 1,3-butadiene and ethylene.]]

'''Method used for optimization and analysis:'''

The geometry of the reactants are optimized at PM6 level and the optimized reactants are used to construct the transition state of the reaction. The distance 2.20 Å is used in the guess of TS for the approximate separation between the terminal carbon atoms in both reactants as this is the intermediate value between a normal C-C single bond and the Van der Waals distance of 2 carbon atoms. The guess TS structure is optimized at PM6 level and the optimized TS is used to run a IRC to obtained the product. The product is again optimized to a minimum at PM6 level.

{| 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>250</size>
<script>frame 16</script>
<uploadedFileContents>BUTADIENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 4</script>
<uploadedFileContents>ETHENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6</script>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>PRODUCT_Q1_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Correlate these MOs with the ones in your MO diagram to show which orbitals interact. What can you conclude about the requirements for symmetry for a reaction (when is a reaction 'allowed' and when is it 'forbidden')? ====

{| class="wikitable"
|+ Table 2. HOMO and LUMO of reactants and transition state (TS)
! style="background: #0D4F8B; color: white;" | Chemical Structure
! style="background: #0D4F8B; color: white;" | HOMO
! style="background: #0D4F8B; color: white;" | LUMO
! style="background: #0D4F8B; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|<jmol>
<jmolApplet>
<title>MO11 (Aysmmetric)</title>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>MO12 (Symmetric)</title>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="3"|[[File:Q1_MO_corrected_llt15.png|thumb|center|550px|Figure 3. Idealized MO diagram of [4+2] cycloaddition with with labelled symmetry (Antisymmetric= A, Symmetric= S).]]
|-
|<nowiki>Ethylene</nowiki>
| <jmol>
<jmolApplet>
<title>MO6 (Symmetric)</title>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_Q1_LLT15_REDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>MO7 (Asymmetric)</title>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_Q1_LLT15_REDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| <nowiki>Transition State</nowiki>
| <jmol>
<jmolApplet>
<title>MO16 (HOMO -1)</title>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
<jmol>
<jmolApplet>
<title>MO17 (HOMO)</title>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>MO19 (LUMO + 1)</title>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
<jmol>
<jmolApplet>
<title>MO18 (LUMO)</title>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The HOMO-LUMO interactions shown in the MO diagram of the cycloaddition between butadiene and ethylene are listed below:
Butadiene HOMO (MO 11, A) + Ethylene LUMO (MO 7, A) = Transition State HOMO (MO 16)
Butadiene HOMO (MO 11, A) - Ethylene LUMO (MO 7, A) = Transition State LUMO (MO 19)<br>
Butadiene LUMO (MO 12, S) + Ethylene HOMO (MO 6, S) = Transition State HOMO (MO 17)
Butadiene LUMO (MO 12, S) - Ethylene HOMO (MO 6, S) = Transition State LUMO (MO 18)

The symmetry label 'A' and 'S' corresponds to whether the molecular orbital (MO) is antisymmetric or symmetrical with respect to the mirror plane orthogonal to the sigma bond which lies in the middle of MO.

According to the Woodward Hoffmann rules, the total number of (4q + 2)<sub>s</sub> + (4r)<sub>a</sub> must be odd for the pericyclic reaction to be thermally allowed. The letters 'q' and 'r' stand for integer starting from zero whereas the suffix 's' stands for suprafacial and 'a' for antarafacial. A suprafacial component forms new bonds on the same face whereas an antarafacial components formes new bonds on opposite faces at both ends. However, the reaction is considered to be thermally forbidden but photochemically allowed if the total number of (4q + 2)<sub>s</sub> + (4r)<sub>a</sub> equals to zero or an even number. The [<sub>π</sub>4<sub>s</sub> +
<sub>π</sub>2<sub>s</sub>] cycloaddition between butadiene and ethylene is allowed as shown:
(4q + 2)<sub>s</sub> + (4r)<sub>a</sub>
= 1 + 0
= 1
= thermally allowed reaction when q and r equal to 0

'''Write whether the orbital overlap integral is zero or non-zero for the case of a symmetric-antisymmetric interaction, a symmetric-symmetric interaction and an antisymmetric-antisymmetric interaction:'''
{| class="wikitable"
|+ Table 3. Effect of the symmetry of interactions on the orbital overlap integral
! style="background: #0D4F8B; color: white;" | Type of interactions
! style="background: #0D4F8B; color: white;" | Orbital overlap integral
|-
| Symmetric-symmetric
| Non-zero
|-
| Symmetric-antisymmetric
| Zero
|-
| Antisymmetric-antisymmetric
| Non-zero
|}

'''Include measurements of the 4 C-C bond lengths of the reactants and the 6 C-C bond lengths of the TS and products. How do the bond lengths change as the reaction progresses?'''

{| class="wikitable"
|+ Table 4. The changes in bond length of the reactants, TS and product molecules as reaction progress
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | C-C Bond lenghths
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | C-C Bond lenghths
|-
| <jmol>
<jmolApplet>
<title> Reactant: Ethylene</title>
<color>white</color>
<size>150</size>
<script>frame 4</script>
<script>select atomno=1, atomno=4; label display</script>
<uploadedFileContents>ETHENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| C1-C4 (double bond)= 1.33 Å
| <jmol>
<jmolApplet>
<title>Reactant: 1,3-Butadiene</title>
<color>white</color>
<size>150</size>
<script>frame 16</script>
<script>select atomno=7, atomno=6, atomno=4, atomno=1; label display</script>
<uploadedFileContents>BUTADIENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| C1-C4 (double bond)= 1.34 Å<br>C4-C6 (single bond) = 1.47 Å<br>C6-C7 (double bond)= 1.34 Å
|-
| <jmol>
<jmolApplet>
<title>Transition State</title>
<color>white</color>
<size>150</size>
<script>frame 4</script>
<script>select atomno=1, atomno=4, atomno=6, atomno=7, atomno=11, atomno=14; label display</script>
<uploadedFileContents>TRIAL_TS_2_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| C1-C4 (double bond-breaking)= 1.38 Å<br> C4-C6 (double bond-forming) = 1.41 Å<br> C6-C7 (double bond-breaking)= 1.38 Å<br> C7-C11 (single bond-forming) = 2.11 Å<br> C11-C14 (double bond-breaking)= 1.38 Å, increased bond length<br> C14-C1 (single bond-forming) = 2.11 Å
| <jmol>
<jmolApplet>
<title> Product: Cyclohexene</title>
<color>white</color>
<size>150</size>
<script>frame 10</script>
<script>select atomno=6, atomno=4, atomno=1, atomno=14, atomno=11, atomno=7; label display</script>
<uploadedFileContents>PRODUCT_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| C6-C4 = 1.34 Å, C=C sp<sup>2</sup>-sp<sup>2</sup> bond<br> C4-C1 = 1.50 Å, C-C sp<sup>3</sup>-sp<sup>2</sup> bond<br> C1-C14 = 1.54 Å, C-C sp<sup>3</sup>-sp<sup>3</sup> bond<br> C14-C11 = 1.54 Å, C-C sp<sup>3</sup>-sp<sup>3</sup> bond<br> C11-C7 = 1.54 Å, C-C sp<sup>3</sup>-sp<sup>3</sup> bond<br> C7-C6 = 1.50 Å, C-C sp<sup>3</sup>-sp<sup>2</sup> bond
|}

==== What are typical sp3 and sp2 C-C bond lengths? What is the Van der Waals radius of the C atom? How does this compare with the length of the partly formed C-C bonds in the TS.====

Typical C-C bond length<ref>Popov, E.M., Kogan, G.A. & Zheltova, V.N., 1972. Theor Exp Chem ''6''(1), pp.11-19. https://doi.org/10.1007/BF00525890</ref>:
:sp<sup>3</sup>-sp<sup>3</sup>: 1.54 Å
:sp<sup>3</sup>-sp<sup>2</sup>: 1.50 Å
:sp<sup>2</sup>-sp<sup>2</sup>: 1.47 Å
Van der Waals radius of a carbon atom: 1.70 Å<br>Van der Waals distance of 2 carbon atoms: 3.40 Å

In the transition state of cycloaddition process between butadiene and ethylene, the partly formed C-C single bond lengths are about 2.115 Å which is an intermediate value between typical sp<sup>3</sup> C-C bond length and Van der Waals distance of 2 carbon atoms. For the breaking double bond, the bond lengths are increased upon the change in the carbon hybridisation from sp<sup>2</sup> to sp<sup>3</sup>. In other words, the reduced in s orbital character from sp<sup>2</sup>(33%) to sp<sup>3</sup>(25%) makes the C-C bond longer and weaker as the electrons are less strongly held to the nucleus. On the other hand, the single bond on butadiene is shorter in the transition state as the carbon is hybridised from sp<sup>3</sup> to sp<sup>2</sup> upon double bond formation.

For cyclohexene, there is only a double bond between the sp<sup>2</sup> hybridised C6 and C7, and the remaining carbons are sp<sup>3</sup> hybridised. Thus, there is no delocalisation of electron cloud in the cyclohexene and the electrons are localised along the C-C bond. This explains the existence of the three different bond lengths (1.34 Å, 1.50 Å and 1.54 Å) as the C-C bond lengths vary based on different carbon hybridisation.

{| class="wikitable"
|+ Table 5. The changes in bond length along the reaction path
! style="background: #0D4F8B; color: white;" | Type of Bond
! style="background: #0D4F8B; color: white;" | Bond Length vs reaction coordinate
! style="background: #0D4F8B; color: white;" | Discussion
|-
|C1-C4 and C6-C7 and C11-C14
|[[File:C1C4_dbbreak_q1_llt15.PNG|250px]][[File:C6C7_dbbreak_q1_llt15.PNG|250px]][[File:C11C14_dbbreak_q1_ethene_llt15.PNG|250px]]
|Change in bond order:<br>double bond to single bond<br>The graphs show that the bond length increase gradually from 1.34 Å to 1.50 Å upon product formation. The increase in bond length indicates the breaking of the C1-C4 and C6-C7 double bonds due to the change in carbon hybridisation (C1, C7, C11 and C14) from sp<sup>2</sup> to sp<sup>3</sup>. This causes a decrease in electron density between two carbons thus the single bonds are weaken and lengthen.
|-
|C4-C6
|[[File:C4C6_dbform_q1_llt15.PNG|250px]]
|Change in bond order:<br>single bond to double bond<br>The graph shows that the bond length decreases gradually from 1.47 Å to 1.34 Å upon product formation. The decrease in bond length indicates the double bond formation between C4-C6 as the C1 and C7 hybridised from sp<sup>2</sup> to sp<sup>3</sup>, this changes the type of bond from a sp<sup>2</sup>-sp<sup>2</sup> double bond to a sp<sup>2</sup>-sp<sup>3</sup> single bond. The additional pi overlap between C4-C6 strengthen the bond and hold the 2 carbon nucleus stronger together resulting in a shorter bond length.
|-
|C7-C11 and C14-C1
|[[File:C7C11_sbform_q1_llt15.PNG|250px]][[File:C14C1_sbform_q1_llt15.PNG|250px]]
|The graphs show a steep decrease in bond length (or distance between 2 carbons) along the reaction coordinate. In this case, the two non-bonding carbon atoms from 1,3-butadiene and ethylene approach each other from Van der Waals distance (3.40 Å) and their orbitals start to overlap across the space in the transition state in order to form the new single bonds in the product stage. All of the 4 carbons change their hybridisation (sp<sup>2</sup> to sp<sup>3</sup>) to form 2 new sigma bonds with typical carbon sp<sup>3</sup>-sp<sup>3</sup> bond length at 1.54 Å.
|-
|}

====Illustrate the vibration that corresponds to the reaction path at the transition state (TS). Is the formation of the two bonds synchronous or asynchronous?====

'''Figure 4. Imaginary vibration of the TS of 1,3-butadiene and ethylene'''
<jmol>
<jmolApplet>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 7; rotate x -20; frank off</script>
<name>TRIAL_TS_2_LLT15_FREQ</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>TRIAL_TS_2_LLT15_FREQ</target>
</jmolbutton>
<jmolbutton>
<script>measure 8 25; measure 7 26</script>
<text>C-C Distances</text>
<target>TRIAL_TS_2_LLT15_FREQ</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>TRIAL_TS_2_LLT15_FREQ</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 7; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i949/cm<sup>-1</sup></text>
<target>TRIAL_TS_2_LLT15_FREQ</target>
</item>
</jmolmenu>
</jmol>

The vibration mode that resembles to the reaction coordinate at TS is shown in figure 2.<br>This mode has a negative force constant which results in an imaginary frequency of value -949 cm<sup>-1</sup>.<br>From the animation, it shows that the concerted formation of the two new C-C bonds is synchronous in terms of the movement of the 2 terminal carbons of 1,3-butadiene and the 2 carbons of ethylene towards each other at the same rate to form the product cyclohexene.

====Additional information====
For exercise 2, go to https://wiki.ch.ic.ac.uk/wiki/index.php?title=Llt15_TS_2<br>
For exercise 3, go to https://wiki.ch.ic.ac.uk/wiki/index.php?title=Llt15_TS_3

log file for IRC calculation is for exercise 1 available at [[File:TRIAL_TS_2_IRC_CORRECTED_LLT15.LOG]]

==References==
<references />

File:Benzene q3 llt15.png

2017-10-21T21:55:10Z

Llt15:

Rep:Llt15 TS 3

2017-10-21T21:51:40Z

===Practice 3: Diels-Alder vs Cheletropic===
<br><br>[[File:reaction_q3_llt15.png|thumb|center|500px|Figure 8. Reaction scheme for reaction between xylylene and SO<sub>2</sub>]]

'''Method used for exercise 3:'''

First of all, the exo-DA adduct is drawn and optimized at PM6 level. Secondly, the bonds between xylylene and SO<sub>2</sub> are broken and the resulting structure are optimized at PM6 level with the C-O separation set at 2.0 Å and the C-S at 2.4 Å. Then, the bonds are froze and optimized to a minimum to give a structure closed to the desired transition state followed by a TS calculation. The optimized TS is ran for the IRC calculation and its frequency is checked to make sure it is the correct TS. The optimized TS from previous steps is used to run a second IRC calculation with the geometry of SO<sub>2</sub> being changed to make the endo-DA adduct. The endo-DA adduct obtained form the IRC calculation is then optimized to a minimum to get a structure with more accurate geometry. Similar process is done for the cheletropic process starting from the product to obtained the TS. The optimized structrures are shown in table 1 and 2.

{| class="wikitable"
|+ Table 1. Structure for reactants for all 3 reactions
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | Reactants
|-
| style="text-align: center;" | Xylylene
| style="text-align: center;" | Sulfur Dioxide
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>XYLYLENE_Q3_LLT15_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16</script>
<uploadedFileContents>SO2_Q3_LLT15_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
<br>

{| class="wikitable"
|+ Table 2. Structure for transition states (TS) and products for all 3 reactions
! rowspan="2" style="text-align: center;" | States
! colspan="2" style="text-align: center;" | Diels Alder Reaction
! rowspan="2" style="text-align: center;" | Cheletropic reaction
|-
| style="text-align: center;" | Exo pathway
| style="text-align: center;" | Endo pathway
|-
| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>DA_Q3_LLT15_PM6_TS_EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>DA_Q3_LLT15_PM6_TS_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>CHE_Q3_LLT15_PM6_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Products
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 72</script>
<uploadedFileContents>DA_Q3_LLT15_PM6_PRODUCT_EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>DA_Q3_LLT15_PM6_PRODUCT_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>CHE_Q3_LLT15_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|+ Table 3. Visualisation of the exo-DA reaction coordinate with an IRC calculation for each path
! style="text-align: center;" | Type of reaction
! style="text-align: center;" | Gif file of IRC output
! style="text-align: center;" | Reaction profile from IRC output
|-
| Diels Alder reaction:<br>exo pathway
| [[File:IRC_DA_llt15_exo_pm6_movie_corrected.gif]]
| [[File:DA_exo_q3_IRC_redo2_RP_llt15.PNG|thumb|center|300px]]
|-
| Diels Alder reaction:<br>endo pathway
| [[File:IRC_DA_llt15_endo_movie.gif]]
| [[File:DA_q3_endo_IRC_RP_llt15.PNG|thumb|center|300px]]
|-
| Cheletropic reaction:
| [[File:IRC_che_q3_llt15_movie.gif]]
| [[File:Che_q3_IRC_RP_llt15.PNG|thumb|center|300px]]
|}

====Visualise the reaction coordinate with an IRC calculation for each path. Include a .gif file in the wiki of these IRCs.Xylylene is highly unstable. Look at the IRCs for the reactions - what happens to the bonding of the 6-membered ring during the course of the reaction====

p-Xylylene is formed from the pyrolysis of p-xylene. The structure of p-xylene consisted of a benzene ring with two methyl groups substituted at ipso and para positions.
Hückel's rule states that for the compounds which are planar and have a contiguous, cyclic array of p-orbitals perpendicular to the plane of ring:<br>
*Those with 4n + 2 π electrons display special stability = aromatic<br>
*Those with 4n π electrons display special instability = anti-aromatic<br>Where n is an integer starting from zero<ref>Jonathan Clayden, Nick Greeves, Stuart Warren, ''Organic Chemistry'', 2nd Ed., OUP Higher Education Devision; ''Chap 7'', pp.161-162</ref><br><br>
Xylylene has a planar structure with conjugated double bond. However, xylylene is overall a non-aromatic molecule as it is not cyclic. By considering only the 6-membered ring, the ring system posses unusual instability due to its anti-aromaticity as it has 4 π electrons. The anti-aromatic character of the 6-membered ring results in a higher energy π electron system and therefore it is highly unstable.

All the three reaction profiles in table 3 depict that all the 3 reactions are highly exothermic indicating the xylylene is highly reactive in order to regain its aromaticity. The IRC gif files show how the double bonds appear to be cyclic and completely conjugated when the 2 new sigma bonds are forming. Along the reaction coordinate, the π electrons quickly rearrange to form a cyclic system and the aromatic stabilisation is acquired from the resonance of the benzene ring structure. All the 3 products are aromatic as each of them consist a benzene ring structure with 6 π electrons (4n + 2 π electrons, obey Hückel's rule). The measurement of the bond lengths of the 6-membered ring structure of xylylene and the 3 products is listed below:<br>
Xylylene:<br>C-C bond length: 1.46 Å, 1.47 Å, 1.49 Å<br>C=C bond length: 1.35 Å<br><br>Exo/Endo Adduct C-C bond length: 1.47 Å<br>Exo/Endo Adduct C-C bond length: 1.47 Å

All the bonds in the 6-membered ring system of the 3 products have the same bond length (1.47 Å) which is an intermediate value between the average C-C (1.54 Å) and average C=C (1.34 Å) bond length. This can be explained by the delocalisation of π electrons in the ring system and the overall structure is an average from all the resonance form of benzene. So, the alternating single bonds have partial double bond character and the double bonds are weaken as the π electrons cloud is no longer localised along the C-C double bonds.

====Calculate the activation and reaction energies (converting to kJ/mol) for each step as in Exercise 2 to determine which route is preferred.Draw a reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels-Alder reactions and the cheletropic reaction====

{| class="wikitable"
|+ Table 5. Energies of reactants, TS, and products of Diels Alder and cheletropic reaction
! rowspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Measurement
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Energies / kJmol<sup>-1</sup>
|-
| colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | Diels Alder Reaction
| rowspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | Cheletropic reaction
|-
| style="background: #0D4F8B; color: white;" style="text-align: center | Exo
| style="background: #0D4F8B; color: white;" style="text-align: center | Endo
|-
| xylylene
| style="text-align: center;" | + 468.25
| style="text-align: center;" | + 468.25
| style="text-align: center;" | + 468.25
|-
| Sulfur dioxide
| style="text-align: center;" | - 313.04
| style="text-align: center;" | - 313.04
| style="text-align: center;" | - 313.04
|-
| Sum of reactant energy
| style="text-align: center;" | + 155.21
| style="text-align: center;" | + 155.21
| style="text-align: center;" | + 155.21
|-
| TS
| style="text-align: center;" | + 241.67
| style="text-align: center;" | + 237.69
| style="text-align: center;" | + 260.00
|-
| Product
| style="text-align: center;" | + 56.31
| style="text-align: center;" | + 56.95
| style="text-align: center;" | + 0.0105
|-
| Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>
| style="text-align: center;" | + 86.46
| style="text-align: center;" | + 82.48
| style="text-align: center;" | + 104.79
|-
| Reaction energy /kJmol<sup>-1</sup>
| style="text-align: center;" | - 98.90
| style="text-align: center;" | - 98.26
| style="text-align: center;" | - 155.20
|}

[[File:Reactionprofile_q3_llt15_adjusted.PNG|thumb|left|600px|Figure 9. A summarized reaction profile summarized for the exo/endo-DA reaction pathway and the cheletropic reaction with the reactants' energy set to zero at infinite separation.]]

From both the table 5 and figure 9,
In terms of thermodynamic, the cheletropic reaction is the most exothermic reaction. Therefore, the cheletropic product is most favourable thermodynamically, followed by the exo-DA adduct then the endo-DA adduct as it yield largest reaction energy.
In terms of kinetics, the endo-DA adduct is the most favourable product, the next is the exo-DA adduct followed by the cheletropic product. This is because this reaction pathway require least activation energy to reach its transition state and hence the endo-DA adduct is formed faster.

==Additional Information==

{| class="wikitable"
|+ Table 6. Links for the log file of IRC calculations using semi-empirical method (PM6 basis set)
! colspan="2" style="text-align: center;" | Diels Alder Reaction
! rowspan="2" style="text-align: center;" | Cheletropic Reaction
|-
| style="text-align: center;" | Exo-pathway
| style="text-align: center;" | Endo-pathway
|-
| [[File:DA_Q3_LLT15_PM6_EXO_IRC_REDO2.LOG]]
| [[File:DA_Q3_LLT15_PM6_IRC_ENDO.LOG]]
| [[File:CHE_Q3_LLT15_PM6_IRC.LOG]]
|}

==References==
<references />

Rep:Llt15 TS 3

2017-10-21T21:31:34Z

Llt15: /* Practice 3: Diels-Alder vs Cheletropic */

===Practice 3: Diels-Alder vs Cheletropic===
<br><br>[[File:reaction_q3_llt15.png|thumb|center|500px|Figure 8. Reaction scheme for reaction between xylylene and SO<sub>2</sub>]]

'''Method used for exercise 3:'''

First of all, the exo-DA adduct is drawn and optimized at PM6 level. Secondly, the bonds between xylylene and SO<sub>2</sub> are broken and the resulting structure are optimized at PM6 level with the C-O separation set at 2.0 Å and the C-S at 2.4 Å. Then, the bonds are froze and optimized to a minimum to give a structure closed to the desired transition state followed by a TS calculation. The optimized TS is ran for the IRC calculation and its frequency is checked to make sure it is the correct TS. The optimized TS from previous steps is used to run a second IRC calculation with the geometry of SO<sub>2</sub> being changed to make the endo-DA adduct. The endo-DA adduct obtained form the IRC calculation is then optimized to a minimum to get a structure with more accurate geometry. Similar process is done for the cheletropic process starting from the product to obtained the TS. The optimized structrures are shown in table 1 and 2.

{| class="wikitable"
|+ Table 1. Structure for reactants for all 3 reactions
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | Reactants
|-
| style="text-align: center;" | Xylylene
| style="text-align: center;" | Sulfur Dioxide
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>XYLYLENE_Q3_LLT15_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16</script>
<uploadedFileContents>SO2_Q3_LLT15_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
<br>

{| class="wikitable"
|+ Table 2. Structure for transition states (TS) and products for all 3 reactions
! rowspan="2" style="text-align: center;" | States
! colspan="2" style="text-align: center;" | Diels Alder Reaction
! rowspan="2" style="text-align: center;" | Cheletropic reaction
|-
| style="text-align: center;" | Exo pathway
| style="text-align: center;" | Endo pathway
|-
| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12</script>
<uploadedFileContents>DA_Q3_LLT15_PM6_TS_EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 20</script>
<uploadedFileContents>DA_Q3_LLT15_PM6_TS_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 42</script>
<uploadedFileContents>CHE_Q3_LLT15_PM6_TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Products
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 72</script>
<uploadedFileContents>DA_Q3_LLT15_PM6_PRODUCT_EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>DA_Q3_LLT15_PM6_PRODUCT_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 22</script>
<uploadedFileContents>CHE_Q3_LLT15_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|+ Table 3. Visualisation of the exo-DA reaction coordinate with an IRC calculation for each path
! style="text-align: center;" | Type of reaction
! style="text-align: center;" | Gif file of IRC output
! style="text-align: center;" | Reaction profile from IRC output
|-
| Diels Alder reaction:<br>exo pathway
| [[File:IRC_DA_llt15_exo_pm6_movie_corrected.gif]]
| [[File:DA_exo_q3_IRC_redo2_RP_llt15.PNG|thumb|center|300px]]
|-
| Diels Alder reaction:<br>endo pathway
| [[File:IRC_DA_llt15_endo_movie.gif]]
| [[File:DA_q3_endo_IRC_RP_llt15.PNG|thumb|center|300px]]
|-
| Cheletropic reaction:
| [[File:IRC_che_q3_llt15_movie.gif]]
| [[File:Che_q3_IRC_RP_llt15.PNG|thumb|center|300px]]
|}

====Visualise the reaction coordinate with an IRC calculation for each path. Include a .gif file in the wiki of these IRCs.Xylylene is highly unstable. Look at the IRCs for the reactions - what happens to the bonding of the 6-membered ring during the course of the reaction====

p-Xylylene is formed from the pyrolysis of p-xylene. The structure of p-xylene consisted of a benzene ring with two methyl groups substituted at ipso and para positions.
Hückel's rule<ref>Jonathan Clayden, Nick Greeves, Stuart Warren, ''Organic Chemistry'', 2nd Ed., OUP Higher Education Devision; ''Chap 7'', pp.161-162</ref> states that for the compounds which are planar and have a contiguous, cyclic array of p-orbitals perpendicular to the plane of ring:<br>
*Those with 4n + 2 π electrons display special stability = aromatic<br>
*Those with 4n π electrons display special instability = anti-aromatic<br><br>Where n is an integer starting from zero.<br><br>
Xylylene has a planar structure with conjugated double bond. However, xylylene is overall a non-aromatic molecule as it is not cyclic. By considering only the 6-member ring, the ring system posses instability due to its anti-aromaticity as it has 4 π electrons. The anti-aromatic character of the 6-member ring results in a higher energy π electron system and therefore it is highly unstable.

All the three reaction profiles in table 3 depict that all the 3 reactions are highly exothermic indicating the xylylene is highly reactive in order to regain its aromaticity. The IRC gif files show how the double bonds appear to be cyclic and completely conjugated when the 2 new sigma bonds are forming. Along the reaction coordinate, the π electrons quickly rearrange to form a cyclic system to acquire the aromatic stabilisation. All the 3 products are aromatic as each of them consist a benzene ring structure (6 π electrons= 4n + 2, obey Hückel's rule). The measurement of the bond lengths of the 6-member ring structure of xylylene and the 3 products is listed below:<br>
xylylene: C-C bond length: 1.46 Å, 1.47 Å, 1.49 Å<br> C=C bond length: 1.35 Å<br><br>Exo/Endo Adduct C-C bond length: 1.47 Å<br>Exo/Endo Adduct C-C bond length: 1.47 Å

All the bonds in the 6-member ring system of the 3 products have the same bond length (1.47 Å) which is an intermediate value between the average C-C (1.54 Å) and average C=C (1.34 Å) bond length. This can be explained by the delocalisation of π electrons in the ring system which average out the alternating single and double bonds.

====Calculate the activation and reaction energies (converting to kJ/mol) for each step as in Exercise 2 to determine which route is preferred.Draw a reaction profile that contains relative heights of the energy levels of the reactants, TSs and products from the endo- and exo- Diels-Alder reactions and the cheletropic reaction====

{| class="wikitable"
|+ Table 5. Energies of reactants, TS, and products of Diels Alder and cheletropic reaction
! rowspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Measurement
! colspan="3" style="text-align: center;" style="background: #0D4F8B; color: white;" | Energies / kJmol<sup>-1</sup>
|-
| colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | Diels Alder Reaction
| rowspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | Cheletropic reaction
|-
| style="background: #0D4F8B; color: white;" style="text-align: center | Exo
| style="background: #0D4F8B; color: white;" style="text-align: center | Endo
|-
| xylylene
| style="text-align: center;" | + 468.25
| style="text-align: center;" | + 468.25
| style="text-align: center;" | + 468.25
|-
| Sulfur dioxide
| style="text-align: center;" | - 313.04
| style="text-align: center;" | - 313.04
| style="text-align: center;" | - 313.04
|-
| Sum of reactant energy
| style="text-align: center;" | + 155.21
| style="text-align: center;" | + 155.21
| style="text-align: center;" | + 155.21
|-
| TS
| style="text-align: center;" | + 241.67
| style="text-align: center;" | + 237.69
| style="text-align: center;" | + 260.00
|-
| Product
| style="text-align: center;" | + 56.31
| style="text-align: center;" | + 56.95
| style="text-align: center;" | + 0.0105
|-
| Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>
| style="text-align: center;" | + 86.46
| style="text-align: center;" | + 82.48
| style="text-align: center;" | + 104.79
|-
| Reaction energy /kJmol<sup>-1</sup>
| style="text-align: center;" | - 98.90
| style="text-align: center;" | - 98.26
| style="text-align: center;" | - 155.20
|}

[[File:Reactionprofile_q3_llt15_adjusted.PNG|thumb|left|600px|Figure 9. A summarized reaction profile summarized for the exo/endo-DA reaction pathway and the cheletropic reaction with the reactants' energy set to zero at infinite separation.]]

From both the table 5 and figure 9,
In terms of thermodynamic, the cheletropic reaction is the most exothermic reaction. Therefore, the cheletropic product is most favourable thermodynamically, followed by the exo-DA adduct then the endo-DA adduct as it yield largest reaction energy.
In terms of kinetics, the endo-DA adduct is the most favourable product, the next is the exo-DA adduct followed by the cheletropic product. This is because this reaction pathway require least activation energy to reach its transition state and hence the endo-DA adduct is formed faster.

==Additional Information==

{| class="wikitable"
|+ Table 6. Links for the log file of IRC calculations using semi-empirical method (PM6 basis set)
! colspan="2" style="text-align: center;" | Diels Alder Reaction
! rowspan="2" style="text-align: center;" | Cheletropic Reaction
|-
| style="text-align: center;" | Exo-pathway
| style="text-align: center;" | Endo-pathway
|-
| [[File:DA_Q3_LLT15_PM6_EXO_IRC_REDO2.LOG]]
| [[File:DA_Q3_LLT15_PM6_IRC_ENDO.LOG]]
| [[File:CHE_Q3_LLT15_PM6_IRC.LOG]]
|}

==References==
<references />

File:CHE Q3 LLT15 PM6 IRC.LOG

2017-10-21T21:31:11Z

Llt15:

File:DA Q3 LLT15 PM6 IRC ENDO.LOG

2017-10-21T21:29:48Z

Llt15:

2017-10-21T14:56:44Z

Llt15: /* Exercise 2: Cycloaddition of Cyclohexadiene and 1,3-Dioxole */

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

Diels Alder (DA) reaction is a streospecific [4+2] pericyclic reaction with its reactivity depending on the relative energies of frontier molecular orbitals. The frontier molecular orbital (FMO) theory simplifies the reactivity of the Diels Alder reaction by assuming the chemistry of conjugated π systems is mostly determined by the interactions between the HOMO of one species and the LUMO of the other. When both the diene and dienophile are cyclic, it is possible to form 2 different products by going through the exo and endo pathway respectively.

[[File:reaction_q2_llt15.png|thumb|center|550px|Figure 1. Reaction scheme for cycloaddition of cyclohexadiene and 1,3-dioxole.]]

The Diels Alder reaction between the cyclohexadiene and 1,3-Dioxole is studied by firstly optimizing their geometries using the semi-empirical method (PM6 basis set) followed by the DFT method (B3LYP631Gd basis set). Similar as exercise 1, the guess TSs are constructed from the optimized reactant. Different orientations of the 2 reactants facing each other lead to exo and endo-DA pathway respectively in the transition state. The guess TS structures are optimized at PM6 level and then reoptimized again with DFT (B3LYP631Gd basis set) method. After that, the optimized TSs are ran for IRC calculation to obtained the desired exo and endo-products. The results are shown in table 1 and 2.

{| class="wikitable"
|+ Table 1. Optimized structure for reactants using DFT method (B3LYP631Gd basis set)
! colspan="2" style="text-align: center;" style="background: #0D4F8B; color: white;" | Reactants
|-
| style="text-align: center;" | Cyclohexadiene
| style="text-align: center;" | 1,3-Dioxole
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18</script>
<uploadedFileContents>CYCLOHEXADIENE_LLT15_FREQ_631G REDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 32</script>
<uploadedFileContents>DIOXOLE_LLT15_Q2_FREQ_631G_REDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|+ Table 2. Structure for transition states (TS) and products for exo and endo DA reactions' pathway
! rowspan="2" style="text-align: center;" | States
! colspan="2" style="text-align: center;" | Diels Alder Reaction
|-
| style="text-align: center;" | Exo pathway
| style="text-align: center;" | Endo pathway
|-
| Transition State
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16</script>
<uploadedFileContents>EXO_Q2_TS_631G_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34</script>
<uploadedFileContents>ENDO_TS_Q2_LLT15_631G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Products
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 14</script>
<uploadedFileContents>EXO_Q2_PRODUCT_631G_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18</script>
<uploadedFileContents>ENDO_PRODUCT_Q2_631G_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable"
|+ Table 3. HOMO and LUMO of the reactant and exo/endo-transition states (TS)
! style="background: #0D4F8B; color: white;" | Chemical Structure
! style="background: #0D4F8B; color: white;" | Occupied Orbitals
! style="background: #0D4F8B; color: white;" | Unoccupied Orbitals
! style="background: #0D4F8B; color: white;" | Energy of the orbitals /kJmol<sup>-1</sup>
! style="background: #0D4F8B; color: white;" | Discussion on MOs
|-
|<nowiki>Cyclohexadiene</nowiki>
|<jmol>
<jmolApplet>
<title>MO 22 (HOMO)</title>
<color>white</color>
<size>200</size>
<script>frame 18; mo 22 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXADIENE_LLT15_FREQ_631G REDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>MO 23 (LUMO)</title>
<color>white</color>
<size>200</size>
<script>frame 18; mo 23 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXADIENE_LLT15_FREQ_631G REDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HOMO (MO 22): -0.20554 a.u.<br>LUMO (MO 23): -0.01711 a.u.
| rowspan="2" |'''The HOMO-LUMO interactions shown in the Diels Alder MO diagram in figure 5 and 6 are listed below:'''<br><br>Cyclohexadiene HOMO (MO 22, A) + 1,3-Dioxole LUMO (MO 20, A) = Exo/Endo TS HOMO - 1 (MO 40)<br>Cyclohexadiene HOMO (MO 22, A) - 1,3-Dioxole LUMO (MO 20, A) = Exo/Endo TS LUMO + 1 (MO 43)<br><br>Cyclohexadiene LUMO (MO 23, S) + 1,3-Dioxole HOMO (MO 19, S) = Exo/Endo TS HOMO (MO 41)<br>Cyclohexadiene LUMO (MO 23, S) - 1,3-Dioxole HOMO (MO 19, S) = Exo/Endo TS LUMO (MO 42)<br><br>Same thing applied for both exo and endo TS.
|-
|<nowiki>1,3-Dioxole</nowiki>
| <jmol>
<jmolApplet>
<title>MO 19 (HOMO)</title>
<color>white</color>
<size>200</size>
<script>frame 32; mo 19 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIOXOLE_LLT15_Q2_FREQ_631G_REDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>MO 20 (LUMO)</title>
<color>white</color>
<size>200</size>
<script>frame 32; mo 20 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIOXOLE_LLT15_Q2_FREQ_631G_REDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HOMO (MO 19): - 0.19594 a.u.<br>LUMO (MO 20): + 0.03794 a.u.
|-
| <nowiki>Exo-Transition State</nowiki>
| <jmol>
<jmolApplet>
<title>MO 40 (HOMO - 1)</title>
<color>white</color>
<size>200</size>
<script>frame 16; mo 40 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO_Q2_TS_631G_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
<jmol>
<jmolApplet>
<title>MO 41 (HOMO)</title>
<color>white</color>
<size>200</size>
<script>frame 16; mo 41 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO_Q2_TS_631G_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>MO 43 (LUMO + 1)</title>
<color>white</color>
<size>200</size>
<script>frame 16; mo 43 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO_Q2_TS_631G_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
<jmol>
<jmolApplet>
<title>MO 42 (LUMO)</title>
<color>white</color>
<size>200</size>
<script>frame 16; mo 42 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO_Q2_TS_631G_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|LUMO + 1 (MO 43): + 0.01018 a.u.<br>LUMO (MO 42): -0.00698 a.u.<br>HOMO (MO 41): -0.18560 a.u.<br>HOMO - 1 (MO 40): -0.19800 a.u.
|[[File:MO_exo_q2_energy_llt15_631G.png|thumb|center|450px|Figure 2. exo-MO diagram for DA reaction between cyclohexadiene and 1,3-dioxole considering only FMO interactions with adjusted energy levels based on calculation]]
|-
| <nowiki>Endo-Transition State</nowiki>
| <jmol>
<jmolApplet>
<title>MO 40 (HOMO - 1)</title>
<color>white</color>
<size>200</size>
<script>frame 34; mo 40 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO_TS_Q2_LLT15_631G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
<jmol>
<jmolApplet>
<title>MO 41 (HOMO)</title>
<color>white</color>
<size>200</size>
<script>frame 34; mo 41 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO_TS_Q2_LLT15_631G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>MO 43 (LUMO + 1)</title>
<color>white</color>
<size>200</size>
<script>frame 34; mo 43 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO_TS_Q2_LLT15_631G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
<jmol>
<jmolApplet>
<title>MO 42 (LUMO)</title>
<color>white</color>
<size>200</size>
<script>frame 34; mo 42 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO_TS_Q2_LLT15_631G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|LUMO + 1 (MO 43): + 0.01543 a.u.<br>LUMO (MO 42): -0.00462 a.u.<br>HOMO (MO 41): -0.19051 a.u.<br>HOMO - 1 (MO 40): -0.19648 a.u.
|[[File:MO_endo_q2_energy_631G_llt15.png|thumb|center|450px|Figure 3. endo-MO diagram for DA reaction between cyclohexadiene and 1,3-dioxole considering only FMO interactions with adjusted energy levels based on calculation]]
|}

====Is this a normal or inverse demand DA reaction?====

Diels Alder reaction is a concerted [4+2] pericyclic reaction between a conjugated diene species and a substituted dienophile species. There are 2 types of Diels Alder reactions, depending on the relative energy of the FMO involved for the formation of 2 new sigma bonds of the diene and dienophile species. The reaction has a normal electron demand when it occurs between an electron rich diene species (high energy HOMO) and an electron deficient dienophile (low energy LUMO). Conversely, the reaction has an inverse electron demand when it occurs between an electron poor diene species (low energy LUMO) and an electron rich dienophile (high energy HOMO). <ref>Sylvie Pugnaud et al., Inverse Electron Demand Diels−Alder Reactions, ''J. Org. Chem.'', 1997, 62 (25), pp 8687–8692, DOI: 10.1021/jo970851y</ref>

The order of TS's MOs symmetry depicted that the reaction has an inverse electron demand. In this case, both of the HOMO (MO 22) and LUMO (MO 23) of cyclohexadiene have lower energy than the HOMO (MO 19) and LUMO (MO 20) of 1,3-dioxole (dienophile).This is due to the presence of oxygen atoms next to the C-C double bond in dienophile with the oxygen as electron donating group. The delocalisation of lone pair at the p orbital of oxygen atoms into the π electron system of the C-C double bond in 1,3-dioxole makes the dienophile more electron rich thus results in a higher energy HOMO and LUMO. Consequently, the diene LUMO-dienophile HOMO energy gap become smaller whereas the diene HOMO-dienophile LUMO energy gap becomes larger. Therefore, the diene LUMO and dienophile HOMO which is closer in energy overlap better and this interaction dominates in an inverse demand DA reaction.

====Tabulate the energies and determine the reaction barriers and reaction energies (in kJ/mol) at room temperature. Which are the kinetically and thermodynamically favourable products?Look at the HOMO of the TSs. Are there any secondary orbital interactions or sterics that might affect the reaction barrier energy?====

{| class="wikitable"
|+ Table 4. Energies of reactants, TS, and products from 2 different optimisation methods
! style="background: #0D4F8B; color: white;" | Species
! style="background: #0D4F8B; color: white;" | Energy calculated from semi empirical method (PM6) / kJmol<sup>-1</sup>
! style="background: #0D4F8B; color: white;" | Energy calculated from DFT method B3LYP (6-31G(d)) / kJmol<sup>-1</sup>
|-
| Cyclohexadiene
| style="text-align: center;" | + 306.766
| style="text-align: center;" | - 6.12399 X 10<sup>5</sup>
|-
| 1,3-Dioxole
| style="text-align: center;" | - 137.207
| style="text-align: center;" | - 7.00967 x 10<sup>5</sup>
|-
| Sum of reactant energy
| style="text-align: center;" | + 169.559
| style="text-align: center;" | - 1.313367 x 10<sup>6</sup>
|-
| Exo-TS
| style="text-align: center;" | + 364.575
| style="text-align: center;" | - 1.313199 x 10<sup>6</sup>
|-
| Exo-Product
| style="text-align: center;" | + 99.675
| style="text-align: center;" | - 1.313431 x 10<sup>6</sup>
|-
| Endo-TS
| style="text-align: center;" | + 362.052
| style="text-align: center;" | - 1.313207 x 10<sup>6</sup>
|-
| Endo-Product
| style="text-align: center;" | + 99.218
| style="text-align: center;" | - 1.313435 x 10<sup>6</sup>
|}

{| class="wikitable"
|+ Table 5. Activation energies and Reaction energies for exo/endo-DA reactions based on 2 different calculation method
! rowspan="2" style="text-align: center;" | Method
! colspan="2" style="text-align: center;" | Semi empirical method (PM6)
! colspan="2" style="text-align: center;" | DFT method B3LYP (6-31G(d))
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
| Activation barrier (E<sub>act</sub>) /kJmol<sup>-1</sup>
| + 195.02
| + 192.49
| + 167.53
| + 159.76
|-
| Reaction energy /kJmol<sup>-1</sup>
| - 69.884
| - 70.341
| - 63.79
| - 67.39
|}

If a reaction required lesser activation energy to achieve its TS, the reaction is more kinetically favoured and vice versa.<br> If the reaction has greater reaction energy, the reaction is more thermodynamically favoured.<br>According to the thermochemistry data obtained from the gaussian output log file using the DFT method B3LYP (6-31G(d)), the activation energy required to reach exo-TS is lower by 7.77 kJmol<sup>-1</sup> and the reaction energy for exo-product is larger by 3.60 kJmol<sup>-1</sup>. This depicts the endo-product forms faster and it is kinetically favourable.

{| class="wikitable"
|+ Table 6. Different interactions of MO in TS and products
! style="background: #0D4F8B; color: white;" | exo-MO
! style="background: #0D4F8B; color: white;" | endo-MO
! style="background: #0D4F8B; color: white;" | Type of interactions
|-
|<jmol>
<jmolApplet>
<title>MO 41 (HOMO of exo-TS)</title>
<color>white</color>
<size>200</size>
<script>frame 16; mo 41 ; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO_Q2_TS_631G_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>MO 41 (HOMO of endo-TS)</title>
<color>white</color>
<size>200</size>
<script>frame 34; mo 41 ; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO_TS_Q2_LLT15_631G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| rowspan="2" | Compared to the exo-TS, endo-TS has lower energy due to the secondary orbital interactions. The secondary orbital interaction occurs significantly in the endo TS and product from the overlap between p orbitals (lone pairs) of oxygen atoms in 1,3-dioxole and the LUMO of cyclohexadiene across the space even though this does not form any bonds. Consequently, this interaction stabilises the TS and lowers the activation barrier thus making the endo-product more favorable kinetically than the exo-product.<br><br> Note that the unfavourable steric interaction appears less significant in both the endo-TS and product and the resulting repulsion arose from steric clash helps to orient the FMOs of the 2 reactants for a better overlap. Overall the steric effect is so minor thus the reaction is deduced to be dominated by electronic factor.<br><br>Both of the DA reactions to yield exo and endo product is exothermic. It is observed that the reaction energy for exo-DA reaction is higher than the endo-DA reaction. This is because of the stabilising effect from the secondary orbital interactions in the endo-product and this interaction is greater when compared to its transition state. The stabilised endo-product has a lower energy thus results in a more exothermic reaction which makes it favourable thermodynamically compared to the exo-product.
|-
|<jmol>
<jmolApplet>
<title>MO 41 (HOMO of exo-product)</title>
<color>white</color>
<size>200</size>
<script>frame 14; mo 41 ; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO_Q2_PRODUCT_631G_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>MO 41 (HOMO of endo-product)</title>
<color>white</color>
<size>200</size>
<script>frame 18; mo 41 ; mo cutoff 0.01; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO_PRODUCT_Q2_631G_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Additional information====

Link for exercise 1: https://wiki.ch.ic.ac.uk/wiki/index.php?title=Llt15_TS<br>
Link for exercise 3: https://wiki.ch.ic.ac.uk/wiki/index.php?title=Llt15_TS_3

{| class="wikitable"
|+ Table 7. Links for log files without JMol'''
! rowspan="2" style="text-align: center;" | States in reaction
! colspan="2" style="text-align: center;" | semi-empirical method (PM6)
|-
| style="text-align: center;" | Exo pathway
| style="text-align: center;" | Endo pathway
|-
| style="text-align: center;" | Cyclohexadiene
| colspan="2" | [[File:CYCLOHEXADIENE_LLT15_FREQ_PM6_REDO.LOG]]
|-
| style="text-align: center;" | 1,3-Dioxole
| colspan="2" | [[File:DIOXOLE_LLT15_Q2_FREQ.LOG]]
|-
| style="text-align: center;" | Transition State
| [[File:EXO_Q2_TS_PM6_LLT15.LOG]]
| [[File:ENDO_TS_Q2_PM6_LLT15.LOG]]
|-
| style="text-align: center;" | Product
| [[File:EXO_Q2_PRODUCT_PM6_LLT15_FREQ.LOG]]
| [[File:ENDO_PRODUCT_Q2_PM6_LLT15_FREQ.LOG]]
|-
| style="text-align: center;" | IRC
| [[File:EXO_Q2_TS_PM6_LLT15_IRC.LOG]]
| [[File:Endo_TS_Q2_LLT15_PM6_IRC.LOG]]
|}

==References==
<references />

Rep:Llt15 TS

2017-10-21T14:52:44Z

Llt15: /* Transition States and Reactivity */

==Transition States and Reactivity==

===Introduction===

A transition state is the saddle point which is a local maxima on the minimum energy path linking reactants and the products where the reactant and products correspond to the minimum in the PES. Therefore, at both minimum point and transition structure, the total gradient of the potential energy surface will have a value of zero. This is defined by the first derivative of potential energy vs bond distances graph: ∂V(r<sub>i</sub>)/∂r<sub>i</sub> = 0

[[File:Usetis_IR_equation_llt15.PNG|thumb|center|400px| Figure 1. Equation to calculate the vibrational frequency (\nu) for diatomic molecules <ref>Donald L. Pavia, Gary M. Lampman, George S. Kriz, James A. Vyvyan, 2009. ''Introduction to Spectroscopy'' 4th ed., ''Chap. 2'', pp.21.</ref>]]

For non-linear molecules, there are 3N - 6 normal vibrational modes or so-called degree of freedom. Using a harmonic oscillator model, each vibrational modes has the restoring force defined by Hookes law:<br>
F = -'''k'''x <br>where ''''k'''' is the force/spring constant<br> 'x' is the displacement of spring which resemble bonds from its equilibrium position.<br>
The reactants and products sit in a well at the minimum and vibrate 'forever' unless sufficient energy is provided for them to react. The transition state has a different mode of vibration along the reaction coordinate which take the TS downhill towards the reactant or product, without a restoring force. This lead to a negative '''k'''. Thus, the calculation of second derivative of the curvature ('''k''') in the PES (∂<sup>2</sup>V(r<sub>i</sub>)/∂r<sub>i</sub><sup>2</sup>) helps to distinguish the minimum and TS. As the frequency calculation involves taking square root of a force constant '''k''' and the square root of negative value leads to an imaginary number, at every transition state there must be only one imaginary frequency as all other coordinates are minimised. Hence, it is concluded that a negative value of second derivative of gradient indicated a transition structure whereas positive value represented the minimum point (reactant and product) of the reaction path and the same thing applies in frequency calculation.

===Exercise 1: Cycloaddition of Butadiene and Ethylene===

<br>
[[File:cycloadd_q1_llt15.png|thumb|center|550px|Figure 2. Reaction scheme for cycloaddition of 1,3-butadiene and ethylene.]]

'''Method used for optimization and analysis:'''

The geometry of the reactants are optimized at PM6 level and the optimized reactants are used to construct the transition state of the reaction. The distance 2.20 Å is used in the guess of TS for the approximate separation between the terminal carbon atoms in both reactants as this is the intermediate value between a normal C-C single bond and the Van der Waals distance of 2 carbon atoms. The guess TS structure is optimized at PM6 level and the optimized TS is used to run a IRC to obtained the product. The product is again optimized to a minimum at PM6 level.

{| 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>250</size>
<script>frame 16</script>
<uploadedFileContents>BUTADIENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 4</script>
<uploadedFileContents>ETHENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6</script>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 40</script>
<uploadedFileContents>PRODUCT_Q1_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

====Correlate these MOs with the ones in your MO diagram to show which orbitals interact. What can you conclude about the requirements for symmetry for a reaction (when is a reaction 'allowed' and when is it 'forbidden')? ====

{| class="wikitable"
|+ Table 2. HOMO and LUMO of reactants and transition state (TS)
! style="background: #0D4F8B; color: white;" | Chemical Structure
! style="background: #0D4F8B; color: white;" | HOMO
! style="background: #0D4F8B; color: white;" | LUMO
! style="background: #0D4F8B; color: white;" | MO interactions
|-
|<nowiki>Butadiene</nowiki>
|<jmol>
<jmolApplet>
<title>MO11 (Aysmmetric)</title>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>MO12 (Symmetric)</title>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|rowspan="3"|[[File:Q1_MO_corrected_llt15.png|thumb|center|550px|Figure 3. Idealized MO diagram of [4+2] cycloaddition with with labelled symmetry (Antisymmetric= A, Symmetric= S).]]
|-
|<nowiki>Ethylene</nowiki>
| <jmol>
<jmolApplet>
<title>MO6 (Symmetric)</title>
<color>white</color>
<size>200</size>
<script>frame 4; mo 6 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_Q1_LLT15_REDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>MO7 (Asymmetric)</title>
<color>white</color>
<size>200</size>
<script>frame 4; mo 7 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_Q1_LLT15_REDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| <nowiki>Transition State</nowiki>
| <jmol>
<jmolApplet>
<title>MO16 (HOMO -1)</title>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
<jmol>
<jmolApplet>
<title>MO17 (HOMO)</title>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>MO19 (LUMO + 1)</title>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
<jmol>
<jmolApplet>
<title>MO18 (LUMO)</title>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18 ; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The HOMO-LUMO interactions shown in the MO diagram of the cycloaddition between butadiene and ethylene are listed below:
Butadiene HOMO (MO 11, A) + Ethylene LUMO (MO 7, A) = Transition State HOMO (MO 16)
Butadiene HOMO (MO 11, A) - Ethylene LUMO (MO 7, A) = Transition State LUMO (MO 19)<br>
Butadiene LUMO (MO 12, S) + Ethylene HOMO (MO 6, S) = Transition State HOMO (MO 17)
Butadiene LUMO (MO 12, S) - Ethylene HOMO (MO 6, S) = Transition State LUMO (MO 18)

The symmetry label 'A' and 'S' corresponds to whether the molecular orbital (MO) is antisymmetric or symmetrical with respect to the mirror plane orthogonal to the sigma bond which lies in the middle of MO.

According to the Woodward Hoffmann rules, the total number of (4q + 2)<sub>s</sub> + (4r)<sub>a</sub> must be odd for the pericyclic reaction to be thermally allowed. The letters 'q' and 'r' stand for integer starting from zero whereas the suffix 's' stands for suprafacial and 'a' for antarafacial. A suprafacial component forms new bonds on the same face whereas an antarafacial components formes new bonds on opposite faces at both ends. However, the reaction is considered to be thermally forbidden but photochemically allowed if the total number of (4q + 2)<sub>s</sub> + (4r)<sub>a</sub> equals to zero or an even number. The [<sub>π</sub>4<sub>s</sub> +
<sub>π</sub>2<sub>s</sub>] cycloaddition between butadiene and ethylene is allowed as shown:
(4q + 2)<sub>s</sub> + (4r)<sub>a</sub>
= 1 + 0
= 1
= thermally allowed reaction when q and r equal to 0

'''Write whether the orbital overlap integral is zero or non-zero for the case of a symmetric-antisymmetric interaction, a symmetric-symmetric interaction and an antisymmetric-antisymmetric interaction:'''
{| class="wikitable"
|+ Table 3. Effect of the symmetry of interactions on the orbital overlap integral
! style="background: #0D4F8B; color: white;" | Type of interactions
! style="background: #0D4F8B; color: white;" | Orbital overlap integral
|-
| Symmetric-symmetric
| Non-zero
|-
| Symmetric-antisymmetric
| Zero
|-
| Antisymmetric-antisymmetric
| Non-zero
|}

'''Include measurements of the 4 C-C bond lengths of the reactants and the 6 C-C bond lengths of the TS and products. How do the bond lengths change as the reaction progresses?'''

{| class="wikitable"
|+ Table 4. The changes in bond length of the reactants, TS and product molecules as reaction progress
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | C-C Bond lenghths
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | C-C Bond lenghths
|-
| <jmol>
<jmolApplet>
<title> Reactant: Ethylene</title>
<color>white</color>
<size>150</size>
<script>frame 4</script>
<script>select atomno=1, atomno=4; label display</script>
<uploadedFileContents>ETHENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| C1-C4 (double bond)= 1.32731 Å
| <jmol>
<jmolApplet>
<title>Reactant: 1,3-Butadiene</title>
<color>white</color>
<size>150</size>
<script>frame 16</script>
<script>select atomno=7, atomno=6, atomno=4, atomno=1; label display</script>
<uploadedFileContents>BUTADIENE_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| C1-C4 (double bond)= 1.33534 Å<br>C4-C6 (single bond) = 1.46817 Å<br>C6-C7 (double bond)= 1.33537 Å
|-
| <jmol>
<jmolApplet>
<title>Transition State</title>
<color>white</color>
<size>150</size>
<script>frame 4</script>
<script>select atomno=1, atomno=4, atomno=6, atomno=7, atomno=11, atomno=14; label display</script>
<uploadedFileContents>TRIAL_TS_2_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| C1-C4 (double bond-breaking)= 1.37976 Å, increased bond length<br> C4-C6 (double bond-forming) = 1.41106 Å, decreased bond length<br> C6-C7 (double bond-breaking)= 1.37975 Å, increased bond length<br> C7-C11 (single bond-forming) = 2.11476 Å<br> C11-C14 (double bond-breaking)= 1.38182 Å, increased bond length<br> C14-C1 (single bond-forming) = 2.11462 Å
| <jmol>
<jmolApplet>
<title> Product: Cyclohexene</title>
<color>white</color>
<size>150</size>
<script>frame 10</script>
<script>select atomno=6, atomno=4, atomno=1, atomno=14, atomno=11, atomno=7; label display</script>
<uploadedFileContents>PRODUCT_Q1_LLT15.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| C6-C4 = 1.33766 Å, C=C sp<sup>2</sup>-sp<sup>2</sup> bond<br> C4-C1 = 1.50034 Å, C-C sp<sup>3</sup>-sp<sup>2</sup> bond<br> C1-C14 = 1.54003 Å, C-C sp<sup>3</sup>-sp<sup>3</sup> bond<br> C14-C11 = 1.54076 Å, C-C sp<sup>3</sup>-sp<sup>3</sup> bond<br> C11-C7 = 1.54003 Å, C-C sp<sup>3</sup>-sp<sup>3</sup> bond<br> C7-C6 = 1.50034 Å, C-C sp<sup>3</sup>-sp<sup>2</sup> bond
|}

==== What are typical sp3 and sp2 C-C bond lengths? What is the Van der Waals radius of the C atom? How does this compare with the length of the partly formed C-C bonds in the TS.====

Typical C-C bond length<ref>Popov, E.M., Kogan, G.A. & Zheltova, V.N., 1972. Theor Exp Chem ''6''(1), pp.11-19. https://doi.org/10.1007/BF00525890</ref>:
:sp<sup>3</sup>-sp<sup>3</sup>: 1.54 Å
:sp<sup>3</sup>-sp<sup>2</sup>: 1.50 Å
:sp<sup>2</sup>-sp<sup>2</sup>: 1.47 Å
Van der Waals radius of a carbon atom: 1.70 Å<br>Van der Waals distance of 2 carbon atoms: 3.40 Å

In the transition state of cycloaddition process between butadiene and ethylene, the partly formed C-C single bond lengths are about 2.115 Å which is an intermediate value between typical sp<sup>3</sup> C-C bond length and Van der Waals distance of 2 carbon atoms. For the breaking double bond, the bond lengths are increased upon the change in the carbon hybridisation from sp<sup>2</sup> to sp<sup>3</sup>. In other words, the reduced in s orbital character from sp<sup>2</sup>(33%) to sp<sup>3</sup>(25%) makes the C-C bond longer and weaker as the electrons are less strongly held to the nucleus. On the other hand, the single bond on butadiene is shorter in the transition state as the carbon is hybridised from sp<sup>3</sup> to sp<sup>2</sup> upon double bond formation.

For cyclohexene, there is only a double bond between the sp<sup>2</sup> hybridised C6 and C7, and the remaining carbons are sp<sup>3</sup> hybridised. Thus, there is no delocalisation of electron cloud in the cyclohexene and the electrons are localised along the C-C bond. This explains the existence of the three different bond lengths (1.34 Å, 1.50 Å and 1.54 Å) as the C-C bond lengths vary based on different carbon hybridisation.

{| class="wikitable"
|+ Table 5. The changes in bond length along the reaction path
! style="background: #0D4F8B; color: white;" | Type of Bond
! style="background: #0D4F8B; color: white;" | Bond Length vs reaction coordinate
! style="background: #0D4F8B; color: white;" | Discussion
|-
|C1-C4 and C6-C7 and C11-C14
|[[File:C1C4_dbbreak_q1_llt15.PNG|250px]][[File:C6C7_dbbreak_q1_llt15.PNG|250px]][[File:C11C14_dbbreak_q1_ethene_llt15.PNG|250px]]
|The graphs show that the bond length increase gradually when the reactants (1,3-butadiene and ethylene) are used to form the product (cyclohexene). The increase in bond length indicates the breaking of the C1-C4 and C6-C7 double bonds due to the change in carbon hybridisation (C1, C7, C11 and C14) from sp<sup>2</sup> to sp<sup>3</sup>. This causes a decrease in electron density between two carbons thus the single bonds are weaken and lengthen.
|-
|C4-C6
|[[File:C4C6_dbform_q1_llt15.PNG|250px]]
|The graph shows that the bond length decreases gradually upon product formation. The decrease in bond length indicates the double bond formation between C4-C6 as the C1 and C7 hybridised from sp<sup>2</sup> to sp<sup>3</sup>, this changes the type of bond from a sp<sup>2</sup>-sp<sup>2</sup> double bond to a sp<sup>2</sup>-sp<sup>3</sup> single bond. The additional pi overlap between C4-C6 strengthen the bond and hold the 2 carbon nucleus stronger together resulting in a shorter bond length.
|-
|C7-C11 and C14-C1
|[[File:C7C11_sbform_q1_llt15.PNG|250px]][[File:C14C1_sbform_q1_llt15.PNG|250px]]
|The graphs show a steep decrease in bond length (or distance between 2 carbons) upon product formation. In this case, the two non-bonding carbon atoms from 1,3-butadiene and ethylene approach each other with their orbitals started to overlap across the space during TS in order to form the new single bonds TS in the product stage. All of the 4 carbons change their hybridisation (sp<sup>2</sup> to sp<sup>3</sup>) to form 2 new sigma bonds.
|-
|}

====Illustrate the vibration that corresponds to the reaction path at the transition state (TS). Is the formation of the two bonds synchronous or asynchronous?====

'''Figure 4. Imaginary vibration of the TS of 1,3-butadiene and ethylene'''
<jmol>
<jmolApplet>
<uploadedFileContents>TRIAL_TS_2_LLT15_FREQ.LOG</uploadedFileContents>
<script>vibrating=0; spinning=0; frame 7; rotate x -20; frank off</script>
<name>TRIAL_TS_2_LLT15_FREQ</name>
</jmolApplet>
<jmolbutton>
<script>if(vibrating==0) vibrating=1; vibration 2; else; vibrating=0; vibration off; endif</script>
<text>Vibration</text>
<target>TRIAL_TS_2_LLT15_FREQ</target>
</jmolbutton>
<jmolbutton>
<script>measure 8 25; measure 7 26</script>
<text>C-C Distances</text>
<target>TRIAL_TS_2_LLT15_FREQ</target>
</jmolbutton>
<jmolbutton>
<script>if(spinning==0) spinning=1; spin; else; spinning=0; spin off; endif</script>
<text>Spin</text>
<target>TRIAL_TS_2_LLT15_FREQ</target>
</jmolbutton>
<jmolmenu>
<item>
<script>frame 7; if(vibrating==0) vibration off; else; vibration 2; endif</script>
<text>i949/cm<sup>-1</sup></text>
<target>TRIAL_TS_2_LLT15_FREQ</target>
</item>
</jmolmenu>
</jmol>

The vibration mode that resembles to the reaction coordinate at TS is shown in figure 2.<br>This mode has a negative force constant which results in an imaginary frequency of value -949 cm<sup>-1</sup>.<br>From the animation, it shows that the concerted formation of the two new C-C bonds is synchronous in terms of the movement of the 2 terminal carbons of 1,3-butadiene and the 2 carbons of ethylene towards each other at the same rate to form the product cyclohexene.

====Additional information====
For exercise 2, go to https://wiki.ch.ic.ac.uk/wiki/index.php?title=Llt15_TS_2<br>
For exercise 3, go to https://wiki.ch.ic.ac.uk/wiki/index.php?title=Llt15_TS_3

log file for IRC calculation is for exercise 1 available at [[File:TRIAL_TS_2_IRC_CORRECTED_LLT15.LOG]]

==References==
<references />